The rigid beam is supported by three 25-mm diameter A-36 steel rods. If the force of P=230 kN is

step 1 This question is from the previous question question 4 .104. But this time we have to find the r

The rigid beam is supported by three 25-mm diameter A-36...

The rigid beam is supported by three $25-\mathrm{mm}$ diameter A-36 steel rods. If the force of $P=230 \mathrm{kN}$ is applied on the beam and removed, determine the residual stresses in each rod. Consider the steel to be an elastic
perfectly plastic material.

Key Concepts

Residual Stress

Residual stress refers to the internal stresses retained in a material even after external loads have been removed. These stresses arise from plastic deformation or thermal changes during processing and affect the material's performance and potential for future failure. In structural elements, residual stresses can influence fatigue behavior and crack propagation.

Elastic Perfectly Plastic Material Model

This material model describes a material that initially behaves elastically, meaning that its deformation is fully recoverable, until a critical yield stress is reached. Beyond this point, the material deforms plastically at a constant stress without strain hardening. This simplification aids in analyzing and predicting the onset of permanent deformations under load.

Load Distribution in Rigid Structures

In structures such as rigid beams or frames, applied loads are shared among the support members based on their stiffness and the geometry of the system. Understanding how loads distribute among supports is essential for assessing the stresses each support experiences, particularly when plastic deformation may occur in some members while others remain in the elastic range.

Plastic Deformation and Yielding

Yielding is the transition point where a material stops behaving elastically and begins to undergo permanent, plastic deformation. This concept is central when analyzing residual stresses because once a material yields, the subsequent unloading does not completely reverse the deformation, leaving behind a residual stress state that can affect the structural integrity and service life.

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