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Synopsis This paper deals with an analytical and experimental investigation of the mechanical properties of cement mortar reinforced with randomly oriented short steel wires. Analytically, the material is treated as a composite and its properties are derived by the laws of mixture. The effect of random orientation of the short wires is taken into consideration by the introduction of dimensionless factors which are derived on the assumption that the geometric centres of the wires are uniformly distributed in space and that any wire has an equal probability of being oriented at any angle to the direction of the applied stress. Explicit expressions are given for the moduli of elasticity and the ultimate strengths in tension and compression. In bending and torsion, the composite is idealized as a bi-linear material to describe its behaviour in the uncracked and in the cracked range provided that the volume fraction and the length of wires used exceed certain values which are suggested. Experiments were conducted and the results obtained are shown to be in good agreement with theoretically predicted values.

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The vibration of a single-story frame with bilinear hysteresis supporting a rotating machine is analyzed. The excitation force caused by the rotating unbalanced mass of the machine has a frequency dependent amplitude. The bilinear hysteresis of the resisting force of the frame to the motion is derived from the bilinear moment-curvature relationship of the frame columns. Solving the equation of motion of the system by the method of slowly varying parameters, the system exhibits unbounded resonance when the product of the machine unbalanced mass and its eccentricity exceeds a critical value. For the purpose of design and analysis of this type of structures, the displacement amplitude is plotted against arguments of the frequency for various values of two parameters involved.

The effect of strain hardening in limiting the forces developed in structures subjected to earthquake motions below those of the elastic behavior is investigated by treating a single degree of freedom system. Response spectra for El Centro earthquake, May 1940 are generated from an idealized bilinear strain hardening resisting force-displacement relation for different values of the strain hardening coefficient and ductility factor. Optimum response spectra are presented in terms of the yield displacements and the maximum displacements. For a system with the optimum yield displacement, the maximum displacement response is always less than that of the elastic system, and thus the optimum response spectra may be used as a guide in selecting members for a displacement constrained design.