A steel cable with nominal diameter 25 mm (see Table 2-1 ) is used in a construction yard to lif

step 1 Here, before calculating the stretch of the cable, first we obtain the properties of the steel c

A steel cable with nominal diameter 25 mm (see Table 2-1 )...

A steel cable with nominal diameter $25 \mathrm{mm}$ (see Table $2-1$ ) is used in a construction yard to lift a bridge section weighing $38 \mathrm{kN},$ as shown in the figure. The cable has an effective modulus of elasticity $E=140 \mathrm{GPa}$ (a) If the cable is $14 \mathrm{m}$ long, how much will it stretch when the load is picked up? (b) If the cable is rated for a maximum load of $70 \mathrm{kN}$ what is the factor of safety with respect to failure of the cable?

A steel cable with nominal diameter $25 \mathrm{mm}$ (see Table $2-1$ ) is used in a construction yard to lift a bridge section weighing $38 \mathrm{kN},$ as shown in the figure. The cable has an effective modulus of elasticity $E=140 \mathrm{GPa}$
(a) If the cable is $14 \mathrm{m}$ long, how much will it stretch when the load is picked up?
(b) If the cable is rated for a maximum load of $70 \mathrm{kN}$ what is the factor of safety with respect to failure of the cable?

Key Concepts

Stress and Strain

Stress is defined as the force applied per unit area within materials, while strain is a measure of the deformation experienced by the material relative to its original length. These concepts are fundamental in analyzing how materials respond to loads, as they obey a linear relationship in the elastic range.

Factor of Safety

The factor of safety is a design metric used to ensure that structures and materials perform reliably under loads by providing a buffer against uncertainties in loading and material behavior. It is calculated as the ratio of the maximum load a component or structure can endure to the actual applied load, thereby ensuring that design limits are not exceeded.

Young’s Modulus

Young’s modulus, or the modulus of elasticity, is the ratio of stress to strain in the linear elastic region of a material's deformation. It quantifies the stiffness of a material and is a crucial parameter for calculating how much a material will deform under a given load.

Axial Deformation

Axial deformation refers to the elongation or compression of a structural element along its length when subjected to axial loads. In the elastic range, the amount of deformation can be determined using the relationship between the applied force, the original length, cross-sectional area, and the material's Young’s modulus as described by Hooke’s Law.

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