# Design of structural elements by W M C McKenzie

By W M C McKenzie

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Each of the point load locations. 25. 25 The same result can be obtained by considering sections from the right-hand side of the beam. The value of the bending moment at any location can also be determined by evaluating the area under the shear force diagram. 2 kNm Note: A maximum bending moment occurs at the same position as a zero shear force. 26. 0x A 9 kN x This is a linear equation in which Vx decreases as x increases. e. the point of zero shear. g. 27. 27 The bending moment can be determined as before, either using an equation or evaluating the area under the shear force diagram.

0), therefore k = (4EI)/L. This is known as the absolute bending stiffness of the element. Since most elements in continuous structures are made from the same material, the value of Young’s Modulus (E) is constant throughout and 4E in the stiffness term is also a constant. This constant is normally ignored, to give k = I/L which is known as the relative bending stiffness of the element. It is this value of stiffness which is normally used in the method of Moment Distribution.

As with shear forces the calculation for bending moments can be carried out at various locations along a beam and the values plotted on a graph; this graph is known as the ‘bending moment diagram’. The bending moment diagram indicates the variation in the bending moment along a structural member. 0 kN load passes through the section being considered and does not produce a bending moment, and can therefore be ignored. 0 x kNm Unlike the shear force, this expression is not a constant and depends on the value of ‘x’ which varies between the limits given.