Francis Franklin

A gold ball on a steel table - effect of its own weight.

A gold ball on a steel table - effect of its own weight.

Hertz contact calculation for ball joint.

Using Mohr's Circle to calculate principal stresses in plane stress 2D case.

Calculate the von Mises stress at the base of a post subject to axial compression, bending and torsion.

Determine the principal stresses for a 3D stress state (with null third invariant).

Calculate invariants and von Mises stress for a general 3D stress state.

Determine maximum pressure in a closed thin-walled cylindrical pressure vessel before yield.

Work backwards from hoop strain measurement to calculate prior gauge pressure in a drinks can.

Calculate direct and shear stress in an axially loaded bar in the XY plane.

Find principal stresses by finding the eigenvalues of the matrix

Use Matlab (or Python) to fit a cubic polynomial to data, and determine where the x-axis is crossed.

Curve fitting, function zeros, sequences, etc.

Tension in bracket-truss.

Tension in a simple triangular truss.

Tension in simple triangular truss.

Euler-Bernoulli simply supported beam bending example with point force and moment.

Estimating the wear rate of a disc from a twin-disc experiment.

Find angular speed of a swinging pendulum.

Finding the zero of a non-polynomial function

Write a loop in,e.g., Matlab or Python to determine terms in a sequence.

Find angular speed and reaction force of a swinging pendulum.

Integrate Paris Law equation to estimate life to failure.

Simple Hertz contact without friction.

These practice questions cover:

• resolving axial forces in a truss structure
• stress & strain in a closed thin-walled pressure vessel (an example of 2D plane stress)
• use of Mohr's circle for determining principal stresses for a 2D plane stress case
• calculation of invariants for general 3D stress case, leading to von Mises stress and principal stresses

Basic calculation of 3D stresses.

Practice for thin-walled pressure vessel and 2D principal stresses

Calculation of pressure in a closed thin-walled pressure vessel (e.g., a drinks can) based on measured hoop strain.

Resolving forces in a simple truss, and 2D stresses in a uniaxially loaded bar.