Question 17.26: Determine reaction of the hinge ‘A’ by using the principle o...
Determine reaction of the hinge ‘A’ by using the principle of virtual work for simple supported beam as shown in Fig. 17.29.
The load of UVL (Uniform Varying Load) will be,
=\frac{1}{2} \times 6 \times 90
= 270 kN
This will act at point ‘L’. Thus AL = =\frac{1}{3} \times 6 = 2 m
Using the principle of virtual work,
R _{ A } \cdot(+\delta y)_{ A }+270 \cdot(-\delta y)_{ L }+0 \cdot(\delta y)_{ B }+600(-\delta y)_{ C }+100 \cdot \delta \theta=0
R _{ A } \cdot(\delta y)_{ A }-270 \cdot(\delta y)_{ L }-600(\delta y)_{ C }+100 \cdot \delta \theta=0 ….. (1)
From the right–angled triangles,
\delta \theta=\frac{(\delta y)_{A}}{10}=\frac{(\delta y)_{L}}{8}=\frac{(\delta y)_{C}}{2}
(\delta y)_{A}=10 . \delta \theta,(\delta y)_{L}=8 . \delta \theta,(\delta y)_{C}=2 . \delta \theta
Substituting the values in equation (1),
R _{ A }(10 . \delta \theta)-270(8 . \delta \theta)-600(2 . \delta \theta)+100 . \delta \theta=0
R _{ A }=326 kN
