Problems-Structural Analysis_Najif Ismail

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Problem 1.1
Choose the one alternative that best completes the statement or answers the question. (20 Marks)
i. When considering the earthquake performance of structures, typical code approach is to apply
equivalent _______ to forces to the building. (2 Marks)
A). vertical B). rotational
C). horizontal D). None of the above
ii. An additional floor slab load is typically considered while designing RC structures to account for
future non-load bearing partition walls, this load is a part of ____________. (2 Marks)
A). dead load B). live load
C). wind load D). earthquake load
iii. The load factors are used to account for worst case scenario, and to obtain the combined effect of
dead load (D) and earthquake load (E) the combination used is 0.9D+1.0E, where (2 Marks)
A). add these two load magnitudes algebraically
and apply to elements
B). apply both loads separately and get the
resultant effect on elements
C). only apply dead loads D). only apply the earthquake load
iv. Stiffness of a reinforced concrete beam in uncracked elastic stage is ____________ what it would
have in cracked – elastic stage. (2 Marks)
A). same as B). smaller than
C). greater than D). have no relation to
v. A taller building when compared to a squat building is likely to have a _______________ natural
period of vibration? (2 Marks)
A). shorter B). longer
C). about the same D). None of the above
vi. The ULS for buildings of normal use (importance level 2) in NZS 1170.5 is typically based around
earthquake motions with a return period of ___________. (2 Marks)
A). 25 years B). 250 years
C). 500 years D). 2500 years
vii.Choosing a high ductility factor will lead to smaller design actions and a _______ structure, which
will sustain _______ damage in an earthquake. (2 Marks)
A). weaker, greater B). stronger, minimal
C). stronger, greater D). weaker, minimal
viii. The building design life (L), probability of exceedance (p), and return period (r) are related by
(2 Marks)
A). r =
L
-ln(1-p)
B). r ≈
L
p(1-p/2)

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C). both A and B D). none of the above
ix. Choosing a high ductility factor will lead to smaller design actions and a _______ structure, which
will sustain _______ damage in an earthquake. (2 Marks)
A). weaker, greater B). stronger, minimal
C). stronger, greater D). weaker, minimal
Problem 1.2
The schematic representation of the building shown in Figure 1.1 is a to be used for as an office building,
which is proposed to have a lateral load resisting system consisting of concrete moment resisting
frames (μ = 3.0). The building is to be built in Upper Hutt in Trentham over at least 30 m deep stiff clay.
The underlying soil has been classified as subsoil type C by geotechnical engineer. The intended design
life of the building is 100 years.
a). Establish appropriate seismic design action coefficient for ultimate strength limit state (ULS) check
for the building described above. (08 Marks)
b). Determine equivalent lateral forces acting at each floor level for the building shown in Figure 1.1, if
the base shear calculated is V = 906.5 kN. (08 Marks)
c). Sketch the approximate shear force and bending moment shape resulting from lateral earthquake
loading for the building shown in Figure 1.2. (04 Marks)
Figure 1.1. Schematic representation of the office building for earthquake analysis
W1 = 287 kN
2.7m
W2 = 296 kN
5.0 m
3.0m
30m
2.7m
W3
= 301 kN
2.7m
W4
= 285 kN
2.7m
W5
= 281 kN
F5
F4
F3
F2
F1
V

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Figure 1.2. Two-dimensional frame with lateral earthquake forces
Problem 1.3
The schematic representation of the building shown in Figure 1.1 is a to be used for as an extension
block to Victoria university Wellington city campus with five 2000 student lecture halls at ground and
first floor. The building is to have a lateral load resisting system consisting of concrete shear walls
(μ = 4.5). The underlying soil has been classified as subsoil type C by geotechnical engineer. The
intended design life of the building is 100 years.
b). Determine equivalent lateral forces acting at each floor level for the building shown in Figure 1.1, if
the base shear calculated is V = 906.5 kN. (08 Marks)
c). Determine the overturning moment due to earthquake forces at the base of the building described
above in parts ‘a’ and ‘b’. (04 Marks)
Problem 1.4
A small emergency hospital with a design life of 50 years is to be built in Nelson. The primary structure
consists of equally spaced single storey high moment-resisting steel frames (see Fig. 1.3) having limited
ductility (µ = 3.0), with a transverse vibration period of T = 0.4 s, founded on shallow soil (subsoil type
C)with no active faults within 20 km. Determine the (acceleration) coefficients for the ultimate and
serviceability limit states. Seismic weight, (G+ψc.Q) amounts to W = 450 kN per frame.
W1 = 287 kN
2.7m
W2 = 296 kN
5.0 m
3.0m
30m
2.7m
W3
= 301 kN
2.7m
W4
= 285 kN
2.7m
W5
= 281 kN
4.0 m 4.5 m

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Figure 1.3. Steel frame geometry for problem 1.4
Problem 1.5
The schematic representation shown in Figure 1.4 is for the building of a three storey high apartment
development. The building is to have steel moment resisting frames (μ = 3.0) and is to be built in Napier
over soil that has been classified as subsoil type D by the geotechnical engineer. The intended design
life of the building is 50 years.
b). Determine equivalent lateral forces acting at each floor level for the building shown in Figure 1.4.
(08 Marks)
c). Sketch the approximate shear force and bending moment shape resulting from lateral earthquake
loading for the building shown in Figure 1.5. (04 Marks)
Figure 1.4. Schematic representation of the apartment building for earthquake analysis
W1 = 587 kN
2.7m
W2 = 496 kN
4.2m2.7m
W3
= 401 kN
F3
F2
F1
V

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Figure 1.5. Two-dimensional frame with lateral earthquake forces to draw rough bending moment diagram
shape
W1 = 287 kN
2.7m
W2 = 196 kN
5.0 m
3.0m
30m
2.7m
W3
= 301 kN
2.7m
W4
= 285 kN
2.7m
W5
= 281 kN
4.0 m 4.5 m

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Problem 2.1
i. The maximum useable compression strain for concrete used in the design as per NZS 3101 is,
(2 Marks)
A). 0.002 B). 0.003
C). 0.004 D). 0.005
ii. A 300 wide and 600 deep reinforced concrete beam (use fy = 420 MPa, d = 550 mm) will have a
neutral axis depth at a balanced failure of, (4 Marks)
A). 0.33 m B). 0.19 m
C). 0.21 m D). None of above
iii. At nominal flexural strength limit state, the concrete compression stress profile in a reinforced
concrete beam is, (2 Marks)
A). parabolic B). represented with an equivalent rectangle
C). inelastic D). All of above
iv. When calculating the nominal strength of a RC beam, for the assumption fs = fy to be true,
(2 Marks)
A). εs = εy B). εs < εy
C). εs > εy D). εy ≤ εs
v. The desirable ductile failure mode of RC beams is when -----------. (2 Marks)
A). steel fails first B). concrete fails first
C). steel and concrete fails at the same time D). None of above
vi. Architect want to use a 300 × 500 RC beam (simply supported) at front porch and the design moment
is M* = 160 kN.m, which of the following combination satisfies the best all ACI code design criteria
(i.e. strength, safety, serviceability). Use f´c = 30 MPa, fy = 500 MPa, and φ = 0.85. (4 marks)
A). 2HD32 B). 2HD19
C). 2HD16 D). None of the above
vii. When designing a reinforced concrete beam to satisfy the “B1: Structures” clause of the building
act, what limit states must be considered? (2 marks)
A). durability B). strength, serviceability
C). economy D). all of above
viii. For a 10 m long singly reinforced simply supported rectangular RC beam which is subjected to
substantial moment demand, the preferred size of the beam required to satisfy the serviceability
limit state (i.e. deflection control) only is. (2 marks)
A). 300, 650 B). 200, 650
C). 200, 400 D). 200, 500

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Problem 2.2
i. A singly reinforced concrete beam will have a strength ____________ than that of doubly reinforced
concrete beam with same size. (2 Marks)
A). smaller B). larger
C). same D). none of above
ii. In a doubly reinforced beam the compression steel fails if the maximum stress in steel (f′s)
reaches___________. (2 Marks)
A). f′c B). equal to fy
C). 0.5fy D). an unpredictable random stress value
iii. What is more economical way of increasing the flexural strength of a reinforced concrete beam?
(2 Marks)
A). adding compression steel B). increasing the height of the beam
iv. A typical idealized stress-strain curve for steel used in analysis/design of RC members is shown in
Figure 2.1. Label the points 1 to 4 from available options A to D by matching letters from list Y to
numbers of list X. (4 Marks)
List X
1.
Figure 2.1. Stress-strain model for reinforcement steel
2.
3.
4.
v. For a doubly reinforced concrete beam, the neutral axis depth ______ if the compression steel is
increased. (2 Marks)
A). increases B). decreases
C). stays same D). None of above
vi. A larger concrete cover used in a RC beam would ________ of the beam. (2 Marks)
A). improve corrosion protection B). improve fire protection
C). result in wider flexural cracks D). all of the above
fs
1
3
2
4
εs
List Y
A). fy
B). εy
C). Es
D). f′c

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vii. When designing a doubly reinforced RC beam, f′s was found to be 250 MPa and A′s was calculated
to be 1020 mm2
. For this beam the area of steel that would need to be added to the tension steel
is _________. Use fy = 500 MPa. (2 Marks)
A). 1025 mm2
C). 510 mm2
B). 2040 mm2
D). none of the above
viii. For a RC beam, a ductile tensile failure of steel reinforcement is a preferred when compared to
concrete crushing in compression because it does provide warning prior to its failure. (2 Marks)
□ True □ False
Problem 2.2
In this problem use concrete compressive strength of 30 MPa (f´c = 30 MPa) and steel yield strength of
500 MPa (fy = 500 MPa). Use a strength-reduction factor of 0.85 (φ = 0.85) as recommended in NZS
3101 for a tension controlled section. Note that each part of this question is independent of the other
parts i.e. data required for to solve each part is given in that part.
a). What is the nominal moment capacity of the beam shown in Figure 2.1. (8 Marks)
Fig. 2.1. Beam cross section for Problem 2.2(a)
b). What is the maximum vertical point load (Ed) that the beam cross-section shown in Figure 2.1 can
take without exceeding the ultimate strength limit state), in addition to the self-weight of the beam?
The load is to act at the center of the beam when used to span over an opening of 8 m (see Fig. 2.2 for
statical diagram. Use the density of reinforced concrete (γc) of 24 kN/m3
. (4 Marks)
Hint: For a bare minimum requirement of ULS, φMn = M*where M* = EdL/4; L = span of the beam.
Fig. 2.2. Beam cross section for Problem 2.2(b)
400 mm
540mm
6HD25
600mm
Ed
4.0 m
A C
B
4.0 m

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c). Perform rebar detailing check and determine the number of layers required to place 4HD32+2HD29
(total 6 bars) main bars in a 300 mm wide and 500 mm deep cantilever beam. Draw a cross section
sketch of the beam, showing longitudinal bar diameter and number of bars, number of layers, cover
used, and overall concrete dimensions. Use a maximum nominal aggregate size of 25 mm, a minimum
concrete cover of 30 mm required from durability standpoint, and D10 stirrups in your calculations. You
may also use the design table. (8 Marks)
Problem 2.3
a). What is the nominal moment capacity of the beam shown in Figure 2.3. (15 Marks)
Fig. 2.3. Beam cross section for Problem 2.3(a)
b). What is the maximum vertical point load (Ed) that the beam cross-section shown in Figure 2.4 can
take without exceeding the ultimate strength limit state), in addition to the self-weight of the beam?
The load is to act at the center of the beam when used to span over an opening of 8 m (see Fig. 2.2 for
statical diagram. Use the density of reinforced concrete (γc) of 24 kN/m3
.
(5 Marks)
Hint: For a bare minimum requirement of ULS, φMn = M*where M* = EdL/4; L = span of the beam.
Problem 2.4
a). Design steel reinforcement for a rectangular (400 × 900 mm2
) concrete beam subjected to a
maximum positive moment of 920 kN.m at critical section i.e. mid-span (M* = 920 kN.m). Use concrete
cover of 30 mm and D10 stirrups in your calculations. Determine the required steel reinforcement to
satisfy NZS3101 requirements of safety and ultimate strength. Your answer should include selected bar
combinations for compression (if any) and tensile steel reinforcement. (10 Marks)
300 mm
810mm
6HD29
900mm
60 mm
2HD29

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b). Perform rebar detailing check and determine the number of layers required to place 4HD32+2HD29
main bars in a 300 mm wide and 500 mm deep cantilever beam. Also draw a cross section sketch of the
beam showing longitudinal bar diameter, number of layers, cover used, and overall concrete
dimensions. Use a maximum nominal aggregate size of 19 mm, min. concrete cover of 30 mm, and D10
closed ring stirrups in your calculations. (04 Marks)
c). Calculate what is the maximum load (in addition to its self-weight) that a rectangular (300 × 600
mm2
) singly reinforced concrete beam, having D13 closed ring stirrups on 150 mm on centers. Use a
maximum nominal aggregate size of 25 mm and used ρw = 0.015. (06 Marks)
Problem 2.5
a). Determine the required size of a rectangular beam section, i.e. select b, d, h (use h = 2.5b), and the
required tension reinforcement, at mid-span for a 6.7 m long simply supported rectangular beam. The
beam supports its self-weight (SW), which can be estimated as SW = 0.15 × (SDL+Q) to start the design
calculation. Use a superimposed permanent actions (SDL) of 18.5 kN/m and a uniform service imposed
action (Q) of 29 kN/m. The concrete compressive strength is 30 MPa, and the tensile yield strength of
the steel reinforcement is 500 MPa. For this question use a singly reinforced cross-section and ignore
contribution from top hanger bars. (12 Marks)
b). Perform reinforcement detailing check and determine the number of layers required to place 5HD29
main bottom bars in a 350 mm wide and 500 mm deep continuous beam. Draw a cross section sketch
of the beam showing longitudinal bars, number of layers, cover used, and overall concrete dimensions.
Use a maximum nominal aggregate size of 19 mm, concrete thickness until stirrup bar surface of
30 mm, and D10 closed ring stirrups in your calculations. (03 Marks)
c). Calculate what is the maximum shear force that a rectangular (300 × 600 mm2
) singly reinforced
concrete beam, having D13 closed ring stirrups on 150 mm on centers can take per criterion given in
NZS 3101. Use a maximum nominal aggregate size of 25 mm and used ρw = 0.015. (05 Marks)
Problem 2.6
a). Design a cantilever reinforced concrete rectangular beam to resist a negative bending moment (Mu)
of 690 kN.m and determine concrete dimensions and area of flexural steel required to provide the
required moment strength following the NZS 3101 provisions. Use concrete cover of 30 mm and D10
stirrups in your calculations. Your answer should include selected bar combinations for compression (if
any) and tensile steel reinforcement. (10 Marks)

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b). Perform checks for minimum and maximum reinforcement requirements as per NZS 3101 provisions
for a beam requiring ρ = 0.019. Comment whether there are any problems and if there are any then
how these problems can be addressed? (04 Marks)
c). For a rectangular reinforced concrete beam, being 300 × 500 mm2
in size, the area of tension steel
required was found to be 2006 mm2
. Select a bar combination, perform checks for reinforcement
placement, and draw a sketch showing proposed cross sections of the beam, showing reinforcement
placement in the beam. Use a maximum nominal aggregate size of 25 mm and used ρw = 0.015.
(06 Marks)

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Problem 3.1
i. Shear failure is ______ in nature and therefore typically a _______ strength reduction factor is used
in design. (4 Marks)
A). brittle, smaller B). ductile, larger
C). brittle, larger D). ductile, smaller
ii. If V* is the shear demand at a critical section and the nominal shear capacity of a reinforced concrete
beam is Vn then the NZS 3101 criterion for ULS can be written as, (2 Marks)
A). Vn > V* B). φVn > V*
C). φVn ≤ V* D). Vu ≤ φV*
iii. The shear capacity of beam A (having u shaped D10 stirrups at 150 mm spacing) is _____ than shear
capacity of beam B (that have u shaped D13 stirrups at 300 mm spacing), if both beams have same
cross sectional properties. Use fyt = 500 MPa. (4 Marks)
C). same D). none of the above
iv. The shear demand V*, for a reinforced concrete beam in a cast in-situ concrete frame, is typically
determined as the value of shear force at a __________. (2 Marks)
A). distance h from the column centreline B). distance d from the column centreline
C). distance h from the column face D). distance d from the column face
v. What would you do when
Vn
bw.d
> smaller of (8 MPa; 0.2f'
c)? Where Vn is the required nominal shear
strength for a reinforced concrete section. (2 Marks)
A). use maximum spacing of stirrups B). revise cross-section
C). calculate stirrup spacing s for use D). none of the above
vi. The photo of a reinforced concrete beam at the conclusion of a two point bending test is shown
below in Figure 3.1. Where is the dominant flexural damage in the beam? (2 Marks)
A). diagonal cracks near support in web B). bottom vertical cracks near mid-span
C). concentrated concrete crushing at supports D). none of the above
Figure 3.1. Damage patterns observed in a beam test

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vii. The damage pattern in the beam of short question ii fits well with shear force and bending moment
diagrams for applied loading, where shear stresses are maximum in ________ and bending moment
is maximum in _______. (2 Marks)
A). middle part, end parts B). end parts, middle part
C). middle part, middle part D). none of the above
viii. Typically, shear stress is ______ and bending stress is _________ at the compression face
along a section in the middle portion of a simply supported RC beam. (2 Marks)
A). zero, maximum C). maximum, zero
B). zero, zero D). none of the above
Problem 3.2
Use of design charts is also permitted. Use the strength reduction factor, φ of 0.75, f´c = 30 MPa, and
fyt = 500 MPa. Determine nominal shear strength (Vn) of a rectangular (300 × 600 mm2
) singly reinforced
concrete beam, having D10 closed ring stirrups spaced at 150 mm on centers. Use a maximum nominal
aggregate size of 25 mm and used ρw = 0.015. (15 marks)
Problem 3.3
Use of design charts is also permitted. Use φ = 0.75, f´c = 30 MPa, nominal aggregate size = 25 mm,
ρw = 0.015, and fyt = 500 MPa.
a). For the 200×400 mm2
reinforced concrete beam, having boundary conditions shown in Figure 3.1,
determine the spacing of D10 closed ring stirrups to provide the required shear strength at the critical
section. The applied factored load wu is 25 kN/m. (15 marks)
Figure 3.1. Shear force diagram for Problem 3.3
133 kN
133 kN

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b). Draw the sketch of beam cross-section designed in part ‘a’ of this question, showing the stirrup
shape, stirrup diameter, and recommended stirrup spacing. Use an assumed distance from centroid of
main steel to face the beam for one layer placement of 60 mm. (5 Marks)
Problem 3.3
Use of design charts is also permitted. Use φ = 0.75, f´c = 30 MPa, nominal aggregate size = 25 mm,
ρw = 0.015, and fyt = 500 MPa.
a). The shear force for a reinforced concrete beam calculated at the face of a 400 mm wide column (bc)
is 360 kN. The beam has an effective depth (d) of 440 mm and is subjected to a uniformly distributed
gravity load of 45 kN/m. Determine the shear demand (V*) at a distance d from the face of the colum
and also calculate the minimum shear strength required from the RC section to satisfy the ULS criterion
of NZS 3101. (6 Marks)
b). Determine spacing of two legged ring shaped stirrups to provide a nominal shear strength (Vn) of
590 kN at the critical section in a beam with width (b) 400 mm and height (h) of 300 mm. Use an
assumed distance from centroid of main steel to face the beam of 60 mm.
(10 Marks)
c). Draw the cross-section sketch of a reinforced concrete beam, which is 600 mm wide and 300 mm
high. The sketch must show D10 stirrups spaced at 150 mm on centres and 4HD29 bars (tension steel)
placed near the bottom face and 4HD16 bars near the top face (compression steel). (4 Marks)

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Problem 4.1
i. Shear failure is ______ in nature and therefore typically a _______ strength reduction factor is used
in design. (2 Marks)
A). brittle, smaller B). ductile, larger
C). brittle, larger D). ductile, smaller
ii. Slenderness ratio indicates the buckling potential of a column, which is calculated using the relation.
(2 Marks)
A).
klu
r
B).
k.r
lu
C).
lu
r
D). none of the above
iii. Slenderness ratio of a 4 m high 500x500 mm2
reinforced concrete column (k = 1) is, (4 Marks)
A). 26.7 B). 32.0
C). 45.0 D). none of the above
iv. For columns when stress in concrete (fc) is less than 0.5f′c, the stress in steel (fs) will be ______. If n
is modular ratio and f’c is the compressive strength of concrete. (2 Marks)
A)
1
𝑛
fs
B). nfc
C).
1
𝑛
fc
D). None of above
v. A concentrically loaded column can take ________ axial load than an eccentrically loaded column.
(2 Marks)
A). less B). more
C). almost same D). None of above
vi. A tied column typically would have __________ strength than a spiral column of the same cross
sectional size. (2 Marks)
C). same D). none of the above
vii. A 300 mm2
square pedestal of concrete with f’c = 80 MPa concrete will have an axial load capacity
____ times the same size column made of concrete with f’c = 30 MPa, assuming that the steel area
and strength is same in both pedestals. (2 Marks)
A). 2.20 B). 2.66
C). 1.66 D). None of above
viii. Use f′c = 28 MPa, and fy = 420 MPa. Analysis of a frame gives the axial force Pn = 1280 kN, and a
moment of Mn = 500 kN.m acting at the top of a 500 mm square column. Assuming a cover of

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75 mm and placement of steel equally on all four faces of the column, the longitudinal steel
requirement can be satisfied by providing 4HD29. (2 Marks)
□True □False
ix. The longitudinal bars in columns should not be smaller than HD13 and a minimum concrete cover
of 40 mm should be maintained, as recommended by ACI 318 code provisions. (2 Marks)
□True □False
Problem 4.2
Use φ = 0.70, f´c = 30 MPa, nominal aggregate size = 25 mm, ρw = 0.015, and fyt = 500 MPa. Note that
each part of this question is independent of the other parts i.e. data required for to solve each part is
given in that part. Use of design charts and interaction diagrams published in NZ reinforced concrete
design hand book is permitted.
a). Design a short square tied column to support an axial design load (N*) of 1460 kN and negligible
moments. Using roughly a longitudinal steel ratio of ρt = 1.2%, with steel bars equally placed on all four
sides of the column. Select the required size of the column to avoid material failure. (12 Marks)
b). Calculate the area of steel required for a column 500×500 mm2
in size that supports an axial design
load (N*) of 1960 kN and a design moment (M*) of 540 kN.m acting along shorter axis of the column.
Select a combination of longitudinal steel bars and place these equally on all four faces. The distance
from centroid of steel bars to face of the column is 75 mm. (08 Marks)
Problem 4.3
Use φ = 0.70, f´c = 30 MPa, nominal aggregate size = 25 mm, ρw = 0.015, and fyt = 500 MPa. Note that
each part of this question is independent of the other parts i.e. data required for to solve each part is
given in that part. Use of design charts and interaction diagrams published in NZ reinforced concrete
design hand book is permitted.
a). Design a short square tied column to support an axial design load (N*) of 1060 kN and negligible
moments. Using roughly a longitudinal steel ratio of ρt = 1.8%, with steel bars equally placed on all four
sides of the column. Select the required size of the column to avoid material failure. (12 Marks)
b). Calculate the area of steel required for a column 400×450 mm2
in size that supports an axial design
load (N*) of 1960 kN and a design moment (M*) of 540 kN.m acting along shorter axis of the column.
Select a combination of longitudinal steel bars and place these equally on all four faces. The distance
from centroid of steel bars to face of the column is 60 mm. (08 Marks)

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Problem 5.1
Design the vertical reinforcement for a 1.8 meter high (H = 1.8 m) cantilevered reinforced concrete
masonry retaining wall shown in Figure 5.2. Use grout compressive strength (f´m) = 12 MPa;
reinforcement steel tensile yield strength (fy) = 500 MPa; density of soil (ρs) = 18 kN/m3
; surcharge
pressure (Q) = 10 kPa; active soil pressure coefficient (ka) = 0.35; and strength-reduction factor
(φ) = 0.85.
Where: CMU = concrete masonry unit; Fs
= resultant force due to surcharge; and Fa
= resultant force
due to active soil pressure.
Figure 5.1. Cantilever reinforced concrete masonry retaining wall
Problem 5.3
Use grout compressive strength (f´m) = 12 MPa; reinforcement steel tensile yield strength
(fy) = 500 MPa; density of soil (ρs) = 18 kN/m3
; surcharge pressure (Q) = 10 kPa; active soil pressure
coefficient (ka) = 0.35; and strength-reduction factor (φ) = 0.85.
a). If vertical reinforcement used in the retaining wall shown in Figure 5.1 is HD16 bars @ 400 mm o.c.
then determine the nominal moment capacity of 1 m wide strip of the retaining wall at ULS using
verification method detailed in NZS 4230. (12 Marks)
b). Use H = 2.5 m for the retaining wall shown in Figure 5.1 and calculate the overturning moment (M*)
from this soil loading, ignoring surcharge pressure (Q = 0 kPa) because there is no surcharge weight in
this case. Does the block work retaining wall have adequate moment capacity (φMn) to resist this design
action moment, M*? (08 Marks)
Fs = ka.Q.H
H
Fa
= ½.ka
.ρs.H2
0.5H
0.33HQ
ka
ρs
H/2.5
Series 20 CMU
900 mm

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Problem 5.4
Use grout compressive strength (f´m) = 12 MPa; reinforcement steel tensile yield strength
(fy) = 500 MPa; density of soil (ρs) = 18 kN/m3
; surcharge pressure (Q) = 9.5 kPa; active soil pressure
coefficient (ka) = 0.35; and strength-reduction factor (φ) = 0.85.
a). If vertical reinforcement used in the retaining wall shown in Figure 5.1 is HD12 bars @ 400 mm o.c.
then determine the maximum height H of the retaining wall that can be used safely without exceeding
the ULS criterion recommended in in NZS 4230. (12 Marks)
b). Use H = 2.2 m for the retaining wall shown in Figure 5.1 and calculate the overturning moment (M*)
from this soil loading. Does the block work retaining wall have adequate moment capacity (φMn) to
resist this design action moment, M*? (08 Marks)

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Problem 6.1
In this problem use concrete compressive strength (f´c) of 30 MPa, tendon tensile yield strength
(fpy) of 1200 MPa, prestress force (P) is 950 kN, and density of concrete (ρc) is 25.2 kN/m3.
Assume that a straight strand profile is used.
Figure 6.1. Prestressed beam cross-section and statical diagram
a). A 6 meter long simply supported beam (L = 6 m) with cross section is shown in Figure 6.1. Determine
the magnitude of extreme (top and bottom) stresses at the beam mid-span location immediately after
the prestress application. Note that this calculation checks stresses prior to applying any imposed
permanent (G) or imposed actions (Q). Use self-weight of the beam in your calculations. (10
Marks)
b). Calculate the maximum service load moment M*, that the beam can support without exceeding a
tensile stress of 0.7√𝑓′ 𝑐 on tension face and 0.45𝑓′ 𝑐 on compression face. (08 Marks)
C). List down the reasons and mechanisms that causes immediate prestress losses. (02 Marks)
Problem 6.2
400 mm
540mm
600mm
300mm
A C
L
U kN/m
400 mm
540mm
600mm
300mm
100 mm
A C
L
U kN/m

20
a). A 6 meter long simply supported beam (L = 6 m) with cross section is shown in Figure 6.2. Determine
the magnitude of extreme (top and bottom) stresses at the beam mid-span location due to
posttensioning force only. Note that this calculation checks stresses prior to applying any permanent
(G) or imposed actions (Q). Ignore self-weight of the beam as well. (10 Marks)
b). Calculate the maximum service load moment M*, that the beam can support without exceeding a
tensile stress of 0.7√𝑓′ 𝑐 on tension face. (08 Marks)
C). List five sources of immediate and long-term prestress losses. (02 Marks)
Problem 6.3
a). A 7.8 meter long simply supported beam (L = 7.8 m) with cross section is shown in Figure 6.3.
Determine the magnitude of extreme (top and bottom) stresses at the beam mid-span location due to
posttensioning force only. Note that this calculation checks stresses prior to applying any permanent
(G) or imposed actions (Q). Ignore self-weight of the beam as well. (10 Marks)
b). Calculate the maximum span that the beam can be used for, without exceeding a tensile stress of
0.7√𝑓′ 𝑐 on tension face. Use a service load (in addition to self-weight of the beam) of 16 kN/m.
(08 Marks)
C). List two types of long term losses and discuss strategies to minimise these losses. (02 Marks)
600 mm
840mm
900mm
400mm
150 mm
A C
L
U kN/m

Problems-Structural Analysis_Najif Ismail

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