Question 17.29: Using the principle of virtual work, determine reaction of r...
Using the principle of virtual work, determine reaction of roller bearing of an overhanging beam as shown in Fig. 17.32.
The weight and their position of C.G. are shown in Fig. 17.32 (a).
Using principle of virtual work,
R_{B}(+\delta y)_{B}+\left[\left(\frac{1}{2} \times 6 \times 20\right)(-\delta y)_{M}\right]+\left[\left(\frac{1}{2} \times 3 \times 20\right)(-\delta y)_{L}\right] +\left[(15 \times 2)(+\delta y)_{N}\right]-80 . \delta \theta+50 . \delta \theta=0
R_{B} \cdot(\delta y)_{B}-60 \cdot(\delta y)_{M}-30 \cdot(\delta y)_{L}+30 \cdot(\delta y)_{N}-30 \cdot \delta \theta=0
From right angle triangles,
\delta \theta=\frac{(\delta y)_{B}}{9}=\frac{(\delta y)_{M}}{5}=\frac{(\delta y)_{L}}{2}=\frac{(\delta y)_{N}}{1}
(\delta y)_{B}=9 . \delta \theta,(\delta y)_{M}=5 . \delta \theta,(\delta y)_{L}=2 . \delta \theta,(\delta y)_{N}=\delta \theta
R_{B}(9 . \delta \theta)-60(5 . \delta \theta)-30(2 . \delta \theta)+30(\delta \theta)-30 . \delta \theta=0
R_{B}=40 kN
