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M@&R JFVz     0 p Im   kkk    m{xvW:n/9zGq /Cɝ/T
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   ?     +  @ @  , @ @  - @ @  . @ @  / @ @  0 @ ?     1      @0Vl h      @'NYh      @'NY5@h        ?WH1h    @   ?    2 cantilever_seq_one ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one 	  3  D
   ?    
   static   L   ]¢  ]¢  ] `  ] `  w  w    @'=`	    @'
@
 	   @'@ 
     @8N
E`  @'E`  @8NE`  @'aT   @8N8   @_N8   @_N6   "@8NDP  @')E  "@8N1DP  @N.EE   @'"QE  C@4%E      @Jր  @9M(sր  @Fր  @=  @'`  @8M3@   C@[:s@!  C@[@3"  @#  4
3$   @&%  @(r&   '  @;1̀(  @&3^@)  C@I:r^@*  C@I@2T+  @ 
Z,   @ - !  .@ M. " B@ ^?@/ # @ 
Z0 $ @ R@2 %  2?MT : & %R ; ' $ Vrv= < ) $ Vrv?V >   @P׬@? * v @ ?'           seq   gotoAndPlay R 
   bend 2  (?MT i @    63 2  ?
P@ seq @ @ @ @ @ @ @ @ @ @ @ @ ?             this   stop R @   ?#    3 07_Cantilever_concentratedload  /   4 Vk  Imѷ!r2ἰW ?    4 bt_square_root 	   5  D
    4  @   ?    5 bt_square_root ?    4 bt_square_root 	%   6  D
    4     @'P@   ?    6 bt_root_three ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row     7 pb(  %Xwk "   8 `	!0$ 	 EES     9 P4	 
 	    : P:	 	 P    ; P2	 	 8     < ph (@  %	 =K@     = r &8  % ;d    > PH	 	 8 ?    4 bt_square_root    ? XF   	 j )   @ `*$ 	 	Q    0:2 ?    4 bt_square_root    A P x 	 /      B rMX X  %Z@     C iB   %XWi    D P0x 	 /  ?     bt_v_axis     E _k      #?    E bt_x_axis ?    # bt_dimension_lines_270    F P, 	      2     G pK      3ff$u ?    G beam_long_(300x18)     H p ~     kkk ^aW 333 0˲~;(˅+b,.Ԅ@0`x- cƟ
>WeAx- mg4e!ܻQ!Lx.´ ?    H beam_long_(300x18)  u   I Ejj no* 333   3. J	2) /xa@|&K+$d@OEG?RDY?=
 ?    I roller_support     J VHj   fffd:fjCx 333 0C4yŸ_Vh%k* sY SMD">Hsd"%\
+!K Ї5B>! ԅ
8,h]gs:ٛy d/D@d@@e  ;   K ]" < f 3%z>Y{U,,KZI?Ui	P    L u
w  
 f 6Vc H c1"\t 061MK)@y `nR0!W%#Aj] N@(r]B1 ܂  c1"\  ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?    4 bt_square_root ?    4 bt_square_root ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18)  e   M p+ 
  kkk   ˳ ׅ|*CdCCdCCdCCȟ CdCCCdCCdCpU4     N w˶ kkk    @]S|N mKTPǪL7qrS%ʏ9	) Z l(
 lwcq?UA-MuME='iQDzV5)6ATHzc{     O wK kkk    _[4TzTN?L}TeiQ| k_bM7CM;,%O3J6IO@1J $zp? GKQlr 6Qm88#c ml;)R     P w kkk    _*2҄Gm*`&1~O{cx5~`O=2-	K~mzk^m{&kl#sm
H!9F ZTLg_|T@ܹXW83fMl?n6_o#n     Q wD0  kkk   =wNvzE:+T@ĝ*dJXsm+LLGuП:鲠lpU	֛f;m
d`F}>ΩOTcq-)Kr^Qmw`Pi}6\VM3s}     R w@ kkk     _g,YFiEcJT}d_gZy+ḩ=҅"(4)!
g߮۾Ɵz.#3אh҈ԩ,=Jqn
6+ܺF+qw@4YIԐ=53?Mií4	_   S  D
   ?     M  @ @  N @ @  O @ @  P @ @  Q @ @  R @ ?    @   ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?    4 bt_square_root ?    4 bt_square_root ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?    4 bt_square_root ?    4 bt_square_root ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?    4 bt_square_root ?    4 bt_square_root ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?    4 bt_square_root ?    4 bt_square_root ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?    4 bt_square_root ?    4 bt_square_root ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?    4 bt_square_root ?    4 bt_square_root ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?    4 bt_square_root ?    4 bt_square_root ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?    4 bt_square_root ?    4 bt_square_root ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?    4 bt_square_root ?    4 bt_square_root ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?    4 bt_square_root ?    4 bt_square_root ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?    4 bt_square_root ?    4 bt_square_root ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?    4 bt_square_root ?    4 bt_square_root ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support  0   T p#K,~p (    %Q>#ܠ_#R 	  U  D
   ?    
   display   L   ]¢  ]¢  ] `  ] `  w  w    @'=`	    @'
@
 	   @'@ 7     ?N	G  M?G 8 8LEY  9  ?N1:   ?N:Џ   @&NG  V?N"	F`  V?NI	F`  /?.G   @IBG   @IEE :  ?N=G@   @3G   @%N9G   @%N6QG  w@"(G  w@"+E  ;  @%N%]G <     @X@   9@G(s@!   @T@"  @KM@# 9 (@4M9 $  c@WC %  c@WIK@& =  '   @Fyր(   @FA)   @FF\*  ̀RC7`+ >  @FM0,  9@5NQ-  ̀+H7d.   @5NXP/ 4  @NX@0   @5NY01 ? g@5Mj2 @  E@#3 4  E?1@4  -@#5 A 4@!Q@6    ?N07   @&Vp8 :   ?[@p9 B  :    @`; 9 C@8Na<   &@8Nf<= C  > D 4@!?    ?@   @&"A  .@ B    @*@C 9 C@8M,"^D   &@8M6z^E    @KxF   @ȏG E  8@YH " L@hI #   @KxJ F @[XK G   @L H   @O & Ų_9dP8P I   @Y	 Q & Ųٌ)-2R J   @JKxS 9   @[pT K  ŻR[ U L   @,Tٻ@ ?'           seq   gotoAndPlay R 
   bend K i @ L i @    6M S  Z seq @ @ @ @ @ @ @ @ @ @ @ @ ?             this   stop R V T  W D (@Ydh    X  @LZUh    Y A (@YEh    Z  @NBPh    [  @Rcw h    \  @Hj h    @   ?    U 03_Simple_moment ?     bt_table_row ?     bt_table_row 	   V  D
         @   ?    V bt_table_row ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row 	   W  D
         ?   ?   ։   ։          @'	    @'Џ
 	   @'l@   ?    W bt_background ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row     X pd0  %Xyk    Y P.܈ 	 و    Z P	 	 8    [ Ph 	      \ P	 	 v     ] p$0  %9k     ^ p>!  %z    _ P  	  h.jh     ` r/^ X  %n      a iB   %XW  +   b p$K'|#     %<#Wv ZrΠZt8@    c P 	      @    d P(g 	      P ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support    e u* 
i  
 f ?Vc H c1"\t 061MK)@y `nR0!W%#Aj] N@Իpb r R1z0H #mK\  ``7)Zr3 ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18)     f w kkk    ˫,*=jXi pg}UOx{Xz?܄4Kט(C4D?/Z<Nr l4qgw	}Ko     g w  kkk   _}uL0v@Jt7R?L4=JɜJ#KMU	S`@~=l?͈뜀#3|m4BD:yAﶆk\_TT PR_<@     h w@ kkk    _riڭ3J9	<"uJPq9iOQAXGE*ڐovabk /zگl=ݿfTlne'TiIA0Sp,QztuDw.9mI"\S|4` }5XMvlLU     i wj  kkk   _BLj]Qp1)Fq&R?RߺߎxMⵘK*nk`6m¦|+)~@i}Dk%(zꊡ}J3XҔ4ֈ|](g #KZICqo(}SMt6wCu֐j%6\KMkʀ    j wD kkk    !wo rRTA,"J'qe!fQ
sNrud>SVCy\{5ǽٗ^qp*&ȃFi_AiyzUgJ=LArO#ȍ
mAjP7=vP 	_   k  D
   ?     M  @ @  f @ @  g @ @  h @ @  i @ @  j @ ?    @   ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support  0   l p#K,~p (    %GH wTb|?EuE 	  m  D
   ?    
   display   L   ]¢  ]¢  ] `  ] `  w  w    @'=`	    @'
@
 	   @'@ X     @	G  ?@G 8 @VP   @: Y  @:   ?:Џ   @>G  H@"	Fp  H@<Fp  i@:$G  i@:'E0  !@*)G Y  @a-G   @a0E   !@3aG   @a6G   @a:	E  Z  @8NSqF    @8N\F  [   @PX!F   [   @PaF ! \  @8NfiF " ]  #   @*3@$  .@'@% 8 @-@&    @*2; ' Y   @*:S ( \   @B#@) ^  * _   ?+    @*@,  7@*NCр-  7@*A`.  X@MS@/  X@MYk̀0  @^@1 Y   @te@2    @tk@3  @p@4 \   @tx@5    @t~3@6 `  7 A 4@!Q@8    ?N09   @&Vp: :   ?[@p; 8   @f<  C@8N_藠= \  &@8Nc>   &@8Ng(`?   &@[i@   &@[l A  6@'oB  ]@8Nx `C \  &@8NrD   &@8Nu E a  F D 4@%G    ?H   @*"I  .@ J 8   @7Z@K  C@=)^L Y  &@=1B^M   &@=8bYN   &@`=^@O   &@`CRTP  6@+HB^Q  ]@=ZRYR Y  &@=O"^S   &@=UbTT b  U c E*V d PRW  q X   @ ȏY E  8@ YZ " L@ h[ # # \ F @ [Q4] G ^ H a & ŲL9d@8b I   @Y	 c & Ųy),2d J   @K8e ' $ sk6Pf ) $ sk=Xh   @8M}p e v @ ?'           seq   gotoAndPlay R 
   bend 	] i @ 	^ i @    6_ k  ?
 mP seq @ @ @ @ @ @ @ @ @ @ @ @ ?             this   stop R i l  j D (@Ydh    k  @LZUh    l A (@YEh    m  @NBPh    n  @Rcw h    o  @Hj h    @   ?    m 02_Simple_concentratedload 	   n  D
   ?     +  @ @  , @ @  - @ @  . @ @  / @ @  0 @ ?     1      @0Vl h      @'NYh      @'NY5@h        ?WH1h    @   ?    n cantilever_seq_one ?    ! bt_x_axis_cantilever 	&   o  D
    !   " @ A@   ?    o bt_x_axis_cantilever ?     bt_background ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270    p m^J,QS?  
 f56e.u(r]F"G%R
P `c ponR0!W%#Aj] N@Իpb r  ?     bt_background ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one 	  q  D
   ?    
   static   L   @ 
Z   @  !  .@ M " B@ ^?@ # @ 
Z $ @ R@	 %  2?MT  & %R  ' $ Vrv=  ) $ Vrv?V    @P׬@ p v @ ?'           seq   gotoAndPlay R 
   bend 	  (?MT i @    6
 2  ?
P@ seq @ @ @ @ @ @ @ @ @ @ @ @ ?@             _parent   play R          this   stop R @   ?#    q 07_Cantilever_concentratedload 	_   r  D
   ?     M  @ @  N @ @  O @ @  P @ @  Q @ @  R @ ?    @   ?    r simple_seq_three ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support    s u4 8w  
 fVc H c1"\t 061MK)@y `= onR0!W%#Aj] N@(r]B1 ܂  c1"\  ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support  0   t p#K,~p (    %Q>#ܠ_#R 	k  u  D
   ?    
   display   L     @Kx   @ȏ E  8@Y " L@h #   @Kx F @[X G   @	 H   @ & Ų_9dP8 I   @Y	  & Ųٌ)-2 J   @JKx 9   @[p K  ŻR[  s   @,In@ ?'           seq   gotoAndPlay R 
   bend  i @ 	 i @    6
 S  Z seq @ @ @ @ @ @ @ @ @ @ @ @ ?@             _parent   play R          this   stop R  t   D (@Ydh      @LZUh     A (@YEh      @NBPh      @2d h    @   ?    u 03_Simple_moment 	_   v  D
   ?     M  @ @  f @ @  g @ @  h @ @  i @ @  j @ ?    @   ?    v simple_seq_two ?    # bt_dimension_lines_270 	   w  D
    #  @   ?    w bt_dimension_lines_270 ?    # bt_dimension_lines_270 	'   x  D
    #   F @ Q@   ?    x bt_dl_with_L ?    E bt_x_axis 	&   y  D
    E   " @ xH@   ?    y bt_x_axis ?     bt_v_axis 	&   z  D
         @  @   ?    z bt_v_axis ?     bt_background 	   {  D
      @   ?    { bt_background ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support    | u 8i  
 fVc H c1"\t 061MK)@y ` o'nR0!W%#Aj] N@Իpb r R1z0H #mK\  ``7)Zr3 ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support :   } p#K,~	 (    %Qꋁ# |> (    %? 	  ~  D
   ?    
   display   L  b   c E* d PR  q    @ ȏ E  8@ Y " L@ h	 # # 
 F @ [Q4 G  H  & ŲL9d@8 I   @Y	  & Ųy),2 J   @K8 ' $ sk6P ) $ sk=X   @8M} | ݀@ ?'           seq   gotoAndPlay R 
   bend 	 i @ 	 i @    6 k  ?
 mP seq @ @ @ @ @ @ @ @ @ @ @ @ ?@             _parent   play R          this   stop R  }   D (@Ydh      @LZUh     A (@YEh      @NBPh      @2cw h    @   ?    ~ 02_Simple_concentratedload ?    I roller_support 	%     D
    & Ų' H I  @   ?     roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) 	     D
    G   H  @   ?     beam_long_(300x18) ?    4 bt_square_root ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?    4 bt_square_root ?    4 bt_square_root ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?    4 bt_square_root ?    4 bt_square_root ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?    4 bt_square_root ?    4 bt_square_root ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?    4 bt_square_root ?    4 bt_square_root ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?    4 bt_square_root ?    4 bt_square_root ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?    4 bt_square_root ?    4 bt_square_root ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?    4 bt_square_root ?    4 bt_square_root ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?    4 bt_square_root ?    4 bt_square_root ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?    4 bt_square_root ?    4 bt_square_root ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?    4 bt_square_root ?    4 bt_square_root ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?    4 bt_square_root ?    4 bt_square_root ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?    4 bt_square_root ?    4 bt_square_root ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?    4 bt_square_root ?    4 bt_square_root ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?    4 bt_square_root ?    4 bt_square_root ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support 	    D
   ?    
   display   L   ]¢  ]¢  ] `  ] `  w  w    @'=`	    @'
@
 	   @'@ 7     ?N	G  M?G 8 8LEY  9  ?N1:   ?N:Џ   @&NG  V?N"	F`  V?NI	F`  /?.G   @IBG   @IEE :  ?N=G@   @3G   @%N9G   @%N6QG  w@"(G  w@"+E  ;  @%N%]G <     @X@   9@G(s@!   @T@"  @KM@# 9 (@4M9 $  c@WC %  c@WIK@& =  '   @Fyր(   @FA)   @FF\*  ̀RC7`+ >  @FM0,  9@5NQ-  ̀+H7d.   @5NXP/ 4  @NX@0   @5NY01 ? g@5Mj2 @  E@#3 4  E?1@4  -@#5 A 4@!Q@6    ?N07   @&Vp8 :   ?[@p9 B  :    @`; 9 C@8Na<   &@8Nf<= C  > D 4@!?    ?@   @&"A  .@ B    @*@C 9 C@8M,"^D   &@8M6z^E    @KxF   @ȏG E  8@YH " L@hI #   @KxJ F @[XK G   @L H   @O & Ų_9dP8P I   @Y	 Q & Ųٌ)-2R J   @JKxS 9   @[pT K  ŻR[ U L   @,Tٻ@ ?'           seq   gotoAndPlay R 
   bend K i @ L i @    6M S  Z seq @ @ @ @ @ @ @ @ @ @ @ @ ?             this   stop R V T  W D (@Ydh    X  @LZUh    Y A (@YEh    Z  @NBPh    [  @Rcw h    \  @Hj h    @   ?     03_Simple_moment ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one 	    D
   ?    
   static   L   ]¢  ]¢  ] `  ] `  w  w    @'=`	    @'
@
 	   @'@ 
     @8N
E`  @'E`  @8NE`  @'aT   @8N8   @_N8   @_N6   "@8NDP  @')E  "@8N1DP  @N.EE   @'"QE  C@4%E      @Jր  @9M(sր  @Fր  @=  @'`  @8M3@   C@[:s@!  C@[@3"  @#  4
3$   @&%  @(r&   '  @;1̀(  @&3^@)  C@I:r^@*  C@I@2T+  @ 
Z,   @ - !  .@ M. " B@ ^?@/ # @ 
Z0 $ @ R@2 %  2?MT : & %R ; ' $ Vrv= < ) $ Vrv?V >   @P׬@? * v @ ?'           seq   gotoAndPlay R 
   bend 2  (?MT i @    63 2  ?
P@ seq @ @ @ @ @ @ @ @ @ @ @ @ ?             this   stop R @   ?#     07_Cantilever_concentratedload ?     bt_table_row ?     bt_table_row ?     bt_background ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_table_row ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support 	    D
   ?    
   display   L   ]¢  ]¢  ] `  ] `  w  w    @'=`	    @'
@
 	   @'@ X     @	G  ?@G 8 @VP   @: Y  @:   ?:Џ   @>G  H@"	Fp  H@<Fp  i@:$G  i@:'E0  !@*)G Y  @a-G   @a0E   !@3aG   @a6G   @a:	E  Z  @8NSqF    @8N\F  [   @PX!F   [   @PaF ! \  @8NfiF " ]  #   @*3@$  .@'@% 8 @-@&    @*2; ' Y   @*:S ( \   @B#@) ^  * _   ?+    @*@,  7@*NCр-  7@*A`.  X@MS@/  X@MYk̀0  @^@1 Y   @te@2    @tk@3  @p@4 \   @tx@5    @t~3@6 `  7 A 4@!Q@8    ?N09   @&Vp: :   ?[@p; 8   @f<  C@8N_藠= \  &@8Nc>   &@8Ng(`?   &@[i@   &@[l A  6@'oB  ]@8Nx `C \  &@8NrD   &@8Nu E a  F D 4@%G    ?H   @*"I  .@ J 8   @7Z@K  C@=)^L Y  &@=1B^M   &@=8bYN   &@`=^@O   &@`CRTP  6@+HB^Q  ]@=ZRYR Y  &@=O"^S   &@=UbTT b  U c E*V d PRW  q X   @ ȏY E  8@ YZ " L@ h[ # # \ F @ [Q4] G ^ H a & ŲL9d@8b I   @Y	 c & Ųy),2d J   @K8e ' $ sk6Pf ) $ sk=Xh   @8M}p e v @ ?'           seq   gotoAndPlay R 
   bend 	] i @ 	^ i @    6_ k  ?
 mP seq @ @ @ @ @ @ @ @ @ @ @ @ ?             this   stop R i l  j D (@Ydh    k  @LZUh    l A (@YEh    m  @NBPh    n  @Rcw h    o  @Hj h    @   ?     02_Simple_concentratedload ?    S simple_seq_three ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    S simple_seq_three ?    I roller_support 	k    D
   ?    
   display   L     @Kx   @ȏ E  8@Y " L@h #   @Kx F @[X G   @	 H   @ & Ų_9dP8 I   @Y	  & Ųٌ)-2 J   @JKx 9   @[p K  ŻR[  s   @,In@ ?'           seq   gotoAndPlay R 
   bend  i @ 	 i @    6
 S  Z seq @ @ @ @ @ @ @ @ @ @ @ @ ?@             _parent   play R          this   stop R  t   D (@Ydh      @LZUh     A (@YEh      @NBPh      @2d h    @   ?     03_Simple_moment ?    2 cantilever_seq_one ?    ! bt_x_axis_cantilever ?     bt_background ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?     bt_background ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one ?     bt_background ?     bt_v_axis ?    ! bt_x_axis_cantilever ?    # bt_dimension_lines_270 ?    2 cantilever_seq_one 	    D
   ?    
   static   L   @ 
Z   @  !  .@ M " B@ ^?@ # @ 
Z $ @ R@	 %  2?MT  & %R  ' $ Vrv=  ) $ Vrv?V    @P׬@ p v @ ?'           seq   gotoAndPlay R 
   bend 	  (?MT i @    6
 2  ?
P@ seq @ @ @ @ @ @ @ @ @ @ @ @ ?@             _parent   play R          this   stop R @   ?#     07_Cantilever_concentratedload ?    k simple_seq_two ?    # bt_dimension_lines_270 ?    E bt_x_axis ?     bt_v_axis ?    bt_background ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support ?     bt_background ?     bt_v_axis ?    E bt_x_axis ?    # bt_dimension_lines_270 ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    k simple_seq_two ?    I roller_support 	    D
   ?    
   display   L  b   c E* d PR  q    @ ȏ E  8@ Y " L@ h	 # # 
 F @ [Q4 G  H  & ŲL9d@8 I   @Y	  & Ųy),2 J   @K8 ' $ sk6P ) $ sk=X   @8M} | ݀@ ?'           seq   gotoAndPlay R 
   bend 	 i @ 	 i @    6 k  ?
 mP seq @ @ @ @ @ @ @ @ @ @ @ @ ?@             _parent   play R          this   stop R  }   D (@Ydh      @LZUh     A (@YEh      @NBPh      @2cw h    @   ?     02_Simple_concentratedload ?    I roller_support ?    H beam_long_(300x18) ?    G beam_long_(300x18) D
   ?  K- Math commaFormatted neo . inputString split neoLen length neoStart charAt - neoLenR noCommas floor FirstBunch substring withCommas SecondBunch , ThirdBunch neolen FourthBunch formatDecimals num isNaN digits cropped round CF tenToPower pow indexOf .0 halves zerosNeeded i 0 toScientific exponent abs log mantissa sigDigs output e       inputString      R< 	         N N<         <            	         N 	R 
I      <  <           R<     ?	         I        	         IL    I >              	         N R< <      I   	                  	         N R<                 	         N R<  G G< 7     I   	                  	         N R<              	         N R<                 	         N R<  G G G G< ?     I * 	                  	         N R<              	         N R<       	       	         N R<  	               	         N R<  G G G G G G<             N NH    G     NG >O      num digits      =  	         J> _         H <        RK<       R< >  
        R<        R K<	     R I     G !    R< " !    N N< #   < " #H    $G ##P        R< >O   %   num sigDigs . J     =   > &      'R      (R	 k@U      R< 	         I   &         & 
        R< ) < )*     )      R +)< &	         I   ++ ,&GG +>O ?  d  nr theRandom length igap Math floor iflag j swapTemp theIndices theLength random theCopy theGiven $ ShellSort2  theRandom theIndices    N<           R< A A A         H g         I                           H     GN  NH    N     GNO   G O 	 N 	  	  GNO 	  G O     P            R % TraceArrays  theRandom theIndices J    N<         <       H   P . FillArrays  theRandom theIndices theLength y          < 
     H M             RO 	      GO P ) CopyArray  theGiven theCopy theLength U          < 
     H )     NO P  ?  D  theRandom Array frameIndex j Math random ShellSort2 subFrameIndex  MakeSequence            @<       @         <    H D              RO   O P        = MakeSubSequence            @<       @         <    H M              RO       GO P        = ?  Q6 UserValue userResponse StripAnyUnitStrings AbsValueFlag Math abs correctResponse bCorrect IsItCorrect formattedCorrect numDigits formatDecimals + checkmark gotoAndStop correctCounter GiveTheCorrectAnswer Correct!!  Well done!  The precise value is    unitString . The correct beam deflection at the specified location is  theBeam question explain outputString sFore sAft LengthOfString LocationOfSpace inputString indexOf substring outputstring LocationOfComma , length isNaN  response user parseFloat tolerance diff correct range ValueMax ValueMin RN random theValue NoSteps StepSize round T EvaluateAnswer  correctResponse numDigits unitString AbsValueFlag correctCounter ]      =<    5         R J     R       =< 	
      R<         H   		G  E         R P 	G G G G K         R 	G G G G   NO >$ StripAnyUnitStrings  inputString  A A A A             R<  I    #                R ! "        < "        #    R< " I    k   $N "              R  "    G      R  G " I > J    %=   &>   J> IsItCorrect  user correct   'A (    )=    %=   '(    )=    > *  ?    < +' ,< * +     RH   >    >+ RandomValue  ValueMin ValueMax StepSize w  -. /< 0         1R< 2/ 0 -G< 32 4     5R< 23 4 2> ?    ?    r!L 3 k{eA	] >~S6|'~8	cÆ\@IRWshl# ]^Su-ylц]@L	B*;	>5 M-GE7]c'"eI[/r l Qغѧ<>+J) d+7M[x<]:yβP-*=uii=3рX.L,=$JV3!#ҠR;뤫5;Y~79J{iü2dJ{ iS\(.Xl׽Vrgn.vd6[i6	S.wd,H)q7Q*RR@))WDaH+&dPO^ud'KkBZΒp97Du-0K 	(HEe!%ĉ`3dJ jiS)9=':П@ X)
 G`` y@'	 8~   	*    g2p0         percentLoaded 
  Y`@ ?   ?  percentLoaded this getBytesLoaded getBytesTotal Math floor %            R          R d        R    G          R          RH           PBL 	 ̒     XN!̀ 
 ̒     XM!  
 ̒     XN  
 ̒     P>L 	 ̒     X!Oa  
 ̒     XN 
 ̒ 	~   b D
      &@4 i @ @   &@4 pi @ @   &@4Ti @D@   &@4TMi @d@   &@4T}@i @@   &@4T@i @@   &@4T i @@   &@4Ui @@   &@4U<i @@   &@4Uli @,   &@4i @ @   &@4U@i @L  &@4pi @ @   &@4U i @p  &@4i @D@   &@4M i @  &@4Mi @d@   &@4i @  &@4}@i @@   &@4ni @ԓ  &@4@i @   &@4i @ @   &@4.i @  &@4 i @ȓ  &@4 i @$@   &@4i @  &@4i @  &@4$" i @D@   &@4i @8  &@4<i @  &@4$T i @h@   &@41i @X  &@4li @,  &@4$ i @@   &@44i @|  &@4@i @L  &@4$ i @@   &@47i @  &@4 i @p  &@4$ i @@   &@4
ji @  &@4 i @  &@4% i @   &@4>i @ @   &@4@i @  &@4i @  &@4%N i @  &@4>i @$@    @4R  &@4	ni @ԓ  &@4% i @<  &@4|&i @H@   &@4
.i @  &@4% i @\  &@4|[@i @l@   &@4
i @  &@4 i @  &@4|i @@   &@4i @8  &@48Xi @  &@4| i @@   &@4i @X  &@49 i @ē  &@4|@i @@   &@4i @|  &@49i @  &@4},i @ @   &@4i @  &@4:i @  &@4}a i @$   &@4i @ @   &@4,*i @  &@4;xi @0  &@4}i @H  &@4 i @$@   &@4XZ@i @  &@48q i @P  &@4}i @l  &@4D" i @D@    @4X
   &@48t i @t  &@4u@i @  &@4DT i @h@   &@48w@i @  &@4,i @  &@4D i @   &@4i @ @   &@4pi @  &@4,i @ܓ  &@4D i @  &@4i @ @   &@4p i @ܒ  &@4,mi @   &@4< i @Г  &@4#i @@@    @4p  &@4,?i @$  &@4= i @  &@4#Gi @`@   &@4Y@i @H  &@4=N i @  &@4#u@i @@   &@4Yӈi @l  &@4= i @<  &@4#@i @@   &@4Yi @  &@4= i @\  &@4# i @@   &@4Yi @  &@4= i @  &@4#i @@   &@4YXi @ܒ  &@4>xXi @  &@4#,i @    &@4Bi @ @    @4Y  &@4>y i @ē  &@4#Zi @   &@4B i @$@   &@4>yi @  &@4#@i @@  &@4," i @D@   &@4>zi @  &@4#@i @`  &@4,T i @h@   &@4>{xi @0  &@4# i @  &@4, i @@   &@4| i @P  &@4GGi @  &@4, i @@   &@4| i @t  &@4Gi @  &@4,| i @@   &@4|@i @  &@4G	i @  &@4,} i @@   &@4|`i @  &@4G
mi @   &@4,}N i @@   &@4|݀i @ܒ  &@4G%i @   &@4,} i @<@    @4|  &@4Fi @@  &@4,} i @\@   &@4Fi @`  &@4,} i @@   &@4FKi @  &@4XXi @@   &@4Fi @  &@4X i @@   &@4Fi @  &@4Xi @@   &@4Fqi @  &@4Xi @@    @4F(  &@4Xxi @0@   &@4X@i @P@   &@4Xi @t@   &@4Xi @@   &@4Xi @@   &@4X`i @@    @4X(@ 	 i @	 i @̉	 i @Љ	 i @؉	 i @܉	 i @	 i @@ 	 i @	 i @	 i @	 i @	 i @	 i @	 i @@ 	 i @@	 i @`	 i @t	 i @	 i @	 i @	 i @@ 	 i @ 	 i @(	 i @D	 i @\	 i @l	 i @|	 i @@ 	 i @	 i @	 i @	 i @4	 i @H	 i @\	 i @h@ 	 i @	 i @	 i @	 i @	 i @$	 i @8	 i @L@ 	 i @@	 i @	 i @	 i @	 i @ 	 i @	 i @,@ 	 i @ 	 i @P	 i @	 i @	 i @܉	 i @	 i @@ 	 i @	 i @	 i @\	 i @	 i @	 i @؉	 i @@ 	 i @	 i @	 i @0	 i @h	 i @	 i @	 i @@ 	 i @@	 i @	 i @ 	 i @<	 i @l	 i @	 i @@ 	 i @ 	 i @x	 i @Љ	 i @	 i @H	 i @t	 i @@ 	 i @ 	 i @D	 i @	 i @	 i @$	 i @T	 i @x@ 	 i @ 	 i @	 i @t	 i @ĉ	 i @ 	 i @0	 i @\@ 	 i @ @	 i @ ؉	 i @D	 i @	 i @܉	 i @	 i @<@ 	 i @  	 i @ 	 i @	 i @p	 i @	 i @	 i @ @  	 i @ l	 i @ 	 i @H	 i @	 i @Љ	 i @ @ 	 i @ 4	 i @ 	 i @ 	 i @l	 i @	 i @@ 	 i @  	 i @ 	 i @ 	 i @H	 i @	 i @@  	 i @ \	 i @ ̉	 i @$	 i @l	 i @@ 	 i @ 0	 i @ 	 i @ 	 i @L	 i @@ 	 i @  	 i @ |	 i @ ܉	 i @(	 i @h@  	 i @ P	 i @ 	 i @	 i @L@ 	 i @ (	 i @ 	 i @ 	 i @,@ 	 i @  	 i @ l	 i @ ȉ	 i @@  	 i @ H	 i @ 	 i @ @ 	 i @ $	 i @ 	 i @ @ 	 i @  	 i @ d	 i @ @  	 i @ D	 i @ @ 	 i @  	 i @ x@ 	 i @  	 i @ \@  	 i @ <@ 	 i @  @ 	 i @  @     )@ HH  @ @ @ @ @ @ @ @ @ @ @ @ @ ?      @   
 ?>             MakeSequence =          theBeam   play R 
   state_the_problem  (    Xa   f f%l0< !_\+@  +    _D   
 f%Ia?2`Cw2{-      H7      /,uɀ$    ` " 	 fwrzMp $    ` " 	  33wrzMp       d>     ar0r             u@Dc        f&I   x     f&I    34  
B    u@Dc 34  
B    @@'t@
         0   x      0    @@'t@
   pl         ì       PnH 
 f%K9Cj~)_:      Z?b ܄ 
 f%iwgF      N%i- f +~)_9wX (    `$
 	 fwrzM (    `$
 	  33wrzM V    H    @)x  @ n@  ^   fk32    f&I     @JKW    x|34  
B    n834  
B      A134  
B     @'[@
   fk32     0     @JKW     0     @)x34  
B   @ n@34  
B     @ A0P34  
B     @'[@
   p`<            @-Wa      Xg  	 fMj      Xg  	  33Mj           @)0   ?x    ?i    @)034  
B    ?x 34  
B    b@'u(    ?i     0    b@'u(  p0           @-g      Xl!   	 frn      Xl!   	  33rn     
    @)0   @ PP  @ P  fk32Ҩ    f&I     @JJA    @)034  
B    @ PP34  
B    @ P34  
B     @'}   fk32Ҩ     0     @JJA     0   Z34  
B     @'}   p@     K      @-uY  %    `	000  f f$=´tP0     &    _a   f f%l0\+A$9        Wԉ 	 fB@   =F     P߇ 	 f  &@   @ORwP &    o__   f%7fa5Y  ;      @  3ff% 
     A    h"P   
 fIH%8@rSчxeSb 䧂       @'U     b6  	 f  &@ !  0k    x$   
 fjh&NB@
=;m'{S
 == Np~ r
Gb =5g'|sX "   @ k(#   d    uiZ  a L ɒ q=h:ϋ:ݨHR{^.|^. |  L Z1N SNN`d.s,Z %  3HNU%?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support 	S   Z D
   
   one  G ɀ @   H ɀ @   & Ų*1 J   ?L}   & Ų'9V I !  '    o  )    ߀@     o     ߀@     o     ߀@     o     ߀@     o     ߀@     'o     '߀@     Go     G߀@     go     g߀@     ԇo     ԇ߀@     קo     ק߀@     o     ߀@     o     ߀@     o     ߀@     'o     '߀@     Go     G߀@     go     g߀@     o     ߀@     o     ߀@     o     ߀@     o     ߀@     o     ߀@     'o     '߀@     #    #@         @     C    C@         @     c    c@         @         @ 
   two         @         2_@         d_@     %    _@     2    _@     >    _@     K    7@     W    7@     d    7@     p    7@ 
   three     }    7@         @         @         @         @         @         @     Ԗ    ԝ@         @         @         @     M     O~ @          ~ @     ͼ     ~ @          ~ @     M     O~ @          ~ @     ͼ     ~ @          ~ @     M     O~ @          ~ @     ͼ     ~ @          ~ @     M     O~ @     ԍ     ԏ~ @     ͼ     ~ @          ~ @     M     O~ @     퍼     ~ @     ͼ     ~ @          ~ @     'o     '߀@     Go     G߀@     go     g߀@     o     ߀@     o     ߀@     o     ߀@     o     ߀@     o     ߀@     'o     '߀@     Go     G߀@     go     g߀@     o     ߀@     o     ߀@     o     ߀@     o     ߀@     o     ߀@     'o     '߀@     Go     G߀@     go     g߀@     o     ߀@      6&  &fI
*@ theBeam    hWR  
 fX_1ܗ@3т
QĀ0M-   oSI1Hfb.A pb K   S<1(F8 0G)GËK r]81    @C0 Krvb@@   nnR0!W%#Aj] N@Իpb	@    	X_1ܗ@#w( 0   	pb9.%rA ``B1K wǚ[    m
0C0Kт 07)Zppct `  pb9.K\r]81 I  SI1K\Cz0H F8v  lc1 f A ǌE.@+R9L于S@ /    @MC'@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ?    (    `-0$ 	 fnnzMr (    `-0$ 	  33nnzMr      ]_0Z  f kxV: (    `-0$ 	 nnzMr  &    ` 0 0 ̙  4JpGoi~Z          @)0   3@'
)    @)034  
B    3@'	S    @-a    @)034 z(0    3@'	S        0  ܨ" @ 0 ?S     bend     btBeam   gotoAndPlay R  one     theBeam   gotoAndStop R  H    l[%  f fSY *&X |i,,> x53D ͘j@  F0    ;oA P ?     02_Simple_concentratedload    61  f8~ # btBeam @ ?     02_Simple_concentratedload @ ?     02_Simple_concentratedload @ ?     02_Simple_concentratedload @ ?     02_Simple_concentratedload @ ?     02_Simple_concentratedload @ ?     02_Simple_concentratedload @ ?     02_Simple_concentratedload @ ?     02_Simple_concentratedload @ ?    ?     02_Simple_concentratedload Q  ܨ, @ 1 Q ?S     bend     btBeam   gotoAndPlay R  two     theBeam   gotoAndStop R ?#     07_Cantilever_concentratedload    61  f8~ - btBeam @ ?#     07_Cantilever_concentratedload @ ?#     07_Cantilever_concentratedload @ ?#     07_Cantilever_concentratedload @ ?#     07_Cantilever_concentratedload @ ?#     07_Cantilever_concentratedload @ ?#     07_Cantilever_concentratedload @ ?#     07_Cantilever_concentratedload @ ?#     07_Cantilever_concentratedload @ ?    ?#     07_Cantilever_concentratedload Q  ܨ6 @ 1 Q ?U     bend     btBeam   gotoAndPlay R  three     theBeam   gotoAndStop R ?     03_Simple_moment    61  f8~ 7 btBeam @ ?     03_Simple_moment @ ?     03_Simple_moment @ ?     03_Simple_moment @ ?     03_Simple_moment @ ?     03_Simple_moment @ ?     03_Simple_moment @ ?     03_Simple_moment @ ?     03_Simple_moment @ ?    ?     03_Simple_moment Q  ܨ@ @ 0 1 Q ?"             theBeam   play R    x  
 f=BL1; ČE0%9L `@<1ڗr  `0C0%APu r]F"FF;  xc.G%ӡ nR F8v 0H F0  o<lb9.pRRA  `j]#G%rvz09.3JԻ@=!pcil `SI1K[т
QĆ`G)wf 9M j]1K[ r]5.    >@5.%EJ$r v`F"G%ӡ nR F8q 0C0"K(wpb PrA `nRLx\t$e 0 0   >bF"H
Q 07)Zppct `SC0 g%Ӄ Ě[ qH$ܥj] F8v 0H %Ӓ @5.Fb- `nR.K1Qď   nL@ :S= H c1"\t 061MK)@Z$`@<1Xf#J亄c #mK `0C0n@RA  `j]"F	b-w[  h0C0Kтǋ   	L@ -nR.u(r]F"G%R
P `=$prnR.[RA pb  ۃ Ի@ $F    m
L@ 2S= H c1"\t 061MK)@Z$`@<1Xf#J亄c #mK `C0 KF<  Ի@  hSI1Hfb.A f  >bgC0$)CRil `lb9.K$t `@C0 G%Ԃu=!K 081NhK z0C0!	&<rvb !x c.C  l>@<1ܗQg%JԻS9.P31 `[C0$)CRil `lb9.%SI`E.	3  c1Q!S9.g%Ԣuj] C  @<1ܗPR#( /    @M( @ @ @ @ @ @ @ @ @ ?    @             ! " # % & / ?-    TotalBeamLength RandomValue theBeam SetupBeamSpans BeamEI theMaxDefl MaxDeflectionEnvelope ActualP RoundToStep Efactor      MaxDeflPa P ComputeDeflections MaxDeflPb MaxDeflPd MaxDeflPe MaxDeflPg Math abs max  SetBeamSpanLoadEI   q$  ?,@@   =       R    <         =          =<    '        R x   H W  x        = 	 '   <	 d    	     R     =  (   H ?      G     =  
G G&  MaxDeflectionEnvelope  P             R<            R<            R<            R<            R<      R      R     R<      R      R      R      R      R      R > ?B     txtInstructions           theBeam   gotoAndStop R 
   cc_set1   ̀Lӕ~y    3`   ͂=US~
    fc2d #    x
I  < f%DD 2sK@    E    xd6      upnwHI-r"#nw$(~#h    @u L    30    @m    3` 	    p]+#3           ( txtInstructions <P ALIGN="LEFT"><FONT FACE="Verdana" SIZE="14" COLOR="#000000">Enter your answer (without units).</FONT></P>   [   $I&21      0 |   wү < 
   3f B@6tC7!&CA$ m6t<9CmrH$ @ 8# 9N俌Dp3	 qr_0#K j`B2g%b$ 0c2ܗybˎS\K;aُr_12fŹN,@ -L	ː?=!P q[0#/Ef.9N qmLj`G)K<9N qa:@2[O YV6owĈ @n^<9CmrH$ @ 8@<b&ܧr_/G@   eg`I    h 	 33  j RpzRmjnr RzR Rrmrw &    Xax 	 33  uI
  ] H    `/ 	 33  Ĉ     "c    RLs   c 	%    _N` 1  33        sEI 60.0  q    xYH      % [~0	93\%7Qw Ky[e7QwX[/uWpV'9%&0[PȖ ?	    Tahoma < > \ |   6Vgv<7arU9Fk 5HBnNoPVD?؄,\]c5c{xI>Qk=I>Q5c~{xI>Q5f尒mn#ԙR  VEI|S0+	3]Iҥ/<)q :`lLDG*TRL[ 5ef8C9J`4izN]mJjv,BwS	]UL]q7m,a[-6.fqo=TM< 5K7oq	@7P<r 5Hy㨯F*qn 5L7n
f, 5/uOݞn,@5g{yYpID 5iZfH ^&oo0fl	2y啞n& tB`<Qoc~	@eje)CXSG \@\s)w@Jy.K,  5aa~J^1HmEM)~N0 5i:f B@#mJLxg%ه1VьՔ@3Yp\PR̖za?Pw2!X 5i& 	m;%#%0{<\l[.ŶPK`3eـoeR4ܜɮl$G2V15/Lu#nex:j鮿rkG]Bv1?>]%`-iS&Ri . 5J݁o?/SݺPekɺ؜WRj< 5i&x,Mi?Ak\E#/*e0\ ([KI(B@?)brvDK[u!7Md\{}pn0 5ff .DZTr7%6ʌY<] 	s :&O&__f7mۓj^MxC0¶%p̓$[ <m*:IADtևΗiPU5%W޺? 5izy40Sm';tD{@ 5fk>sZ3e z@A9G@>CLlȤ!4+KWPp
'q\Cf3"J2ShJ#6HXb=%`90#Cų_siK	J䤮$*,8Li>VcH$Ts\:!?*kED?m-K!84-/tkI6y-O@5ifC _>n#nG oovc8vڎT]΢7#|4l6[fm-Kg3tZ1I򔜒.51b BR$4EB`Xw|L+ə/s Hp]jIH8h(Zc 5HybnSgT{u 5Iy㨯F*qn
:Or<X 5hz ˒yxv\mzD\*oʋ9j3JK0LuH-`IK@RYݵm]ބmpFBhIH ,;rw|b5ix,-KW	;8 5k.yWF3<rF7N֫VU5e@$i$PU($HsK">}o<mEK]/YG]f`I ^}^tv'' TdIIю] hg@ 5Mif7ZYm7 5kN 1Ve0lbiE mܨp'cĘq쉒)Cܨp'7aƺ$
`QWҫd+0	ʜV2<s.   !"'()+,-./0123456789:;?ENekm  ,_F@@OttDv`i XL"t`  X@6X<X753g X(3Sg Xa\ WPnWI!<  X;>sQ X'L$ XbIX  XLM$  X4K  XN` X<K` X1MT( X;K`  X MX"Kt$Xb"w<  X&7<\X8C$  XMH`  XMYt`  XI6XCN  XCrV    	'    Xw_` 1             text 8.8 m 	     D
     q;x@   ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support     P	 	 d     P4	 	 T     P	 	 ,     P4 	      P4	 	      P4Չ 	      P	 	  	(    g$W1       ( text 120 kN 	=     D
    '      )          @8LO@   	(    g$W1        ( text 120 kN 	<     D
    '      )          @8Hd@   	   h 3 f         question <P ALIGN="LEFT"><FONT FACE="Verdana" SIZE="14" COLOR="#FFCC66"><B>10 Compute the resultant force in the pin at C.   </B><B>If the allowable shear stress is 50 MPa, what is the minimum diameter required for the pin at C? </B>[]</FONT></P><P ALIGN="LEFT"><FONT FACE="Verdana" SIZE="14" COLOR="#FFCC66"><B>1</B></FONT></P><P ALIGN="LEFT"><FONT FACE="Verdana" SIZE="14" COLOR="#FFCC66"><B>2</B></FONT></P><P ALIGN="LEFT"><FONT FACE="Verdana" SIZE="14" COLOR="#FFCC66"><B>3</B></FONT></P><P ALIGN="LEFT"><FONT FACE="Verdana" SIZE="14" COLOR="#FFCC66"><B>4</B></FONT></P><P ALIGN="LEFT"><FONT FACE="Verdana" SIZE="14" COLOR="#FFCC66"><B>5</B></FONT></P> ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support ?    G beam_long_(300x18) ?    H beam_long_(300x18) ?    I roller_support 	\    D
   ?  &v sEI BeamEI Math formatDecimals sActualP _parent ActualP  kN sActingAt sFindAt Pa _visible text A Pb B Pd D Pe E Pg G findVa findVb findVd findVe findVg hint correct_answer abs RandomValue RoundToStep sHint  mm question The simply supported beam shown is subjected to a concentrated load of <B> </B> acting at <B> .</B>   Determine the <B><FONT COLOR="#FFFFFF">beam deflection at  </FONT></B> produced by the concentrated load (in mm).
 [Upward deflection = +; Downward deflection = ]
 <FONT COLOR="#99CCCC">Hint:  The beam deflection magnitude is less than  .</FONT> vA vB vD vE vG ab LengthA LengthB cd LengthC LengthD cde LengthE de sAB  m sA sB sC sCD sCDE sDE sE sF LengthF momentTemp thetaTemp vTemp vTemp1 PaFlag UnitP Cant_vTip Simple_M_theta1 Cant_vElasticCurve Simple_M_vElasticCurve Simple_M_theta2 PbFlag Cant_thetaTip PdFlag Simple_P_theta1 Simple_P_vElasticCurve Simple_P_theta2 PeFlag PgFlag MaxDefl Max vtip P L pow EI thetaTip v x Lb theta1 theta2 La M TotalLength a b c d e f NoSteps theValue StepSize round range ValueMax ValueMin RN random  PoseTheQuestion   	             R  N G A 	A 
 N   
 O     N    O     N    O  W   N    O  )   N    O     	 _     	 F     	 -     	      	      R"   ?      @      ?       =  	   H   	   	    	   @    G    = (   H   (          R     R    H       G   !G "#G $G G %G "" &G 	G 'G "" (G "" )G  G *G@ ComputeDeflections  UnitP PaFlag PbFlag PdFlag PeFlag PgFlag   N +         ,         -         .         /         01 2G 34 5G 63 7G 85 7G 90 :G ;1 :G <2 :G =4 :G >3 :G ?6 :G @8 :G A7 :G BC :G DA EA FA GA H Z DI 0 ++  0 I    J= F 6 D    K= 0 ++ F ,,  2 0 I    L= F 6 D    K= 2 ,, F --  4 6 D    M=G ..  3 6 D    M=G //  6 D    N= C O  DI 2 ++  2 I    J= G 2 I    P= 1 F 6 D    K= 0 ++ G F ,,  2 I    J= F 6 D    K= 2 ,, F --  4 6 D    M=G ..  3 6 D    M=G //  6 D    N= C Q  ++  8 6 I    R= 0G ,,  8 6 I    R= 2G --  4 8 6 I    S= ..  7 4 6 I    S= //  4 6 I    T= CG U  ++  7 6 I    R= 0G ,,  7 6 I    R= 2G --  4 7 6 I    S= ..  3 7 6 I    S= //  3 6 I    T= CG V $ DI C ++  6 D    N= 0 ,,  6 D    N= 2 --  8 6 D    M=G ..  7 6 D    M=G //  C I    J= F 6 D    K= C // F W,     R +     R     XR< W-     R W     XR W.     R W     XR W/     R W     XR    +         ,    d     -    A     .         /    W> Cant_vTip  P L EI =  YZ    [     \R     ]< Y> Cant_thetaTip  P L EI =  ^Z    [     \R     ]< ^>  Cant_vElasticCurve  P L x EI Q  _Z    `     \R     ]    [ `< _>' Simple_P_vElasticCurve  P L Lb x EI   _Z a `    [ ]    [     \R    a     \R    `     \R< _> Simple_P_theta1  P L Lb EI e  bZ a    [ ]    [     \R    a     \R< b> Simple_P_theta2  P L La EI e  cZ d    [ ]    [     \R    d     \R< c>$ Simple_M_vElasticCurve  M L x EI   _e `    [ ]       [     \R    [ `    `     \RG< _> Simple_M_theta1  M L EI $  be [    ]< b> Simple_M_theta2  M L EI $  ce [    ]< c> SetupBeamSpans  TotalLength  1?UU?UUUUf    = 2??rqf    = 4?q?qf    = 5?UU?UUUUf    = 7??rqf    = C??88f    = g	    1     RO h	    2     RO i	    4     RO j	    5     RO k	    7     RO l	    C     RO ClearBeamLoadsDeflections   n  
  O   O   O   O   O          " RoundToStep  theValue StepSize 8  mn o     pR< nm o n>+ RandomValue  ValueMin ValueMax StepSize w  qr s< t         uR< ns t qG< mn o     pR< nm o n> ?  z ClearBeamLoadsDeflections Pe _visible findVd Pg Pd Pb Pa _parent ActualP ComputeDeflections PoseTheQuestion explain Use the elastic curve from the <B>simple span with concentrated load</B> case to find the deflection at <B>D.</B>  The span length L is the distance between the supports at C and F, x is the distance between C and D, and b equals the distance between E and F.           =  O   N  N  N  N  N  	N    
=         =    @ ?x  @ S8W  @ gW  @ ]W      &    @BOha    &    @\b    &
    @N c    &    @FP=d    &    @g=e    &    @~@=f  G ɀ @   H ɀ @   & Ų*1 J   ?L}   & Ų'9V I !     @I9    @K~C    @MD`9    @M_X9    @N^p    @8Ntx    @OE   &  X@ EPg    &$  o Pe    &)   Pd    &.  xPb    &3  Pa 8    @G@ ?   ClearBeamLoadsDeflections Pa _visible findVa Pg Pe Pd Pb _parent ActualP ComputeDeflections PoseTheQuestion explain Two cases are necessary.  First, use the <B>cantilever with P</B> case to find the deflection at <B>A,</B> using L =  sAB  as the span length.   Next, use the <B>SS with M</B> case to compute the slope at C caused in the  sCDE  simple span by the overhang moment M = ( sActualP )( ).  Multiply this slope by the   overhang length to find the deflection at A.  Add these two deflections.           =  O   N  N  N  N  N  	N    
=         = G G  G G G G G G G G G @ ?e   ClearBeamLoadsDeflections Pd _visible findVg Pg Pe Pb Pa _parent ActualP ComputeDeflections PoseTheQuestion explain One case but two steps are needed to find the deflection at <B>G.</B>  Use the <B>simple span with concentrated load</B> case to find the slope at F, where L =  sCDE  and a =  sCD .  Multiply this slope by the  sF  overhang length to compute the deflection at G.   The deflection is upward.             =  O   N  N  N  N  N  	N    
=         = G G G G G G  G @ ?   ClearBeamLoadsDeflections Pg _visible findVb Pe Pd Pb Pa _parent ActualP ComputeDeflections PoseTheQuestion explain To find the deflection at <B>B,</B> two steps are required.  First, use the <B>simple span with concentrated moment</B> case to find the slope at C caused in the  sCDE  simple span by the overhang moment M = ( sActualP )( sF ).  Next, multiply this slope by the  sB  overhang length between B and C to find the deflection at B.             =  O   N  N  N  N  N  	N    
=         = G G G G G G G G @ ?   ClearBeamLoadsDeflections Pb _visible findVe Pg Pe Pd Pa _parent ActualP ComputeDeflections PoseTheQuestion explain The elastic curve for the <B>simple span with concentrated moment</B> case will be used to find the deflection at <B>E.</B>  The concentrated moment produced by the overhang is M = ( sActualP )( sB ).  Use this moment in the elastic curve equation along with L =  sCDE  and x =  sCD  to find the deflection at E.   The deflection is upward.             =  O   N  N  N  N  N  	N    
=         = G G G G G G G G  G @ ?y   ClearBeamLoadsDeflections Pd _visible findVe Pg Pe Pb Pa _parent ActualP ComputeDeflections PoseTheQuestion explain Use the elastic curve from the <B>simple span with concentrated load</B> case to find the deflection at <B>E.</B>  The span length L is the distance between the supports at C and F.   In using the elastic curve equation, mentally flip-flop the beam so that x is measured from F towards C and the distance term b equals the distance between C and D.           =  O   N  N  N  N  N  	N    
=         =   G @ ?
   ClearBeamLoadsDeflections Pb _visible findVa Pg Pe Pd Pa _parent ActualP ComputeDeflections PoseTheQuestion explain Three steps are required.  First, use the <B>cantilever with P</B> case to find the deflection and slope at the tip, using L =  sB .   Next, multiply this slope by  sA  to find the additional cantilever deflection beyond the load location.   Finally, use the <B>SS with M</B> case to compute the slope at C caused by M = ( sActualP )( ).  Multiply this slope by the  sAB  overhang length to find the deflection at A.           =  O   N  N  N  N  N  	N    
=         = G G  G G G  G G G G G G G @ ?d   ClearBeamLoadsDeflections Pe _visible findVb Pg Pd Pb Pa _parent ActualP ComputeDeflections PoseTheQuestion explain One case but two steps are needed to find the deflection at <B>B.</B>  Use the <B>simple span with concentrated load</B> case to find the slope at C, where L =  sCDE  and b =  sE .  Multiply this slope by the  sB  overhang length to compute the deflection at B.   The deflection is upward.             =  O   N  N  N  N  N  	N    
=         = G G G G G G  G @ ?   ClearBeamLoadsDeflections Pa _visible findVg Pg Pe Pd Pb _parent ActualP ComputeDeflections PoseTheQuestion explain To find the deflection at <B>G,</B> two steps are required.  First, use the <B>simple span with concentrated moment</B> case to find the slope at F caused in the  sCDE  simple span by the overhang moment M = ( sActualP )( sAB ).  Next, multiply this slope by the  sF  overhang length between F and G to find the deflection at G.             =  O   N  N  N  N  N  	N    
=         = G G G G G G G G @ ?   ClearBeamLoadsDeflections Pg _visible findVd Pe Pd Pb Pa _parent ActualP ComputeDeflections PoseTheQuestion explain The elastic curve for the <B>simple span with concentrated moment</B> case will be used to find the deflection at <B>D.</B>  The concentrated moment produced by the overhang is M = ( sActualP )( sF ).  Use this moment in the elastic curve equation along with L =  sCDE  and x =  sDE  to find the deflection at D.   The deflection is upward.             =  O   N  N  N  N  N  	N    
=         = G G G G G G G G  G @ ?  | ClearBeamLoadsDeflections Pd _visible findVd Pg Pe Pb Pa _parent ActualP ComputeDeflections PoseTheQuestion explain Use the elastic curve from the <B>simple span with concentrated load</B> case to find the deflection at <B>D.</B>  The span length L is the distance between the supports at C and F, x is the distance between C and D, and b equals the distance between D and F.             =  O   N  N  N  N  N  	N    
=         =  @ ?  
 ClearBeamLoadsDeflections Pa _visible findVb Pg Pe Pd Pb _parent ActualP ComputeDeflections PoseTheQuestion explain Two cases are necessary.  First, use the elastic curve from the <B>cantilever with P</B> case to find the deflection at <B>B,</B> using L =  sAB  and x =  sB .   Next, use the <B>SS with M</B> case to compute the slope at C caused in the  sCDE  simple span by the overhang moment M = ( sActualP )( ).  Multiply this slope by the   overhang length to find the deflection at B.  Add these two deflections.           =  O   N  N  N  N  N  	N    
=         = G G G G  G G G G G G G G G @ ?e   ClearBeamLoadsDeflections Pe _visible findVa Pg Pd Pb Pa _parent ActualP ComputeDeflections PoseTheQuestion explain One case but two steps are needed to find the deflection at <B>A.</B>  Use the <B>simple span with concentrated load</B> case to find the slope at C, where L =  sCDE  and b =  sE .  Multiply this slope by the  sAB  overhang length to compute the deflection at A.   The deflection is upward.             =  O   N  N  N  N  N  	N    
=         = G G G G G G  G @ ?   ClearBeamLoadsDeflections Pb _visible findVg Pg Pe Pd Pa _parent ActualP ComputeDeflections PoseTheQuestion explain To find the deflection at <B>G,</B> two steps are required.  First, use the <B>simple span with concentrated moment</B> case to find the slope at F caused in the  sCDE  simple span by the overhang moment M = ( sActualP )( sB ).  Next, multiply this slope by the  sF  overhang length between F and G to find the deflection at G.             =  O   N  N  N  N  N  	N    
=         = G G G G G G G G @ ?   ClearBeamLoadsDeflections Pg _visible findVe Pe Pd Pb Pa _parent ActualP ComputeDeflections PoseTheQuestion explain The elastic curve for the <B>simple span with concentrated moment</B> case will be used to find the deflection at <B>E.</B>  The concentrated moment produced by the overhang is M = ( sActualP )( sF ).  Use this moment in the elastic curve equation along with L =  sCDE  and x =  sE  to find the deflection at E.   The deflection is upward.             =  O   N  N  N  N  N  	N    
=         = G G G G G G G G  G @ ?  z ClearBeamLoadsDeflections Pd _visible findVd Pg Pe Pb Pa _parent ActualP ComputeDeflections PoseTheQuestion explain Use the elastic curve from the <B>simple span with concentrated load</B> case to find the deflection at <B>D.</B>  The span length L is the distance between the supports at C and F, x is the distance between C and D, and b equals the distance between D and F.           =  O   N  N  N  N  N  	N    
=         =  @ ?   ClearBeamLoadsDeflections Pg _visible findVg Pe Pd Pb Pa _parent ActualP ComputeDeflections PoseTheQuestion explain Two cases are necessary.  First, use the <B>cantilever with P</B> case to find the deflection at <B>G,</B> using L =  sF  as the span length.   Next, use the <B>SS with M</B> case to compute the slope at F caused in the  sCDE  simple span by the overhang moment M = ( sActualP )( ).  Multiply this slope by the   overhang length to find the deflection at G.  Add these two deflections.           =  O   N  N  N  N  N  	N    
=         = G G  G G G G G G G G G @ ?e   ClearBeamLoadsDeflections Pd _visible findVb Pg Pe Pb Pa _parent ActualP ComputeDeflections PoseTheQuestion explain One case but two steps are needed to find the deflection at <B>B.</B>  Use the <B>simple span with concentrated load</B> case to find the slope at C, where L =  sCDE  and b =  sDE .  Multiply this slope by the  sB  overhang length to compute the deflection at B.   The deflection is upward.             =  O   N  N  N  N  N  	N    
=         = G G G G G G  G @ ?   ClearBeamLoadsDeflections Pg _visible findVa Pe Pd Pb Pa _parent ActualP ComputeDeflections PoseTheQuestion explain To find the deflection at <B>A,</B> two steps are required.  First, use the <B>simple span with concentrated moment</B> case to find the slope at C caused in the  sCDE  simple span by the overhang moment M = ( sActualP )( sF ).  Next, multiply this slope by the  sAB  overhang length between A and C to find the deflection at A.             =  O   N  N  N  N  N  	N    
=         = G G G G G G G G @ ?   ClearBeamLoadsDeflections Pa _visible findVe Pg Pe Pd Pb _parent ActualP ComputeDeflections PoseTheQuestion explain The elastic curve for the <B>simple span with concentrated moment</B> case will be used to find the deflection at <B>E.</B>  The concentrated moment produced by the overhang is M = ( sActualP )( sAB ).  Use this moment in the elastic curve equation along with L =  sCDE  and x =  sCD  to find the deflection at E.   The deflection is upward.             =  O   N  N  N  N  N  	N    
=         = G G G G G G G G  G @ ?  z ClearBeamLoadsDeflections Pe _visible findVe Pg Pd Pb Pa _parent ActualP ComputeDeflections PoseTheQuestion explain Use the elastic curve from the <B>simple span with concentrated load</B> case to find the deflection at <B>E.</B>  The span length L is the distance between the supports at C and F, x is the distance between C and E, and b equals the distance between E and F.           =  O   N  N  N  N  N  	N    
=         =  @ ?   ClearBeamLoadsDeflections Pb _visible findVb Pg Pe Pd Pa _parent ActualP ComputeDeflections PoseTheQuestion explain Two cases are necessary.  First, use the <B>cantilever with P</B> case to find the deflection at <B>B,</B> using L =  sB .   Next, use the <B>SS with M</B> case to compute the slope at C caused in the  sCDE  simple span by the overhang moment M = ( sActualP )( ).  Multiply this slope by the   overhang length to find the deflection at B.  Add these two deflections.           =  O   N  N  N  N  N  	N    
=         = G G  G G G G G G G G G @ ?f   ClearBeamLoadsDeflections Pd _visible findVa Pg Pe Pb Pa _parent ActualP ComputeDeflections PoseTheQuestion explain One case but two steps are needed to find the deflection at <B>A.</B>  Use the <B>simple span with concentrated load</B> case to find the slope at C, where L =  sCDE  and b =  sDE .  Multiply this slope by the  sAB  overhang length to compute the deflection at A.   The deflection is upward.             =  O   N  N  N  N  N  	N    
=         = G G G G G G  G @ ?   ClearBeamLoadsDeflections Pa _visible findVg Pg Pe Pd Pb _parent ActualP ComputeDeflections PoseTheQuestion explain To find the deflection at <B>G,</B> two steps are required.  First, use the <B>simple span with concentrated moment</B> case to find the slope at F caused in the  sCDE  simple span by the overhang moment M = ( sActualP )( sAB ).  Next, multiply this slope by the  sF  overhang length between F and G to find the deflection at G.             =  O   N  N  N  N  N  	N    
=         = G G G G G G G G @ ?   ClearBeamLoadsDeflections Pa _visible findVd Pg Pe Pd Pb _parent ActualP ComputeDeflections PoseTheQuestion explain The elastic curve for the <B>simple span with concentrated moment</B> case will be used to find the deflection at <B>D.</B>  The concentrated moment produced by the overhang is M = ( sActualP )( sAB ).  Use this moment in the elastic curve equation along with L =  sCDE  and x =  sC  to find the deflection at D.   The deflection is upward.             =  O   N  N  N  N  N  	N    
=         = G G G G G G G G  G @ ?   ClearBeamLoadsDeflections Pa _visible findVd Pg Pe Pd Pb _parent ActualP ComputeDeflections PoseTheQuestion explain The elastic curve for the <B>simple span with concentrated moment</B> case will be used to find the deflection at <B>D.</B>  The concentrated moment produced by the overhang is M = ( sActualP )( sAB ).  Use this moment in the elastic curve equation along with L =  sCDE  and x =  sC  to find the deflection at D.   The deflection is upward.             =  O   N  N  N  N  N  	N    
=         = G G G G G G G G  G @      >  >Er i @  K theBeam     d5L@ f O1Ykv\g)ARt짏)r w~%_)q f n 41ʴ8  f kir_ZɓxL;RGֽŉ@+Sj%kMgę@=
fni|z,Z77<|yM0>@4_K,z  <    a     C1k	3/f 8И=<d ?    d6Ԇ7 ff %](eI@% *ٸfo.q"ܫIEYj'ԋ	km	jYu0Bp[[~G'G 9ԇV2Q3)JU(D2EeD(g'uY^  u    d6= <   3%j=e	٦V5ݕqZ4ѻAIg@	 6ZYMZGez%Xǌ~[(
qJ{*Nx;.RҠ 4    h5.P   	   3 nxrn~Ćz`ǐ  ;    a    3 oSfN 91`<,& Л#<`Ӎ	3 4    h5.P   	  nxrn~Ćz`ǐ r            3`      uU@             @'A       &I        `      uU@       =?B      QuestionThisSet      Set1_CorrectCounter           TotalQuestions_Set1              SetBeamSpanLoadEI =  grouping          frameIndex   shift R              MakeSubSequence = G    K @   G ?j    txtInstructions Enter your answer (without units). UserResponse  GiveTheCorrectAnswer checkmark gotoAndStop questionNumDisplay QuestionThisSet frameIndex length MakeSequence grouping subFrameIndex theBeam             R  	 
N	         I           =       NG     R 
   set1 ?D    pt#ȣ  @<    5m̫V3ʪ <UV4@]\u` D*Հ   	1    W1          ( questionNumDisplay 10   z@'q'	4    h ) 3ff        UserResponse 123456.12 	  c  X    e-mW f  IUotS:;|%A{U8zukv{9x\yfӜ&  	&    D
   ?    @ ?q   0  correct Sound correct_sound attachSound start           @	      R           R   뇮 @ ?u   4  incorrect Sound incorrect_sound attachSound start           @	      R           R   뇮v@@      6
  ܣƀL checkmark    	 "    X{!!M 	 frnrw "    X{!   	  33rnrw "    X{!   	 rnrw           @)0   @'
f+     @)034  
B    @'
f    @-a    @)034 z(0    @'
f       ?  Set1_CorrectCounter mm theBeam correct_answer EvaluateAnswer          N    = G  L 	w    xU 1         GiveTheCorrectAnswer The 5orrect beam deflection at the specified location is 55.555 mm. K  z@     ` &   Pf C(弝	ʇ D    f	 
   M=`qh˒ [5+ gf@ ,/         5БԨ       5А   @ D\  5БԨ     `   5А      
0    @ D\     3   6MА        5БԨ     `    @ Gh      9       `      N  L  XL ?    fc H. 	   njvzYYrr YzYvx YP         5БԨ       5А   @ D\  5БԨ     `   5А      
0    @ D\     3   6MА        5БԨ     `    @ Gh      9       `      O  P  |SXL D    f  
   M=`qh˒ [5+ gf@ ,=         5БԨ       5А   @ D\  5БԨ     `   5А      
0    @ D\     3   6MА        5БԨ     `    @ Gh      9       `      P  T  XL @ G L P T ?:   4  txtInstructions  Click <B>continue</B> to proceed.   A    \`|<x f3 hqIHxG@
,gn惋O
 (    `2H" 	 333nǐz`ǒr (    `2H" 	 fnǐz`ǒr (    `2H" 	 3nǐz`ǒr      x   33@ a    &C0    `@'_-  33@ a    0    `@'`/  32@ a      `    `@'`/    &  QuestionThisSet TotalQuestions_Set1    P   H 
  L    Q  G  M @        	 
  G ?'     bend     bt   gotoAndPlay R 
	   simple_P 	 i @  ?     02_Simple_concentratedload    6L  C N bt 3    ` &  333 CP:Å|   Pf Ж/Ep      Xz  	  ىu/ 6    ` &   3f CP:Å|    ` Ӣ8`΄      Xz  	  ىu/ 6    ` &  333 `>P:Å|   Pf CP:Å      Xz  	    ىu/ Z     L       @ 	s       @'	s      @'
Cp        L    d N @ L ?'     bend     bt   gotoAndPlay R 
   cantilever_P ?#     07_Cantilever_concentratedload    6L  C O bt @ L ?'     bend     bt   gotoAndPlay R 
	   simple_M ?     03_Simple_moment    6L  C P bt @ K L  ?   O  txtInstructions  Click <B>continue</B> to go to the printout page and finish. A  runningScore  You have correctly answered   Set1_CorrectCounter G
   of the  G  TotalQuestions_Set1 G   problems. G 
   after_set1   ̀Lӕ~y    3`   ͂=US~
    fc2d      @u L    30    @m    3`   $I&21      0 i    qΥ     	  B@6߀XzXn~ q @nxrn~׈zm䐒 @ q~ q~ qjvjzXt   J      0      x   33@ a    &C0    `@'_-  33@ a    0    `@'`/  32@ a      `    `@'`/     R  G  Q 	]    w[11 @  3        runningScore You have correctly answered 0 out of 10 problems. J  @ i4@ u    d6= <   3%j=e	٦V5ݕqZ4ѻAIg@	 6ZYMZGez%Xǌ~[(
qJ{*Nx;.RҠ Y            3`      u             @'O       &I        `      u      ?O      QuestionThisSet      Set1_CorrectCounter          L           SetBeamSpanLoadEI =          MakeSubSequence =  grouping          frameIndex   shift R     K    @ V͞ Q @     G J K ?   A  runningScore  You have correctly answered   Set1_CorrectCounter G
   of the  G  TotalQuestions_Set1 G   problems. G 
	   printout ?   ?  myDate Date txtDate toString txtIdentifier Math random round           @           R          R       R 
   #P  0G*U     ?  ̀Lӕ~y    3`   ͂=US~
    fc2d     @u L    30    @m    3`   @  '    a6 $
  	 333wrwn     @'U  &    ]_]([   f f%t#=´tP0 "    X` 	      fzB_  *    ]_]([  33 f f5t#^Z:(@ "    X` 	  33  fzB_  $    \`]_  33    5k|+GEp ~    V       e@ 
5`      e@ 
5`      e@ 
5`     =8      printasbitmap:  _level0    	 R 	4   xĘ  1  333         txtDate 12 pt Verdana  @ A f   pK 
 
   3$PfMK3 亄c Q$ǌE!K)C v`F"H[т `I1G   &@ `	%   w
!)   3         txtName   %@LN	1   g+/
P1    3        txtIdentifier 999999     $I&21      0 	]   w[11 @  3        runningScore You have correctly answered 0 out of 10 problems.  @ i4@@   