TIMO Structural Community

Mechanics of Materials Toolbox for Maple => James M. Gere and Barry J. Goodno => Topic started by: rocketTester on January 23, 2012, 11:40:38 PM

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Title: 4.3-1..4.3-3
Post by: rocketTester on January 23, 2012, 11:40:38 PM
Problem 4.3-1

(http://forum.orlovsoft.com/forumimages/example_tgg_431.png)

General Solution
(http://forum.orlovsoft.com/forumimages/example_tgg_431_1.png)
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
Title: 4.3-2
Post by: rocketTester on January 24, 2012, 12:38:39 AM
Problem 4.3-2

(http://forum.orlovsoft.com/forumimages/example_tgg_432.png)

General Solutions
(http://forum.orlovsoft.com/forumimages/example_tgg_432_1.png)

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

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:
\[
M_{{1}}=1/8\,{\frac { \left( 4\,q{a}^{2}-4\,qab+q{b}^{2}+6\,aF \right) z}{a}};
 \]
\[    
M_{{2}}=1/8\,{\frac {4\,zq{a}^{2}-4\,zqab+zq{b}^{2}-2\,zaF+4\,q{a}^{3}-4\,q{a}^{2}b+aq{b}^{2}+6\,{a}^{2}F}{a}};
 \]
\[
M_{{3}}=1/8\,{\frac {4\,zq{a}^{2}-4\,zqab+zq{b}^{2}-2\,zaF-8\,q{a}^{2}b+2\,aq{b}^{2}+8\,q{a}^{3}+4\,{a}^{2}F}{a}};
 \]
\[
M_{{4}}=1/8\,{\frac {4\,zq{a}^{2}-4\,zqab+zq{b}^{2}-2\,zaF-8\,q{a}^{2}b+2\,aq{b}^{2}+8\,q{a}^{3}+4\,{a}^{2}F}{a}}.
 \]
Title: 4.3-3
Post by: rocketTester on January 24, 2012, 01:20:30 AM
Problem 4.3-3

(http://forum.orlovsoft.com/forumimages/example_tgg_433_1.png)

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

(http://forum.orlovsoft.com/forumimages/example_tgg_433.png)