A long, thin metal bar of length $l$ is clamped rigidly at its ends at temperature ${\text{t}}_0$. When the temperature is increased to t, the expanding bar will bow out, as shown below. If the bowing is not too large, a fair first approximation to the shape of the bar is two equal straight segments in the form of a wide V. What is the arch $\text{δ}$ of the bow as a function of t? (This is the distance between the corner of the V and the straight line that represents the form of the bar at  ${\text{t}}_0$)