Strength of Materials

8.6 MOMENT AREA METHOD

This is a semigraphical method of dealing with the problem of deflection of beams subjected to bending. Figure 8.25 shows a beam AB carrying some type of loading and the corresponding BM.

 

 

Fig. 8.25 Moment area method.

 

Let the beam bend to a shape of A, P, Q, B.

An element PQ of length dx at a distance x from B is considered.

Let R be the radius of curvature of deflected part of the beam.

Let dθ be the angle subtended by the arc P₁ Q₁ at the centre in radians and M be the BM between P and Q.

From the geometry of the bent up beam, we have P₁Q₁ = Rdθ.

Substituting P₁Q₁ = dx, we have

 

dx = Rdθ

 

 

But, for a loaded ...