Question 1

A simply supported beam of 5.5 m long and subject to a system of a trapezoidal distributed load w1 - w2 and a concentrated load P is shown in Figure 1. The concentrated load P is located 2 m away from the pinned support A. Assume that the beam is made of steel (360 UB 50.7, E=200x103 MPa) and is loaded in its strong axis direction (section properties are available in OneSteel catalogue).

(a) Use the method of superposition along with statics analysis techniques of your choice (equilibrium method, graphical method, or standard formulae method) to analyse the beam. Draw neat and fully labelled Shear Force Diagrams and Bending Moment Diagrams for each individual load and the resultant of combined loads. Evaluate and select the critical design values of shear and moment for strength design

(b) Use the method of superposition to enable an approximate calculation of the total maximum deflection of the beam. Evaluate whether the beam is satisfactory in serviceability if the total maximum deflection must ≤ span/300

Your personal design data (w1, w2, P)

Use the last three digits of your student ID, denoted 'xyz' to work out the values of these three parameters as follows: w1 (kN/m) = 6 +x/10; w2 (kN/m) = 1+y/10; P (kN) = 8+z*2/10.

For instance, a student has an ID of 0123456 will have ‘xyz' = 456 and therefore w1 = 6 + 4/10 = 6.4 kN/m; w2= 1 +5/10 = 1.5 kN/m; P= 10+6*2/10= 11.2 kN.

Hints: To apply the method of superposition, the load system needs to be decomposed into individual loads each of which is applicable for use with standard formulae as covered in module 2