Partially Restrained Tapered Bar:
Let us assume the bar of Figure, but now assume it be free to extend by an amount ΔL′(ΔL′ < ΔL) . By following same arguments as in the previous section, the compressive load P now developed in the bar shall be specified by
P = πE d1 d2 (ΔL - ΔL′) / 4L
= πE d1 d2 (L α ΔT - ΔL′) / 4L
and therefore,
and the maximum stress,
σmax = E d1 (L α ΔT - ΔL′)/ Ld2