Consider a *Simply Supported Beam AB of span l and carrying a point load W at its mid -point C as shown in Fig. 1.1(a). Since the load is at the Mid-span of the beam, therefore the reaction at the support A,
RA = RB = 0.5 W
Thus we see that the shear force at any section between A and C (i.e., up to the point just before the load W) is constant and is equal to the unbalanced vertical forces, i.e., + 0.5 W. Shear force at any section between C and B (i.e., just after the load W) is also constant and is equal to the unbalanced vertical forces, i.e., – 0.5 W aes shown in Fig.1.1.(b).
We also see that the Bending moment at A and B is zero. It increases by a straight line law and is maximum at centre of beam, where shear force change sign as shown in Fig. 1.1.(c).
Therefore bending moment at C,
Mc = (W/2) × (1/2) = Wl/4. ......(plus sign due to sagging)
Note. If the point load does not act at the mid-point of the beam, then the two reaction are obtained and the diagram are drawn as usual.
[*Simply supported beam: It is beam whose both the ends are supported or resting freely on the walls columns]
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