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Fig. 1: Critical stress vs slenderness ratio for steel, for E = 200 GPa, yield strength = 240 MPa.. Euler's critical load or Euler's buckling load is the compressive load at which a slender column will suddenly bend or buckle.
Euler–Bernoulli beam theory (also known as engineer's beam theory or classical beam theory) [1] is a simplification of the linear theory of elasticity which provides a means of calculating the load-carrying and deflection characteristics of beams. It covers the case corresponding to small deflections of a beam that is subjected to lateral ...
In solid mechanics and structural engineering, section modulus is a geometric property of a given cross-section used in the design of beams or flexural members.Other geometric properties used in design include: area for tension and shear, radius of gyration for compression, and second moment of area and polar second moment of area for stiffness.
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.
For an elastic body with a single degree of freedom (DOF) (for example, stretching or compression of a rod), the stiffness is defined as = where, F {\displaystyle F} is the force on the body δ {\displaystyle \delta } is the displacement produced by the force along the same degree of freedom (for instance, the change in length of a stretched ...
Macaulay's method has been generalized for Euler-Bernoulli beams with axial compression, [3] to Timoshenko beams, [4] to elastic foundations, [5] and to problems in which the bending and shear stiffness changes discontinuously in a beam. [6]
The compressive strength of the material corresponds to the stress at the red point shown on the curve. In a compression test, there is a linear region where the material follows Hooke's law. Hence, for this region, =, where, this time, E refers to the Young's modulus for compression. In this region, the material deforms elastically and returns ...
In this case, the equation governing the beam's deflection can be approximated as: = () where the second derivative of its deflected shape with respect to (being the horizontal position along the length of the beam) is interpreted as its curvature, is the Young's modulus, is the area moment of inertia of the cross-section, and is the internal ...
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