Axial deformation formula (Hooke’s law in tension/compression):\nFor an axially loaded prismatic bar, what is the change in length Δl in terms of P, l, A, and E?

Introduction / Context:
Determining axial deformation of bars under tension or compression is foundational in structural and machine design. The linear-elastic relation connects load, geometry, and material stiffness to elongation or shortening.

Given Data / Assumptions:

• Bar is prismatic with constant cross-section A and length l.
• Applied axial load P; Young’s modulus E of the material.
• Small deformation; linear elasticity; uniform stress distribution.

Concept / Approach:
Hooke’s law in uniaxial form relates stress and strain: σ = E * ε. With σ = P/A and ε = Δl / l, combining these gives the classic deformation formula Δl = (P * l)/(A * E).

Step-by-Step Solution:

Verification / Alternative check:
Dimensional check: N * m / (m^2 * N/m^2) reduces to m, consistent with length. Experimental tests on tensile specimens confirm linear proportionality in the elastic range.

Why Other Options Are Wrong:

• Other expressions scramble variables and units, failing dimensionally or physically.

Common Pitfalls:
Using incorrect area (net vs. gross); neglecting temperature or secondary effects; applying beyond the elastic limit where the relation is no longer linear.

Final Answer:
Δl = (P * l) / (A * E)