Normal strain Learning Goal: To understand the relationship between normal strai

Question

Normal strain Learning Goal: To understand the relationship between normal strain and member properties Because loaded members can fail when subjected to normal and shear stresses and strains. it is important to understand the magnitude and distribution of these stresses and strains under a variety of loading conditions and m members that have different geometric and material properties Normal strain is defined as the normal strain in the direction of the applied load. Relationship between area and normal strain Four axially loaded members are shown below All members have the same value for E (Young's modulus). Rank the members from largest average normal strain to smallest normal strain at cross section M shown in the figure.

Explanation / Answer

Strain = Stress/E = (Load/Area)/E

Memeber 1: Strain = (P/2)/(A/2)/E = P/AE

Member 2: Strain = 2P/(2A)/E = P/AE

Member 3: Strain = P/(A)/E = P/AE

Member 4: Strain = 3P/(3A)/E = PAE

Hence all have equal strain.

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