Assignment 1
Due: 26th March 2025, 23:59
Q1 [Max total marks: 10] The following stress components represent 2D stress condition as given below:
σx = 200 MPa σy = 250 MPa τxy = - 30 MPa
(a) Draw the element clearly showing its coordinate system and indicate all acting stresses [1 mark];
(b) Construct a Mohr s circle of stress and find the principal stresses and the orientation of the principal axes relative to the x,y axes indicating the point on circle corresponding to the element as B. Provide a typed table containing the following data: coordinates of the centre; radius of the circle, angle between the radius vector of the point A and the abscissa i.e. horizontal axis in degrees (anticlockwise) [3 marks];
(c) determine the stresses acting on an element, rotated in the x-y plane 60° counterclockwise from its original position [3 marks];
(d) Produce a typed table containing the principal stresses and the maximum shear stress [3 marks]
Q2 [Max total marks: 10] The state of stress at a point of an elastic solid is given in the x-y- z coordinates by:
(a) What type of state is this — 3D stress, 3D Strain, plane stress or plane strain? Justify your answer [2 marks];
(b) Using the matrix transformation law, determine the state of stress at the same point for an element rotated about the z-axis 60° clockwise in the xy-plane from its original position [3 marks];
(c) Produce a typed table containing the principal stresses [3 marks]; Please note 2 marks are awarded for correct workout upload.
Q3 [Max total marks: 10]
The figure below shows a concrete mixer parked on a single span bridge prior to commencing repair works. Assuming that the weight of the truck is acting as a single force through the centre of mass of the truck as indicated on the figure produce
(a) Free body diagram of the bridge [4]
(b) What type of structural element represents the bridge; How many reaction forces are acting and why [2]
(c) Fill a table with the reaction force values [4]
Question 4
For the structure below
(a) Produce a free body diagram [4]
(b) Answer how many reactions are occurring due to the applied load and why [2]
(c) Place all the values of the reaction forces in a table using appropriate units [4]