Design of structural elements by W M C McKenzie

By W M C McKenzie

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A number of standard frequently used load cases for which the elastic deformation is required are given in Appendix 3 in this text. In many cases beams support complex load arrangements which do not lend themselves either to an individual load case or to a combination of the load cases given in Appendix 3. Provided that deflection is not the governing design criterion, a calculation which gives an approximate answer is usually adequate. The equivalent UDL method is a useful tool for estimating the deflection in a simply supported beam with a complex loading.

9/AE) Resultant ‘R’ A similar calculation can be carried out to determine the vertical deflection at joint D. 12. 5 Shear Force and Bending Moment Two parameters which are fundamentally important to the design of beams are shear force and bending moment. These quantities are the result of internal forces acting on the material of a beam in response to an externally applied load system. 13 carrying a series of secondary beams each imposing a point load of 4 kN. e. +ve ΣFy = 0 The sum of the vertical forces must equal zero.

An American engineer, Professor Hardy Cross, developed a very simple, elegant and practical method of analysis for such structures called Moment Distribution. 10. e. Force = Stiffness × Displacement P = kδ where: P is the applied force, k is the stiffness, δ is the displacement. e. ’ The displacement can be a shear displacement, an axial displacement, a bending (rotational) displacement or a torsional displacement, each in turn producing the shear, axial, bending or torsional stiffness. When considering beam elements in continuous structures using the moment distribution method of analysis, the bending stiffness is the principal characteristic which influences behaviour.

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