Problem 4.3-5

General Solutionsz 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