Question 17.25: An overhanging beam is supporting point load, UDL and moment...
An overhanging beam is supporting point load, UDL and moment as shown in Fig. 17.28. Using the principle of virtual work, determine reaction of roller bearing.
Using the principles of virtual work,
\left[R_{D}(+\delta y)_{D}\right]+\left[(5 \times 2)(-\delta y)_{L}\right]+10 . \delta \theta+\left[40(-\delta y)_{B}\right]=0
R_{D} \cdot(\delta y)_{D}-10 \cdot(\delta y)_{L}+10 . \delta \theta-40(\delta y)_{B}=0 ….. (1)
From the right–angled triangles,
\delta \theta=\frac{(\delta y)_{L}}{7}=\frac{(\delta y)_{D}}{6}=\frac{(\delta y)_{B}}{2}
(\delta y)_{L}=7 . \delta \theta,(\delta y)_{D}=6 . \delta \theta \text { and }(\delta y)_{B}=2 . \delta \theta
Substituting the values of virtual distances in equation (1),
R _{ D }(6 . \delta \theta)-10(7 . \delta \theta)+10 . \delta \theta-40(2 . \delta \theta)=0
R _{ D }=23.33 kN
