Title: Re: 4.3-4..4.3-6
Post by: rocketTester on June 14, 2012, 12:14:41 AM
Problem 4.3-5 (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