In figure the maximum bending moment at the fixed end of the cantilever caused by the UDL is M.
The bending moment at a section //5 from the free end is
The shear force along the beam shown in the figure is
The correct shear force diagram for the beam shown in the figure is
A simply supported beam of span l is loaded (as shown) with a udl of intensity w1 per unit length at A and w2 per unit length at B the shear force at the support B is given by
The beam shown in the given figure has a design value of bending moment of
A cantilever beam is subjected to moments as shown in the given figure. The BM diagram for the beam will be
The bending moment due to 50 kNm moment would be hogging. Similarly the bending moment due to 30 kNm would be sagging. Therefore the bending moment diagram is,
The fixed end moment MA of the beam shown in the given figure is
∑FV = 0
⇒ RA + RC = 20
MB = 0 [from right]
∴ RC x 4 - 20 x 6 = 0
⇒ Rc x 4 = 20 x 6
MB = 0 [from left]
RA x 4 - MA = 0
⇒ MA = RA x 4 = -10 x 4
= - 40 kNm
The fixed end moment at A will be in clockwise direction, opposite to the direction shown in the figure.
∴ MA = -40 kNm
A simply supported beam with equal overhang ori both sides is loaded as shown in the figure. If the bending moment at mid-span is zero, then the percentage overhang on each side will be
Let the overhang percentage in 100p.
So overhang = pl
The shear force diagram will be,
For B.M. at mid point to be zero, area of shear force diagram under (1) should be equal to that of (2),
1/2w(pl)2 = 1/2w[(0.5 - P)l]2
or p2 = (0.5 - p)2 = 0.25 - p + p2
∴ p = 0.25 or 25%
A propped cantilever beam shown in the figure given is having interna! hinge at its mid-span. Which one of the following is the shape of bending moment diagram for the given loading?
Due to hinge at C the part CB of beam be have s as simply supported beam. Thus reaction at B will be in upward direction and equals half of the load in span BC.
Span CA be haves as a cantilever beam. There fore B.M.D. will be sagging in BC and hogging in AC and it will be parabolic.
For a cantiiever B.M.D. will be as shown below.
Combining all the arguments answer will be (d) which is given with BM plotted on tension side.
In the case of l-section, the web resists mainly
In the case of (-section, nearly 80-90% shear force, is resisted by web and only 10-20% is resisted by flanges, whereas in bending. 80-90% moment is resisted by flanges and only 10-20% by the web.