### Composite bar in tension or compression 1

Date : 2016-06-23 12:24:21

INTRODUCTION:

• A composite bar is one made of two materials, such as steel rods embedded in concrete.
• The construction of the bar is such that constituent components extend or contract equally under load.
• To illustrate the behaviour of such bars consider a rod made of two materials, 1 and 2, Figure 1; A,, A, are the cross-sectional areas of the bars, and E,, E, are the values of Young's modulus.
• We imagine the bars to be rigidly connected together at the ends; then for compatibility, the longitudinal strains to be the same when the composite bar is stretched we must have  Fig: 1

where sigma 1, and sigma 2 are the stresses in the two bars. But from equilibrium considerations,  PROBLEM:

A concrete column, 50 cm square, is reinforced with four steel rods, each 2.5 cm in diameter, embedded in the concrete near the comers of the square.
If Young's modulus for steel is 200 GN/mz and that for concrete is 14 GN/mz, estimate the compressive stresses in the steel and concrete when the total thrust on the column is 1 MN. SOLUTION:

Suppose subscripts c and s refer to concrete and steel, respectively. The cross-sectional area of steel is 