Tutorial 1 Problem 3 (ENGR5004)

Tutorial 1 Problem 3Exercise sheetCurrent spec2:212 min

A beam has a constant circular cross section of radius 20 mm, and is subject to a tensile axial load of 4 kN.

Formulas you may need

Eccentric axial loading: $F = P$ , $M = Pd$ , $\sigma_x = \dfrac{P}{A} - \dfrac{My}{I}$ (on the formula sheet)
Solid circle: $A = \pi r^2$ , $I = \dfrac{\pi r^4}{4}$ (on the formula sheet)

(a)
Determine the magnitude of the maximum stress in the cross section when the axial load is applied at the centre of the section.
sigma_max =MPa
(b)
In the loading condition (a), state whether a neutral axis exists or not, and explain why.
(c)
State whether the maximum normal stress in the cross section when the axial load is applied at 10 mm from the centre of the section is compressive or tensile and explain why.
(d)
In the loading condition (c), determine the magnitude of the maximum compressive and tensile stresses in the cross section.
sigma_max tensile =MPa
sigma_max compressive (magnitude) =MPa
(e)
In the loading condition (c), determine the distance of the neutral axis from the centre of the cross section.
y_NA =mm