A cylindrical rod of steel (E=207 GPa, 30 ×.10^6 psi ) having a yield strength of 310 MPa (45,0

step 1 So in this problem I can write the value of stress is equal to E multiplication del l by L putti

A cylindrical rod of steel (E=207 GPa, 30 ×.10^6 psi )...

A cylindrical rod of steel $(E=207 \mathrm{GPa}, 30 \times$ $\left.10^{6} \text { psi }\right)$ having a yield strength of $310 \mathrm{MPa}$ $(45,000 \mathrm{psi})$ is to be subjected to a load of $11,100 \mathrm{N}\left(2500 \mathrm{lb}_{\mathrm{f}}\right) .$ If the length of the rod is $500 \mathrm{mm}(20.0 \text { in. }),$ what must be the diameter to allow an elongation of $0.38 \mathrm{mm}(0.015 \text { in. }) ?$

Key Concepts

Cross?Sectional Area of Cylindrical Members

The cross?sectional area of a cylindrical member, calculated as A = (?d²)/4, is essential in determining the distribution of stress and, consequently, the deformation under axial loads. It directly affects how the applied load is resisted and influences the elongation of the rod.

Axial Deformation

Axial deformation refers to the change in length (elongation or contraction) of a member when a force is applied along its length. The standard formula, ?L = (F × L)/(A × E), relates the applied force, original length, cross-sectional area, and Young's Modulus to predict the amount of deformation.

Yield Strength

Yield strength is the material property that defines the maximum stress a material can withstand while still returning to its original shape upon load removal. It serves as a safety limit, ensuring that the component operates within the elastic region where Hooke's Law is valid.

Young's Modulus

Young's Modulus is a measure of a material's stiffness, indicating the ratio of stress to strain in the elastic region. It is fundamental in predicting how much a material will deform under a given load and is used in the calculation of axial deformation.

Hooke's Law for Axial Loading

Hooke's Law establishes the linear relationship between stress and strain within the elastic range of a material's behavior. In axial loading scenarios, it implies that deformation is directly proportional to the applied load, which is crucial for determining elongation of rods and beams.

Transcript

Please give Ace some feedback