OTH396: A solid rectangular cross-section beam, 80mm wide by 120mm deep, is loaded as shown in Figure Q1: Civil Engineering – Statics and Mechanics of Materials Home Work, NUS, Singapore

Question 1

A solid rectangular cross-section beam, 80mm wide by 120mm deep, is loaded as shown in Figure Q1. Calculate (a) the distance of the location of the maximum bending moment from point A and (b) the magnitude of the maximum bending stress in the beam.

Question 2

A box beam supports the loads shown in Figure Q2. Compute the maximum value of P if the allowable stress σall = 18 MPa, and P > 20 kN.

Question 3

A beam is loaded as shown in Figure Q3. It has the cross-section shown in the figure. Determine the maximum bending stress in the beam.

Question 4
A bridge over a stream rests on simple supports. It consists of a single plank of wood with dimensions L = 2.4m long, t = 200mm thick and b = 1m wide (see Figure A of Q4). At a certain time, it carries a distributed load q(x) = 10x kN/m, as shown in Figure B of Q4. Determine the maximum bending moment and maximum bending stress σmax in the beam.

Question 5
A concentrated moment, M0 = 110 Nm, is applied at the free end of a cantilever (see Figure A of Q5). The beam has a length L = 1.5m and a Young’s Modulus E = 200 GPa. Two crosssections with the same area are proposed for the beam: an H-section and an I-section (see Figure B of Q5). Determine: a) the slopes at the free end of the H-beam and I-beam b) the deflection at the free end of the H-beam and I-beam c) From your answers in (a) and (b) decide if the statement “The I-beam is stiffer than the Hbeam” is true or false.

Question 6
A cantilever of length L = 2.2m is subjected to two loads, namely a uniformly distributed load p and a linearly varying load w(x) as shown in Figure Q6. Determine the magnitude of the deflection and slope at the free end. EIz = 200×104 Nm2 ; p = 1.6 kN/m ; w0 = 3 kN/m.

Question 7
A uniformly distributed load of intensity w =1.5kN/m is applied to a simply supported tubular beam of length L = 3m. A load P is applied at the mid-point B (see Figure A of Q7). The design specifies an allowable deflection of 3.6mm. Determine the maximum value of P. The dimensions of the tube cross-section are shown in Figure B of Q7. E=200GPa.