Introduction to structural systems practice questions.

A rectangular timber joist is loaded in bending. Where across the depth of the joist is the bending stress smallest?

• At the upper face, where the fibres are being compressed
• At the neutral axis, halfway through the depth
• At the lower face, where the fibres are being stretched
• Uniformly across the depth, because bending stress does not vary

Answer: At the neutral axis, halfway through the depth

Bending stretches the fibres on one face and squashes those on the other, so the stress has to pass through zero on a line between them, and in a symmetrical section that line sits at mid-depth. This is why an I-beam keeps most of its material in the top and bottom flanges and only a thin web at the middle.

Two overlapping steel plates are joined by a single rivet and are then pulled apart in line with each other. How is the rivet loaded?

• In tension, because the plates are pulled apart
• In torsion, because the plates twist about the rivet
• In shear, because the two plates slide across the rivet section
• In compression, because the rivet head clamps the plates together

Answer: In shear, because the two plates slide across the rivet section

The plates apply opposed forces across the plane of the rivet, so the rivet section is cut rather than stretched. Reading the direction of the applied load relative to the section is what separates shear from tension.

A tensile test on a metal specimen produces a stress-strain graph. Which quantity is given by the gradient of the initial straight portion of that graph?

• The Young's modulus of the material
• The ultimate tensile strength of the material
• The toughness of the material
• The yield stress of the material

Answer: The Young's modulus of the material

In the elastic region stress is proportional to strain, so the gradient is stress divided by strain, which is Young's modulus and therefore a measure of stiffness. Ultimate tensile strength is read as the peak height of the curve and toughness as the area beneath it.

A lifting eye for a workshop hoist is specified with a factor of safety of 5. Which statement states what this value means?

• The eye is tested five times before it leaves the factory
• The eye is five times heavier than the load it is designed to carry
• The eye will fail after five times its rated number of lifting cycles
• The failure stress of the eye is five times its working stress

Answer: The failure stress of the eye is five times its working stress

Factor of safety compares ultimate stress with working stress, so it is a ratio of two stresses and not a mass, a test count or a fatigue life. A high value covers uncertainty in loading, variation between batches of material and damage picked up in service.

A concrete road bridge carries its own deck, parapets and surfacing, and is crossed by traffic. Which of these acts as a live load on the structure?

• The permanent self-weight of the concrete deck
• The mass of the steel parapets fixed to it
• The lorries crossing the bridge
• The asphalt surfacing layer laid on the deck

Answer: The lorries crossing the bridge

Dead loads are the permanent, unchanging weights of the structure itself, whereas live loads vary in size and position with use. Treating traffic as a dead load understates the moving, changing case that actually governs the design of the deck.

A tie of solid square section carries a fixed axial tensile load. The side of the square is doubled and nothing else is changed. What happens to the direct stress in the tie?

• It doubles, because the side is twice as long.
• It halves, because the side is twice as long.
• It falls to a quarter, because the area is four times larger.
• It is unchanged, because the load and the material are the same.

Answer: It falls to a quarter, because the area is four times larger.

Direct stress is sigma = F / A, and the area of a square goes with the square of its side, so doubling the side multiplies the area by four and divides the stress by four. Assuming the stress falls in step with the side is the usual slip; it is the area, not the width, that appears in the formula.