Find the bending radius and temperature change delta t E bod

Solution

Take an arc of the strip which is bent.

The difference in arc length is Theta *(t2-t2) where theta is the bending angle.

(t2-t1)*theta = (a2-a1) LdT, where dT is the change in temp, a2, a1 the thermal expansion coefficients

theta = (a2-a1)/(t2-t1)L*dT

By definition L/R= theta, if we neglect the smal difference between L2 and L1

R = L/theta = [(t2-t1)/(a2-a1)]/dT

This analysis neglects the equality of stress between the two strips involving E1 and E2.

The exact relation is Timoshenko as 1/R = kdT/s where s = (t1+t2) and k is the specific curvature.