By W M C McKenzie
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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.
45. Determine the maximum timber and steel stresses induced in the cross-section when the beam is subjected to a bending moment of 70 kNm. 45 150 mm (a) Transformed section based on timber Equivalent width of timber to replace the steel plate = (n × 150) mm where: Esteel 205 × 10 3 = 25 nB = (25 × 150) = 3750 mm n = = E timber 8200 The maximum stresses occur in the timber when y = 150 mm, and in the steel (or equivalent replacement timber) when y = 160 mm. 5 N/mm2 (b) Transformed section based on steel Equivalent width of steel to replace the timber beam = (n × 150) mm where: E timber 1 1× 250 n = = 10 mm = nB = Esteel 25 25 10 mm x x 10 mm 300 mm 10 mm The maximum stresses occur in the timber (or equivalent replacement steel) when y = 150 mm, and in the steel when y = 160 mm.
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. This is a linear expression which should be reflected in the calculated values of the bending moment. 0 kNm at point B. e. 6 kNm at point C. e. 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.
Design of structural elements by W M C McKenzie