Question: A rigid beam ABC is supported at C by a pin support, and at A and B by timber struts AD and BE which are

A rigid beam ABC is supported at C by a pin support, and at A and B by timber struts AD and BE which are in turn supported by pin supports at D and E respectively (Figure 1). The struts AD and BE are constructed using F11 timber (refer Figure 2) with square cross section 40 mm x 40 mm. A uniformly distributed load of 10 kN/m acting horizontally to the right is applied along the complete length ABC. Under the action of this load, in addition to any changes in the lengths of the struts, the pin support at C settles by 1 mm to the right.

Assume that the beam and struts are weightless and that the struts will not buckle. (a) Using equilibrium and compatibility considerations determine the support reactions at C, D and E. Hint: Since the struts AD and BE can transfer only axial force, the reactions at D and E act horizontally (that is, there are no vertical reaction components at D and E). (b) Find the normal stress, normal strain and change in length of strut AD.

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