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Author Topic: Beam Bending Sample #1  (Read 4842 times)

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MechOfMat

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Beam Bending Sample #1
« on: January 19, 2012, 01:13:51 AM »


Below is Maple code
Code: [Select]
restart:
Result:=BeamBending[GeneralBending](
[2*a,a,a,a],   
[0,7*q*a,0,0,-4*q*a],   
[-7*q*a^2,q*a^2,0,0,0],
[3*q,0,-2*q,0],
["ms","","","ms",""],
[Jx,Jx,Jx,Jx],
[E,2*E,3*E,E],
[5,   
Yes_Float = false]);

Shearing Forces (from left to right):
$$
3\,qz-{\frac {29}{4}}\,qa;   
{\frac {23}{4}}\,qa;   
-2\,qz+{\frac {23}{4}}\,qa
$$

Bending Moments:
\[
3/2\,q{z}^{2}-{\frac {29}{4}}\,qaz-7\,q{a}^{2};   
{\frac {23}{4}}\,qaz-{\frac {29}{2}}\,q{a}^{2};   
-q{z}^{2}+{\frac {23}{4}}\,qaz-{\frac {35}{4}}\,q{a}^{2}
 \]

Angles of Bending
\[
{\frac {1}{96}}\,{\frac {q \left( 48\,{z}^{3}-348\,a{z}^{2}-672\,{a}^{
2}z+1939\,{a}^{3} \right) }{E{\it Jx}}};   
-{\frac {1}{96}}\,{\frac {qa \left( -138\,{z}^{2}+696\,az+413\,{a}^{2}
 \right) }{E{\it Jx}}};   
-{\frac {1}{288}}\,{\frac {q \left( 32\,{z}^{3}-276\,a{z}^{2}+840\,{a}
^{2}z+2913\,{a}^{3} \right) }{E{\it Jx}}}
 \]

Deflections:
\[
{\frac {1}{96}}\,{\frac {qz \left( 12\,{z}^{3}-116\,a{z}^{2}-336\,{a}^
{2}z+1939\,{a}^{3} \right) }{E{\it Jx}}};   
{\frac {1}{96}}\,{\frac {qa \left( 46\,{z}^{3}-348\,a{z}^{2}-413\,{a}^
{2}z+1798\,{a}^{3} \right) }{E{\it Jx}}}
 \]
\[
{\frac {1}{288}}\,{\frac {q \left( -8\,{z}^{4}+92\,a{z}^{3}-420\,{a}^{
2}{z}^{2}-2913\,{a}^{3}z+3249\,{a}^{4} \right) }{E{\it Jx}}}
 \]
Code: [Select]
a:=2: q:=5000:
# Sample Data for Deflection calculation
E:=2*10^11: Jx:=100*10^(-8):
BeamBending[FullBending](
[2*a,a,a,a],   
[0,7*q*a,0,0,-4*q*a],   
[-7*q*a^2,q*a^2,0,0,0],
[3*q,0,-2*q,0],
["ms","","","ms",""],
[Jx,Jx,Jx,Jx],
[E,2*E,3*E,E],
[5,     
Yes_Float = false]);


« Last Edit: March 17, 2012, 02:58:22 AM by TimoAdmin »