When a compound bar is constructed from members of different materials, lengths and
areas and is subjected to an external tensile or compressive load W the load carried by any
single member is given by
F1 =- L1 w
where suffix 1 refers to the single member and X -
is the sum of all such quantities for all the
Where the bars have a common length the compound bar can be reduced to a single
equivalent bar with an equivalent Young's modulus, termed a combined E.
Combined E = -
The free expansion of a bar under a temperature change from Tl to T2 is
where a is the coefficient of linear expansion and L is the length of the bar.
If this expansion is prevented a stress will be induced in the bar given by
To determine the stresses in a compound bar composed of two members of different free
lengths two principles are used:
(1) The tensile force applied to the short member by the long member is equal in magnitude
(2) The extension of the short member plus the contraction of the long member equals the
This difference in free lengths may result from the tightening of a nut or from a temperature
change in two members of different material (Le. different coefficients of expansion) but of
equal length initially.
If such a bar is then subjected to an additional external load the resultant stresses may be
obtained by using the principle ofsuperposition. With this method the stresses in the members
to the compressive force applied to the long member by the short member.
difference in free lengths.
Mechanics of Materials
arising from the separate effects are obtained and the results added, taking account of sign, to
give the resultant stresses.
N.B.: Discussion in this chapter is concerned with compound bars which are symmetri-
cally proportioned such that no bending results.
2.1. Compound bars subjected to external load
In certain applications it is necessary to use a combination of element