Strength of Materials

8.2 SLOPE DEFLECTION AND RADIUS OF CURVATURE

A small portion PQ of the beam, bent into an arc is considered (Figure 8.3).

 

 

Fig. 8.3 Deflection of element.

 

Let ds be the elemental length PQ of the beam

R be the radius of the arc

C be the centre of the arc (into which the beam has been bent)

ψ be the angle which the tangent at P makes with x − x axis

and (ψ + dψ) be the angle which the tangent at Q makes with x − x axis

From the geometry of Figure 8.3, ∠PCQ = dψ

and ds = R. dψ

 

 

If x and y are the coordinates of point P, then