□ A shear force is any force acting perpendicularly to the longitudinal axis of the structure. We can now turn our attention to shear forces and start with a simple definition these stresses, can be represented with their force resultants that ultimately form a couple or internal bending moment,.where we have strains, we must have stresses (remember Young’s modulus).strains develop (which we see at a larger scale as structural deflections).Hopefully now you can clearly see how bending moments arise Where is the second moment of area for the cross-section. …which relates the stress, at a distance from the neutral axis, to the moment. We do this using the Moment-Curvature equation a.k.a. However, more often it’s the case that we know the value of the bending moment at a point and use this to work out the maximum values of normal stress at that location. If we know the state of longitudinal or normal stress due to bending at a given section in a structure we can work out the corresponding bending moment. The bending moment diagram shows how (and therefore normal stress) varies across a structure. □ The internal bending moment, is the bending moment we represent in a bending moment diagram. You might recognise this pair of forces as forming a couple or moment. parallel to each other (and perpendicular to the cut face).equal in magnitude (must be to maintain force equilibrium).So for example the compression force is given by,Īs a result of the external loading on the structure and the deflection that this induces, we end up with two forces acting on the cut cross-section. The compression stresses can be represented by a compression force (stress resultant) while the tensile stresses can be replaced by an equivalent tensile force. The same is true for the stress acting on the cut face of the beam. We know that if we multiply a stress by the area over which it acts, we get the resultant force on that area. This simply means we need to multiple the strain at some point in the beam by the Young’s modulus (modulus of elasticity) to get the corresponding stress at that point in the beam. We can assume this beam is made of a linearly elastic material and as such the stresses are linearly proportional to the strains. Tensile strains occur in the bottom because the fibres are extending or getting longer. In this case we’re considering the longitudinal strain or strain perpendicular (normal) to the cut face.Ĭompression strains above the neutral axis exist because the longitudinal fibres in the beam are getting shorter. Remember, strain is just the change in length divided by the original length. Consider a simply supported beam subject to a uniformly distorted load. Let’s start with a basic question what is a bending moment? To answer this we need to consider what’s happening internally in a structure under load.
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