Determine the support reactions and draw the bending moment diagram for the propped cantilever shown in Figure 4.80.
Figure 4.80
Solution
Fixed-End Moment for Propped Cantilever: Consider the beam fixed at both supports.
The values of the fixed-end moments for encastre beams are given in Appendix 2.
The moment MB must be cancelled out by applying an equal and opposite moment at B which in turn produces a carry-over moment equal to-(0.5xMB) at support A.
Consider the rotational equilibrium of the beam:
Consider the rotational equilibrium of the beam:
Consider the vertical equilibrium of the beam:
Equation (1)
Consider the vertical equilibrium of the beam:
Equation (2)
+ (10 x 8.0 x 4,0) - (8.0 x f[W) = 0 .■- Kbh»- + 4A.0 fcN J Equation
Beams 315 Consider the vertical equilibrium of the beam:
Equation (2)
The final vertical support reactions are given by (i)+(ii):
The final vertical support reactions are given by (i)+(ii):
Check the vertical equilibrium: Total vertical force =+50.0+30.0 =+80 kN
MO.OlNm
MO.OlNm
Note the similarity between the shape of the bending moment diagram and the final deflected shape as shown in Figure 4.82.
Figure 4.82
The position of the maximum bending moment can be determined by finding the point of zero shear force as shown in Figure 4.83.
Figure 4.83
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