LECTURE 12 By D V Ramana Reddy Assistant

LECTURE 12 By D. V. Ramana Reddy Assistant Professor Department of Mechanical Engineering

Lecture 12 TOPICS : Shear Force and Bending Moment diagrams

Sign Conversion

CANTILEVER BEAM WITH POINT LOAD Let us consider a cantilever beam subjected to point load as shown in Fig. Fx = Shear Force at section x Mx = Bending Moment at section x Shear Force calculations: Load W acting right side of the section and download direction then it is positive shear. In between two points no load acting then shear force is constant. Constant graphical representation is Rectangle

Bending Moment Calculations: At X=0 there is no bending moment (Because no perpendicular distance). Load is acting Right side of section and it is clock wise moment then it is negative Bending Moment at section x-x = -W * x If x=0 B. M = -W * 0= 0 If x=L B. M = -w* L= -WL Bending Moment equation = -W * x (if x value varies B. M changes linearly)

CANTILEVER BEAM WITH UDL LOAD Let us consider a cantilever beam subjected to Uniformly distributed load as shown in Fig. Consider a section x-x at a distance of x from the free end. Fx = Shear Force at section x Mx = Bending Moment at section x Shear Force calculations: Distributed Load w N/m acting right side of the section and download direction then it is positive shear. Shear force = w * x = w x If x=0 then S. F = 0 If x=L then S. F= w*L=w. L And graphical representation is linear increment (Triangle)

Bending Moment Calculations At X=0 there is no bending moment (Because no perpendicular distance). Load is acting Right side of section and it is clock wise moment then it is negative Bending Moment at section x-x = -w * x*(x/2)= -wx 2/2 If x=0 B. M = -W * 0= 0 If x=L B. M = -w* L= -WL 2/2 Bending Moment at section x-x = -w * x*(x/2)=-wx 2/2 (if x value varies B. M changes with parabola curvature)

X W N/m A B x L w. L x +Ve X=0 X=L - ve

CANTILEVER BEAM WITH UVL LOAD Let us consider a cantilever beam subjected to Uniformly varying load as shown in Fig. Consider a section x-x at a distance of x from the free end. Fx = Shear Force at section x Mx = Bending Moment at section x

Shear Force calculations: Distributed Load wx/L N/m acting right side of the section and download direction then it is positive shear. Shear force = (½)* x*wx/L=wx 2/2 L If x=0 then S. F = 0 If x=L then S. F= w. L/2 And graphical representation is parabolic curvature

Bending Moment Calculations If x=0 B. M = -W * 0= 0 If x=L B. M = -w* L= -WL 2/6 Bending Moment at section x-x = (if x value varies B. M changes with cubic curvature)

SIMPLY SUPPORTED BEAM WITH POINT LOAD Let us consider a simply supported beam subjected to point load as shown in Fig.

Simply supported beam with UDL load

SSB WITH UVL LOAD