Choose the best material for A light DISK$-$BRAKE CALIPER. The brake caliper can be idealized as two beams of length $L,$ depth $b,$ and thickness h$,$ locked together at their ends. Each beam is loaded in bending when the brake is applied, and because braking generates heat, it gets hot. Its length $L$ and depth $b$ are given. The beam stiffness $S$ is critical: If it is inadequate the caliper will flex, impairing braking efficiency and allowing vibration. Its ability to transmit heat, too, is critical since part of the heat generated in braking must be conducted out through the caliper.

The mass of the caliper scales with that of one of the beams. Its mass per unit area is simply