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Post by: rocketTester on February 25, 2012, 02:09:11 AM
(http://forum.orlovsoft.com/forumimages/example_tgg_434.png)
General Solutions
(http://forum.orlovsoft.com/forumimages/example_tgg_434_1.png)
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
Post by: rocketTester on June 14, 2012, 12:14:41 AM
(http://forum.orlovsoft.com/forumimages/example_tgg_435.png)
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
(http://forum.orlovsoft.com/forumimages/example_tgg_435_1.png)
Maple 15 file is attached below