ASSIGNMENT - SLOPE AND DEFLECTION OF BEAMS

Macauley's method can be used to find the slope and deflection of beams in some cases where the loading is complex.

a) Use Macauley's method to answer the following questions:

i) Using Macauley's method prove that the maximum deflection for a simply supported beam, length L, flexural stiffness EI and carrying a midpoint load of F is FL³/48EI.

ii) Using Macauley's method prove that the maximum deflection for a simply supported beam, length L, flexural stiffness EI and carrying a UDL of W N/m along the whole length of the beam is 5WL⁴/384EI.

b) A beam ABCDE is simply supported at the ends A and E and carries point loads of 25 kN at B, 18 kN at C and 28 kN at D. The beam is 5 m long and AB is 1.5m, BC is 1.0 m and CD is 2.5 m.

Calculate:-

• The position and magnitude of maximum deflection
• The slope at end A

c) For the beam below:-

Derive the Macauley's expressions for slope and deflection at any point Calculate the position and magnitude of maximum deflection using an iterative method.

Take EI = 200 x 10³ kNm²

d) A beam is subject to the loading as detailed below.

Data:

Material: Select a suitable material

Safety Factor: To be between 1.5 and 3.

 Maximum Deflection: 3mm

i) Calculate the position of the maximum deflection from the LH end of the beam using a practical engineering method. Fully explain your method.

ii) Calculate a suitable I section to give the required deflection. Hence find the section dimensions to obtain this I value.

iii) Calculate the bending stress in the beam and hence find the applied safety factor for your chosen material and compare the calculated safety factor with the allowed safety factor.