Answer Happy

b = 225mm
t = 6mm
L/h = 14.5
2) A timber beam, with rectangular cross section (h * 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/m3, ptimber = 1150 kg/m3, 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 . 0 . 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.