Example exam questions
Q1 (15 marks)
Consider the interior 12m span of a continuous beam in Figure 2(a) with the sagging cross
sections in Figure 2(b) and the hogging cross section in Figure 2(c).
a) Determine the short term service deflection due to the load ws = 20kN/m
b) Determine the total long term deflection when the sustained load is wl = 16kN/m. Take
the shrinkage strain to be 600 microstrain.
300mm
600mm
60mm
60mm
600mm2
2800mm2
300mm
600mm
60mm
60mm
600mm2
2800mm2
Figure 2(b): cross section
sagging region
Figure 2(c): cross section
hogging region
12000mm
w = 20kN/m
w = 16kN/m
s
l
f = 25MPa
= 0.85
f = 400MPa
E = 200000MPa
E = 24000MPa
c
y
S
c
Figure 2(a): interior span of continuous beam
Q2 (25 marks)
a) A 500mm square column is reinforced symmetrically by 2400mm2 of steel at each of
the 2 critical faces as shown in Figure 3(a). Construct the section capacity line as
shown in Figure 3(b), that is determine the relationship between the moment M and
the axial load N of points A-E. For the bending analysis take the depth to the neutral
axis to be 76mm from the compression face. (20 marks)
b) If the cross section in Figure 3(a) is used to construct an unbraced column of length
3000mm where the end conditions may be idealised as pins. Determine the maximum
axial load N which can be applied to the column at an eccentricity of e = 265mm from
the plastic centroid (5 marks)
65mm
65mm
2600mm2
2600mm2
500mm
500mm
f = 20MPa
= 0.85
f = 300MPa
E = 200000MPa
E = 24000MPa
c
y
S
c
A-squash load
B-transition point
C-balance
point
D-pure bending
E-tensile failure
Figure 3(b): column
interaction curve
N
M
Figure 3(a): column
cross section
Q3 (25 marks)
An elevation of a regular rectangular framed building is shown in Figure 4 where the columns are at
7000mm centres each way. All columns in the level have a cross section of 400x600mm. The floor to
floor heights are 3400mm and the width of the column strip of the flat slab floors is 3200mm. Relative
sway between the floors is not prevented. Using the section capacity lines in Figure 5 determine the
d to be 0.7
and the effective depth of the column do to be 526mm.
Figure 4: Elevation of a regular rectangular framed building
280mm
600mm
210kNm
400kNm
1100kN 1100kN2000kN2000kN2000kN
1000kN 1000kN1900kN1900kN 1900kN
3400mm
7000mm 7000mm 7000mm 7000mm
A
A
B
B
C
C
D
D
E
E
280mm
Q 4 (10 marks)
For the section and material properties shown in Figure 1 calculate the moment and
corresponding curvature given a compressive strain at the top fibre of 0.003 and a
neutral axis depth of 286 mm.
Perform only one iteration regardless of convergence.
Figure 1
(c) (d) P(a) section
concrete material properties
Es=200GPa
reinforcement material properties
d =286mmNA
590mm
650mm
350mm top=0.003
f =500MPay
0.0015
30MPa
A = 3000mmst
2
Q5 (10 marks)
Considering the rectangular reinforced concrete beam as shown in Figure 2:
Figure 2
a. Assuming the stress-strain relationship for the concrete is linear,
determine the maximum moment that can be carried without stressing
the concrete beyond 0.4fc (5 marks)
b. Assuming the concrete to have a rectangular stress block, find the
ultimate moment capacity of the section (5 marks).
710mm
360mm
3N32
f =400MPa
f =34MPa
f =3.4MPa
E =25000MPa
E =200GPa
y
c
ct
c
s
Q6 (5 marks)
Determine the quantity of stirrups required for the cross section in Figure 1 to resist a shear
load of V*=3300kN. You may present your answer as the ratio of Asv/s. Take the maximum
aggregate diameter to be 20 mm.
At the critical section M* = 0kNm.
Figure 1
500
f =40MPa
f =f =500MPa
c
y ys
A = 5600mmst layer 2
2
Q7. (15 marks)
The T-section in Figure 2 has been designed to carry positive in span moments, but is also required
to resist a negative moment of 1400kNm at the interior support. For architectural reasons the depth
of the section cannot be increased. Design the section for the negative moment.
Figure 2
400
f = 32 MPa
f = 500MPa
= 0.0025
c
y
y
Q8. (11 marks)
a) Confirm the adequacy of the reinforced concrete box section in Figure 3 to resist a design
bending moment of M*=6200 kNm
(5 marks)
b) Design the shear reinforcement required such that the box section can resist a design
shear force of V* = 2500 kN, at the critical section M* = 0kNm.
(6 marks)
Figure 3: Reinforced concrete box section
250 250
2000
2500
250
1000
A = 3820mmsc 2
A = 11220mmst 2
f = 40 MPac
f = 500 MPay
30
Q9. (15 marks)
Figure 2: beam subjected to in service load
The cross section in Figure 2(a) is subjected to the serviceability loads in Figure 2(b).
a. Determine the instantaneous and long term deflection if the design shrinkage
strain is . (7 marks)
b. Determine the crack spacing, short term and long term crack widths. (6
marks)
c. Comment on the suitability of the cross section to perform adequately under
the given service conditions. (2 marks)
280 mm
380 mm
420 mm
30 mm
A = mm
A = mm
f = 32 MPa
E = 25000 MPa
E = 200000 MPa
= 600
rt
rc
c
c
s
cs
2
2
603
226
P short term load:
P = P + P
long term load:
P = P +
short G s Q
long G L Q
G
Q
s
L
P
P = 28kN
P = 30kN
= 0.7
=0.4
6800 mm
(a)
(b)d = 16 mmb