Most research studies on inelastic material behavior of steel structures under earthquake ground motions are concentrated on general uniaxial cyclic loading conditions. Very limited attention has been given to the responses of structures subjected multiaxial and nonproportionl loading condition. The primary objectives of these experiments are to obtain quantitative information on the cyclic and nonproportional loading behavior of wide-flanged A-36 structural steel, and to substantiate a plasticity model to describe the material behavior under severe earthquake loading condition by using a computer-controlled testing system. The response of W-shaped A-36 structural steel specimens subjected to selected pure bending, pure bending with constant axial loads, and the random nonproportional loadings are examined.