#Part–8/ #simply-support-beam-with -a-point-load at it's mid-point. ( With free pdf note 📚 link 👇🏻)

 #Simply Supported Beam Carrying a Concentrated Load at Mid-span.

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Taking moment about R2, we have (fig. 1.1 a)

                RA × l = W × ½
                 RA = RB = W/2

 Taking a section at a distance x from R1, for values of x lying between RA and W, the shear force is W/2 and it is negative. For values of x lying between W and RB, the shear force is (W – W/2) =W/2, and it is negative in nature. Hence the S.F. diagram is shown in Fig. 1.1(b)

Similarly for values of x lying between RA and W, the Bending moment at any point is Wx/2, and is positive in nature. This bending moment is maximum at x = l/2, i.e. at the Mid-span and is given by, 

         Mmax = Wl/4

           For values of x lying between W and RB, the Bending moment is 

     This bending moment is also positive. Hence the B.M. diagram is as shown in Fig. 1.1.

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