Assessment questions 4

Objectives

This assessment item relates to the course learning outcomes 1, 2, 3 and 4

Question 1                                                                                                      

Topic: Section Properties:

For the beam below (see dimensions below);

• Calculate, dimension and sketch the location of the horizontal centroidal axis
• Calculate the Second Moment of Area Ixx (horizontal axis only)
• Calculate the Section Modulus Zxx (horizontal axis only) Make sure you show all calculations

The dimensions for the beam are as follows:

bf= 150mm (both flanges) d = 200 mm

tf = 12 mm (both flanges)

tw = 10 mm

h = 176 mm

Question 2                                                                                                                                         

Topic: Analysis of statically determinate trusses

The truss below has been designed to support a 60 kN load.

Using the Method of Joints

• Calculate both the horizontal and vertical reactions at A and E
• Calculate the force in each member of the truss
• Draw a truss diagram showing the force in each member and show which member is in tension or compression
• Calculate the force in member BF using the method of sections

Note:

• For your calculations you can assume all truss members are pin connected
• Ignore the self-weight of the truss.
• Make sure you show all workings.

Question 3

Topic: Beams- shear force and bending moment

For the beam below;

• Calculate the beam reactions at A and C.
• Calculate the bending moment at A, B, C and D.
• Draw shear force and bending moment diagrams for the beam and label values for the maximum shear force and bending moment – Show all workings.

Question 4

Topic: Bending and shear stresses: 

The timber beam below spans 7.0m and carries a uniformly distributed load of 1.5 kN/m (including the self-weight of the beam).  The beam is 75 mm wide and 240 mm deep.

(1) Calculate the average vertical shear stress at;

1. x = 3.5m
2. x = 1.75m and
3. x = 0 (at the support)

(2)  Sketch the shear force diagram and indicate maximum and minimum values

(3)  Calculate the horizontal (longitudinal shear stress) at x = 1.75m at each of the following points of the section.

1. at the top surface
2. at 60mm and
3. at 120mm from the top
4. 180mm from the top

(4) Sketch the internal horizontal shear stress distribution diagram where the maximum vertical shear stress is located. Indicate shear stress values.