A timber beam AB of length L and rectangular cross section carries a single concentrated load P at its midpoint C. (a) Show that the ratio Om /Tm of the maximum values of the shearing and normal stresses in the beam is equal to h/2L, where h and L are, respectively, the depth and the length of the beam. (b) Determine the depth h and the width b of the beam, knowing that L = 4 m, P = 60 kN, Tm= 960 kPa, and om=12 MPa. L/2- L/2 - B

A simply supported wood beam of length L = 8 ft carries a concentrated load P at midspan, as shown. The cross- sectional dimensions of the beam are b = 7 in. and h = 13 in. If the allowable shear strength of the wood is 130 psi, determine the maximum load P that may be applied at midspan. Neglect the effects of the beam's self-weight. 12 Answer: P = IM P B 7/2 C X lb N b h

A reinforced concrete T-beam has the following properties: Flange width, bf = 1,350 mm Width of web, bw = 300 mm Gross depth, h = 500 mm Effective depth, d = 420 mm Concrete strength, f’c = 21 MPa Steel strength, fy = 415 MPa 10. If the beam is reinforced with 3-20-mm-diameter bars at the bottom (in single layer), determine the resulting depth of rectangular stress block at ultimate stage. = mm (2 decimal places) 11. What is the condition of failure? = (Balanced, Tension controlled, Compression controlled, Transition) 12. Calculate the design moment strength of a typical interior beam. = kN⋅m (whole number)