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in these formulas the following parameters are used: = Stress in outer fibers at midpoint, = load at a given point on the load deflection curve, = Support span, (mm) = Width of test beam, (mm) = Depth or thickness of tested beam, (mm)
Shear and Bending moment diagram for a simply supported beam with a concentrated load at mid-span. Shear force and bending moment diagrams are analytical tools used in conjunction with structural analysis to help perform structural design by determining the value of shear forces and bending moments at a given point of a structural element such as a beam.
The flexural strength is stress at failure in bending. It is equal to or slightly larger than the failure stress in tension. Flexural strength, also known as modulus of rupture, or bend strength, or transverse rupture strength is a material property, defined as the stress in a material just before it yields in a flexure test. [1]
The formula to calculate average shear stress τ or force per unit area is: [1] =, where F is the force applied and A is the cross-sectional area.. The area involved corresponds to the material face parallel to the applied force vector, i.e., with surface normal vector perpendicular to the force.
For a 3-point test of a rectangular beam behaving as an isotropic linear material, where w and h are the width and height of the beam, I is the second moment of area of the beam's cross-section, L is the distance between the two outer supports, and d is the deflection due to the load F applied at the middle of the beam, the flexural modulus: [1]
Stress resultants are simplified representations of the stress state in structural elements such as beams, plates, or shells. [1] The geometry of typical structural elements allows the internal stress state to be simplified because of the existence of a "thickness'" direction in which the size of the element is much smaller than in other directions.
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Chapter 2 – Stress and Strain: Important Relationships Chapter 3 – The Behavior of Bodies Under Stress Chapter 4 – Principles and Analytical Methods Chapter 5 – Numerical Methods Chapter 6 – Experimental Methods Chapter 7 – Tension, Compression, Shear, and Combined Stress Chapter 8 – Beams; Flexure of Straight Bars