Continued overleaf
Page 1 of 4

UNIVERSITY OF GLASGOW

Degrees of MEng, BEng, MSc and BSc in Engineering

STRUCTURAL CONCRETE C5 (ENG5224)

Friday 20 December 2013
09:30 – 11:00

Attempt TWO questions

The numbers in square brackets in the right-hand margin indicate the marks allotted to the
part of the question against which the mark is shown. These marks are for guidance only.

An electronic calculator may be used provided that it does not have a facility for either
textual storage or display, or for graphical display.

Continued overleaf
Page 2 of 4

Q1 (a) A concrete specimen shown in Figure Q1a is analysed using the finite element
method. One of the finite elements of different size has a slightly smaller
strength than the others (shown in grey). The load-displacement curve is
shown in Figure Q1b. Furthermore, the stress-strain curve used in the analysis
is shown in Figure Q1c.

(i) Determine the geometrical parameters a, h and he shown in
Figure Q1a.

(ii) Determine the fracture energy for the parameters in (i).

Figure Q1a

Figure Q1b Figure Q1c
[30]

(b) Describe the principles for the design on the basis of the theory of plastic limit analysis. What is meant by the “lower bound solution” in comparison to the “upper bound solution”? What requirements, according to the principles of the plastic theory, should be fulfilled by the strut and tie model and by the materials? [20]

Continued overleaf
Page 3 of 4

Q2 (a) The deep beam shown in Figure Q2 is subjected to two concentrated loads at
the top. The design loads are P1 = 600 kN and P2 = 600 kN. The deadweight of
the beam can be disregarded.

Determine the necessary primary reinforcement by a strut and tie model and
check nodes and struts.

Design compressive strength of concrete fcd = 30 MPa.
Design yield stress of reinforcement: fyd = 435 MPa.
Thickness of the deep beam: t = 200 mm.
Concrete cover: c = 40 mm.

Figure Q2
[30]

(b) Explain the design steps of the strip method for slabs with free edges. [20]

End of question paper
Page 4 of 4

Q3 (a) A rectangular concrete slab, shown in Figure Q3, is free along one long edge,
while the other edges are simply supported. The slab is subjected to a
uniformly distributed load with design value qd = 12 kN/m2 in the ultimate
limit state (including the dead weight).

Figure Q3
Use the strip method to find an appropriate reinforcement arrangement and
calculate the required bending moment capacities. The load distribution and
the subdivison in strips should be presented for the entire slab.
[30 marks]

(b) Describe the tensile failure of plain concrete in a deformation controlled
uniaxial test specimen. Explain how the material response can be expressed
independently of the length of the test specimen used.
[20]