Question 17.22: Determine support reactions for overhanging beam as shown in...
Determine support reactions for overhanging beam as shown in Fig. 17.25.
Let the beam is turned about hinge B by virtual angle \delta \theta in anti–clockwise direction as shown in Fig. 17.25 (a). Weight of UDL will be 18 kN which will act at its mid length, i.e., at point L.
Using the principle of virtual work,
R _{ C } \cdot(+\delta y)_{ C }+10 .(-\delta y)_{ D }+18 .(-\delta y)_{ L }+12(+\delta y)_{ A }=0 ….. (1)
From right angle triangles,
\delta \theta=\frac{(\delta y)_{D}}{4}=\frac{(\delta y)_{C}}{3}=\frac{(\delta y)_{L}}{1.5}=\frac{(\delta y)_{A}}{2}
(\delta y)_{D}=4 . \delta \theta,(\delta y)_{C}=3 . \delta \theta,(\delta y)_{L}=1.5 \delta \theta,(\delta y)_{A}=2 \delta \theta
Substituting the values in equation (1),
R _{c}(+3 . \delta \theta)-10(4 . \delta \theta)-18(1.5 \delta \theta)-12(2 . \delta \theta)=0
R _{c}=15 kN
Since, R _{ B }+ R _{ C }=12+18+10=40
R _{ B }=40-14.33=25.66 kN
