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Author Topic: 4.3-1..4.3-3  (Read 3412 times)

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rocketTester

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4.3-1..4.3-3
« on: January 23, 2012, 11:40:38 PM »
Problem 4.3-1



General Solution

Reactions:

\[
R_{{A}}={\frac {cF_{{2}}+cF_{{1}}+bF_{{1}}}{a+b+c}};   
R_{{B}}={\frac {aF_{{1}}+aF_{{2}}+bF_{{2}}}{a+b+c}}
 \]

Shearing Forces:
\[
Q_{{1}}={\frac {cF_{{2}}+cF_{{1}}+bF_{{1}}}{a+b+c}};   
Q_{{2}}=-{\frac {aF_{{1}}-cF_{{2}}}{a+b+c}};   
Q_{{3}}=-{\frac {aF_{{1}}+aF_{{2}}+bF_{{2}}}{a+b+c}}
 \]

Bending Moments:
\[
M_{{1}}={\frac { \left( cF_{{2}}+cF_{{1}}+bF_{{1}} \right) z}{a+b+c}};   
M_{{2}}={\frac {-zaF_{{1}}+zcF_{{2}}+acF_{{2}}+acF_{{1}}+abF_{{1}}}{a+
b+c}};   
M_{{3}}={\frac { \left( aF_{{1}}+aF_{{2}}+bF_{{2}} \right)  \left( -z+
c \right) }{a+b+c}}
 \]
Maple 15 file is attached below
« Last Edit: June 14, 2012, 12:57:42 AM by TimoAdmin »

rocketTester

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4.3-2
« Reply #1 on: January 24, 2012, 12:38:39 AM »
Problem 4.3-2



General Solutions


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\[
R_{{A}}=1/8\,{\frac {4\,q{a}^{2}-4\,qab+q{b}^{2}+6\,aF}{a}};   
R_{{B}}=1/8\,{\frac {12\,q{a}^{2}-4\,qab-q{b}^{2}+2\,aF}{a}}
 \]

Shearing Forces:
\[
Q_{{1}}=1/8\,{\frac {4\,q{a}^{2}-4\,qab+q{b}^{2}+6\,aF}{a}};   
Q_{{2}}=-1/8\,{\frac {-4\,q{a}^{2}+4\,qab-q{b}^{2}+2\,aF}{a}};
 \]
\[    
Q_{{3}}=-1/8\,{\frac {-4\,q{a}^{2}+4\,qab-q{b}^{2}+2\,aF}{a}};   
Q_{{4}}=-1/8\,{\frac {8\,qza-4\,q{a}^{2}+4\,qab-q{b}^{2}+2\,aF}{a}}
 \]

Bending Moments:
\[
M_{{1}}=1/8\,{\frac { \left( 4\,q{a}^{2}-4\,qab+q{b}^{2}+6\,aF \right) z}{a}};
 \]
\[    
M_{{2}}=1/8\,{\frac {4\,zq{a}^{2}-4\,zqab+zq{b}^{2}-2\,zaF+4\,q{a}^{3}-4\,q{a}^{2}b+aq{b}^{2}+6\,{a}^{2}F}{a}};
 \]
\[
M_{{3}}=1/8\,{\frac {4\,zq{a}^{2}-4\,zqab+zq{b}^{2}-2\,zaF-8\,q{a}^{2}b+2\,aq{b}^{2}+8\,q{a}^{3}+4\,{a}^{2}F}{a}};
 \]
\[
M_{{4}}=1/8\,{\frac {4\,zq{a}^{2}-4\,zqab+zq{b}^{2}-2\,zaF-8\,q{a}^{2}b+2\,aq{b}^{2}+8\,q{a}^{3}+4\,{a}^{2}F}{a}}.
 \]
« Last Edit: June 14, 2012, 12:58:23 AM by TimoAdmin »

rocketTester

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4.3-3
« Reply #2 on: January 24, 2012, 01:20:30 AM »
Problem 4.3-3



Reactions:
\[
R_{{A}}=P;    R_{{B}}=-P;
 \]

Shearing Forces:
\[
Q_{{1}}=-P;    Q_{{2}}=0;    Q_{{3}}=-P
 \]

Bending Moments:
\[
M_{{1}}=-Pz;    M_{{2}}=0;    M_{{3}}=-Pz+Pb
 \]

Bonus  ;)
Deflections:
\[
w_{{1}}=-1/6\,{\frac {P \left( {z}^{3}-3\,{b}^{2}z+2\,{b}^{3} \right) }{E{\it Jx}}};   
w_{{2}}=0;   
w_{{3}}=1/6\,{\frac {P{z}^{2} \left( -z+3\,b \right) }{E{\it Jx}}}
 \]

« Last Edit: June 14, 2012, 12:59:49 AM by TimoAdmin »