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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.
The section modulus combines all the important geometric information about a beam's section into one quantity. For the case where a beam is doubly symmetric, c 1 = c 2 {\displaystyle c_{1}=c_{2}} and we have one section modulus S = I / c {\displaystyle S=I/c} .
The four-point flexural test provides values for the modulus of elasticity in bending, flexural stress, flexural strain and the flexural stress-strain response of the material. This test is very similar to the three-point bending flexural test .
Flexural modulus measurement 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 ...
The farther a given amount of material is from the neutral axis, the larger is the section modulus and hence a larger bending moment can be resisted. When designing a symmetric I-beam to resist stresses due to bending the usual starting point is the required section modulus. If the allowable stress is σ max and the maximum expected bending ...
is the cross section area. is the elastic modulus. is the shear modulus. is the second moment of area., called the Timoshenko shear coefficient, depends on the geometry. Normally, = / for a rectangular section.
where is the area moment of inertia of the cross-section, is the cross-sectional area, is the shear modulus, is a shear correction factor, and () is an applied transverse load. For materials with Poisson's ratios ( ν {\displaystyle \nu } ) close to 0.3, the shear correction factor for a rectangular cross-section is approximately
The stiffness of a structural element of a given material is the product of the material's Young's modulus and the element's second moment of area. Stiffness is measured in force per unit length (newtons per millimetre or N/mm), and is equivalent to the 'force constant' in Hooke's Law.