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Author Topic: 4.3-4..4.3-6  (Read 2714 times)

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rocketTester

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4.3-4..4.3-6
« on: February 25, 2012, 02:09:11 AM »
Problem 4.3-4



General Solutions


Reactions:
\[
R_{{A}}=2\,qb+F; 
M_{{A}}=-6\,q{b}^{2}-bF
 \]

Shearing Forces:
\[
Q_{{1}}=2\,qb+F; 
 \]
\[    
Q_{{2}}=2\,qb;
 \]
\[
Q_{{3}}=-qz+2\,qb
 \]

Bending Moments:
\[
M_{{1}}=2\,qbz+zF-6\,q{b}^{2}-bF;
 \]
\[    
M_{{2}}=2\,qbz-4\,q{b}^{2}; 
 \]
\[
M_{{3}}=-1/2\,q{z}^{2}+2\,qbz-2\,q{b}^{2}
 \]

Answer:
\[
Force=2\,qb+F;   
Moment=1/2\, \left( 2\,qb+F \right) b-6\,q{b}^{2}-bF
 \]
Maple 15 file is attached below
« Last Edit: June 14, 2012, 12:53:08 AM by TimoAdmin »

rocketTester

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Re: 4.3-4..4.3-6
« Reply #1 on: June 14, 2012, 12:14:41 AM »
Problem 4.3-5



General Solutions
z coordinate is from left to right within each segment (4 segments)
Reactions:
\[
R_{{A}}=3/4\,{\frac {q_{{1}}{a}^{2}-q_{{2}}{b}^{2}}{a}}; 
R_{{B}}=1/4\,{\frac {q_{{1}}{a}^{2}+3\,q_{{2}}{b}^{2}+4\,q_{{2}}ba}{a}}
 \]

Shearing Forces:
\[
Q_{{1}}=1/4\,{\frac {-4\,q_{{1}}za+3\,q_{{1}}{a}^{2}-3\,q_{{2}}{b}^{2}}{a}};
 \]
\[  
Q_{{2}}=-1/4\,{\frac {q_{{1}}{a}^{2}+3\,q_{{2}}{b}^{2}}{a}};   
 \]
\[
Q_{{3}}=q_{{2}}b;   
 \]
\[  
Q_{{4}}=-q_{{2}}z+q_{{2}}b
 \]

Bending Moments:
\[
M_{{1}}=1/4\,{\frac {z \left( -2\,q_{{1}}za+3\,q_{{1}}{a}^{2}-3\,q_{{2}}{b}^{2} \right) }{a}};
 \]
\[    
M_{{2}}=1/4\,{\frac {-zq_{{1}}{a}^{2}-3\,q_{{2}}{b}^{2}z+q_{{1}}{a}^{3}-3\,aq_{{2}}{b}^{2}}{a}}; 
 \]
\[
M_{{3}}=q_{{2}}bz-3/2\,q_{{2}}{b}^{2};   
 \]
\[
M_{{4}}=q_{{2}}bz-3/2\,q_{{2}}{b}^{2}
 \]

Numerical values for reactions (at data a=10; b=6; q[1]=400; q[2]=300)

\[
R_{{A}}=2190;   
R_{{B}}=3610
 \]
Numeric results as diagrams of internal factors



Maple 15 file is attached below
« Last Edit: June 14, 2012, 12:51:56 AM by TimoAdmin »