Impact Loading on a Vertical Rod – How to Reduce Maximum Axial Stress A vertical rod PQ of length L is fixed at its top end P and has a flange at the bottom end Q. A weight W is dropped vertically from a height h (with h < L) onto the flange. Which change reduces the maximum axial stress developed in the rod due to impact?

Introduction / Context:When a weight drops onto a member, part of the potential energy W * h is converted into strain energy in the rod. The resulting peak stress is higher than for a static load and depends on the member's stiffness and energy absorption capacity. Designers must recognize which parameters reduce the maximum impact stress to improve safety and durability.

Given Data / Assumptions:

• Rod: prismatic, length L, cross-sectional area A, modulus E.
• Impact: weight W dropped from height h (< L) onto a rigidly attached flange at the free end.
• Material remains within elastic range for the discussion.

Concept / Approach:

For elastic impact, peak stress approximately follows from equating strain energy to drop energy, giving a peak stress that increases with stiffness and decreases with greater compliance. A representative relation shows peak stress increasing with E and decreasing with L and A. Thus, making the member more compliant (larger L and/or larger A for energy capacity per unit stress) reduces the maximum stress developed.

Step-by-Step Solution:

Verification / Alternative check:

Energy methods or exact elastic-impact formulas with static extension terms both show σ_max decreasing with increasing L and A, and increasing with E.

Why Other Options Are Wrong:

• Decreasing L: Makes the bar stiffer; increases σ_max.
• Decreasing A: Increases stress for the same force; also lowers energy capacity.
• Increasing E: Stiffer bar yields higher σ_max for the same drop energy.

Common Pitfalls:

Confusing static and impact loading; ignoring that energy balance, not just force equilibrium, governs peak stress under impact.

Final Answer:

Increasing the length of the rod