Chapter 1 · 1 hour

Load on Structure and Response of Material

Practice questions

Practice questions and answers

2 exam-style questions on this chapter, written for this site from the official syllabus. We haven’t found past IOE papers for this subject yet; if you have some, share them in the community.

Practice · 5 marks

Classify the loads that act on a structure. Explain the effect each kind of load produces in a member.

Answer

A load is any external action (force, moment, pressure, temperature change, support settlement) that makes a structure deform and develop internal stresses. Loads are classified in more than one way.

Classification of loads

Basis	Types	Examples
Duration / variation with time	Static, dynamic, impact, cyclic (fatigue)	Self weight; machine vibration; falling weight; rotating shaft
Permanence	Dead, live	Self weight of beam; people, vehicles
Environmental	Wind, snow, earthquake, thermal	Wind on a tower; temperature rise in a rail
Distribution	Point, line (UDL, UVL), surface	Column on a beam; slab on a beam; water pressure

Static load: applied slowly, so inertia forces are negligible.
Impact load: applied suddenly with kinetic energy, so stresses can be several times those of the same static load.
Cyclic load: repeated many times; failure can occur below the yield stress (fatigue).

Effect of load on a member

The effect depends on how the load acts relative to the axis of the member.

Load	Internal action	Resulting stress	Example
Axial (tension or compression)	Normal force $N$	$\sigma = N/A$	Tie rod, column
Transverse (shear)	Shear force $V$	$\tau = VQ/(Ib)$	Rivet, beam web
Transverse load or couple	Bending moment $M$	$\sigma = My/I$	Floor beam
Twisting couple	Torque $T$	$\tau = Tr/J$	Transmission shaft
Internal or external pressure	Hoop and axial stress	$\sigma_\theta = pr/t$	Boiler shell
Temperature change	Thermal strain	$\sigma = E\alpha\Delta T$ if restrained	Bridge deck

In practice members carry combined loading, for example a shaft in bending and torsion, or an eccentric column in compression and bending. The stresses are then found for each action separately and combined by superposition, valid for linear elastic response and small deformation. The combined stress state is then examined with the stress tensor to find principal stresses and check failure.

Practice · 5 marks

Differentiate between (a) elastic and non-elastic response of a solid, (b) isotropic and anisotropic materials, and (c) a homogeneous and a continuous body. State how temperature affects the elastic and plastic range of a solid.

Answer

(a) Elastic and non-elastic response

Point	Elastic	Non-elastic (plastic, viscoelastic)
After unloading	Body returns fully to original shape	Some permanent (residual) strain remains
Stress-strain	Loading and unloading follow the same path	Unloading path differs; energy is dissipated
Region	Up to the elastic limit (yield)	Beyond yield
Example	Steel spring below yield	Steel after necking; clay; lead

Linear elastic response obeys Hooke's law, $\sigma = E\varepsilon$ .

(b) Isotropic and anisotropic

Point	Isotropic	Anisotropic
Properties	Same in all directions at a point	Depend on direction
Independent elastic constants	2 ( $E$ , $\nu$ )	Up to 21 (9 for orthotropic)
Example	Mild steel, aluminium (ideal)	Timber, fibre composites, rolled sheet

(c) Homogeneous and continuous

Homogeneous: properties are the same at every point of the body (they do not change with position). A concrete block with voids and variable aggregate is not exactly homogeneous.
Continuous: the body has no gaps or voids, so matter is distributed without break and quantities such as stress, strain and displacement are continuous functions of position. This allows calculus to be used.

A body can be homogeneous but anisotropic (a straight timber log of uniform fibre direction).

Effect of temperature

As temperature rises, $E$ and yield strength fall; the elastic range shortens and the plastic range (ductility) usually increases. Mild steel loses most of its strength near 500 to 600 $^\circ$ C.
At low temperature, yield strength rises but ductility falls, so steel can become brittle (ductile-brittle transition).
At high temperature under steady load, materials creep (strain increases with time).
If expansion is restrained, a thermal stress $\sigma = E\alpha\Delta T$ develops.

Written from the official syllabus. Questions and answers are written for this site; check them against your class notes.

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