Basis of Strength of Materials: Stress, strain, strength,
Stresses
Stress is the same as pressure in compression or normal (pushing perpendicular, σ ), tension (pulling perpendicular, σ ), or shear (parallel or tangential, τ (tau),). The force applied on surface area. The stress on an object:
σ, tensile stress = F, Force on object/A, area
σ : tensile stress,
F : force on object
A: cross-sectional area of the object
τ, tensile stress = F, Force on object/A, area
τ = the shear stress
Strain
When the object is pulled or pushed, the object is under strain. In case of pulling, the object elongates. The level of deformation and displacement is known by strain. Strain is the change in distance of elongation by the original distance.
Hooke’s Law– Hooke’s law of elasticity is an approximation that states that the extension of a spring is in direct proportion with the load added to it as long as this load does not exceed the elastic limit, Linear elasticity.
Young’s Modulus– material property that describes the stiffness of a elastic material.
E= tensile stress/tensile strain= σ/e= (F/A0)/( ΔL/L0)
E is the Young’s modulus (modulus of elasticity)
F is the force applied to the object;
A0 is the original cross-sectional area through which the force is applied;
ΔL is the amount by which the length of the object changes;
L0 is the original length of the object.
Stress vs. Strain curve typical of structural steel
1. Ultimate Strength: The maximum stress a material can withstand when subjected to tension, compression or shearing. It is the maximum stress on the stress-strain curve.
2. Yield strength: The stress at which material strain changes from elastic deformation to plastic deformation, causing it to deform permanently.
3. Rupture
4. Strain hardening region
5. Necking region.
A: Apparent (engineering) stress- Academic
B: Actual (true) stress
Breaking strength– The stress coordinate on the stress-strain curve at the point of rupture.
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