The load of 2000 lb is to be supported by the two vertical...

The load of 2000 lb is to be supported by the two vertical steel wires for which $\sigma_{Y}=70$ ksi. Originally wire $A B$ is 60 in. long and wire $A C$ is 60.04 in. long. Determine the force developed in each wire after the load is suspended. Each wire has a cross-sectional area of 0.02 in $^{2} . E_{\mathrm{st}}=29.0\left(10^{3}\right) \mathrm{ksi}$

Key Concepts

Axial Stiffness

Axial stiffness is a measure of a structural member's resistance to axial deformation and is given by the product of the material's modulus of elasticity and cross-sectional area divided by its length. This parameter is crucial in determining how variations in length or material properties affect the distribution of forces among members in a composite or parallel system.

Stress Calculation and Yield Criteria

Stress is determined by dividing the force in a structural member by its cross-sectional area. It is important to calculate this stress to ensure that it remains below the material's yield stress, preventing permanent deformation. The yield criterion helps in assessing whether the material is operating within its elastic limit.

Axial Deformation and Hooke's Law

This concept describes how a material deforms under axial loads according to Hooke’s law. The deformation (elongation) in a tensile member is directly proportional to the applied force, with the constant of proportionality being the member's axial stiffness, which is derived from its material modulus of elasticity, cross-sectional area, and length.

Load Sharing in Parallel Structural Members

When multiple members support a common load, they do so in parallel. The load is distributed among them based on their individual stiffnesses. The compatibility condition requires that all members undergo the same amount of deformation once the load is applied, while equilibrium demands that the sum of the forces in each member equals the total applied load.

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