Question

A three hinged parabolic arch has a span of 20 m and a rise of 3 m. If a point load of 20 kN moves across the span from left to right then the maximum positive bending moment at a section 5m from left support will be _____ kN.

Answer 1

\(y=\dfrac{4hx}{l^2}(l-x).. \text{equation of parabolic arch}\)

\(y=\dfrac{4\times 3\times 5}{20^2}(20-5)=2.25~m\)

\(\sum M_A = 0\\\)
\(V_B\times20=20\times5\\\)
\(V_B=5~kN\\\)
\(\therefore V_A=20-5=15~kN\)

BM about hinge at C,

\( V_B \times 10 = H \times 3\)

\(\therefore H= \dfrac{50}{3}~kN\)

Maximum positive BM occurs when load acts at the section only.

\(Max. +ve= 15\times 5 -\dfrac{50}{3} \times 2.25\)

\(=37.5~kN\)