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Analysis of Internal Forces

Let us take an arbitrary body which is cut by plane AA’ (Fig. 1.2). Plane AA’ is perpendicular to axis. The body’ is in equilibrium under the forces We now consider the left half of the body. As the body was in equilibrium before cutting, so the forces external to the left half must be balanced by the forces and moments developed internally over the surface of the body as shown in Fig. 1.3.

Pxx = Axial force =acting on the x surface in the direction of + ve x axis. If it pulls cit is tensile force and if it pushes, it is compressive force. Tensile force elongates the member while compressive force shortens the member.

P xy’ P xz = Shear forces which act along the (parallel) to the surface x. It gives resistance against sliding the member.

The resultant shear is denoted by V. Its components in x and y directions are Vx and Vy respectively.

Mu à Torque, it is responsible for giving resistance against twisting the member. It is denoted as T.

Mx11, Mxz à Bending moments : It is responsible for giving resistance against bending of the member

If BB’ (Ref. Fig. 1.4) is taken such a way that R is perpendicular to it. So only normal forces are produced .

If the external forces act on xy plane. There will be three components of internal effects namely Pxx (or P), shear force P xy (or V) and bending moment Mxz (or M).