Answer Happy

h = 300mm b =190mm t = 4mm L/h =12.5
A timber beam, with rectangular cross section (h x b) will be reinforced with steel plates of thickness t securely connected on the top, left and right sides, and thickness 2t on the bottom. This will ensure composite action in bending. The section is then used as a simply supported beam of length L (given by the span to depth ratio L/h below). The beam is oriented such that the minor principal axis is vertical. It should be taken that Psteel = 7850 kg/m², Ptimber = 1150 kg/m², Etimber = 10500 MPa and Esteel = 200000 MPa, and that both materials exhibit linear elastic behaviour. The design engineer needs to ensure the following: Timber bending stress in tension s 7 MPa • Timber bending stress in compression s 7.5 MPa Steel bending stress (tension or compression) s 175 MPa Ignore stresses due to shear a) Consider self weight only. Draw the stress and strain distributions at midspan. b) Now ignore self weight. The beam is loaded by two vertical point loads, each of magnitude P, that act at L/3 and 2L/3 along the beam. What is the maximum value of P so that the stress criteria above are satisfied? Draw the stress and strain distributions (values required) for both the steel and the timber on the critical cross-section for this value of P. c) Use your answers to comment on the following (about 150 words for each item) (i) The significance of self-weight (ii) The effectiveness/appropriateness of using 2t on the bottom, rather than t.