1. WORKSHEET1 Loads, Supports, Moments and Equilibrium

2. A. loads Q1. a) what is the main force acting on and in buildings?
gravity
b) in what direction does it act?
vertically downwards

3. A. loads Q2. a) what do loads do?
tend to destabilise building - overturn
tend to break elements
deform elements - change of shape, deflection
b) what must the structure do?
produce reactions - provide equilibrium
resist tendency to break - be strong enough

4. A. loads Q3. What are: a) Static loads?
basically loads which when applied, do not move
remain during the life of the building
may be dead loads, live load (movable but static),
settlements, thermal effects
b) dynamic loads
basically loads which move - change over time
continuous - e.g. earthquakes, wind
impact / instantaneous

5. A. loads Q3. What are: c) Dead loads?
static - permanent loads - fixed (mostly vertical)
weight of structure and elements, heavy built-ins & equipment
d) Live loads
static loads which may or may not be acting all the time
occupants, contents, moveable partitions, snow
e) What other loads are there?
wind, earthquake, thermal, settlement, impact

6. A. loads Total Load = Dead Load + Live Load + Self-Weight
Q4. What makes up the total load on a structure
Total Load =
Dead Load +
Live Load +
Self-Weight

7. A. loads kN kN / m kPa (kN / m2 ) Q5. What are the units for:
a) a point or concentrated load? kN
b) a load distributed over a length?
kN / m
c) a load distributed over an area?
kPa (kN / m2 )

8. A. loads 1 kPa up -suction (roof pitch < 30o)
Q6. a) In a non-cyclone area what is approximately the magnitude
of the wind loads?
1 kPa
b) If the roof on a house has a pitch of 27o, what is the
direction of the wind load on the roof?
up -suction (roof pitch < 30o)
c) If the roof is of lightweight construction, weighing 0.3 kPa,
what considerations need be taken into account?
(i) securing the roof down - more nails, ties, etc
(ii) making the roof heavier
(may not be a design option)

9. B. supports M H V 3 - V, H & M 1 - V V 1 - V V 2 - V & H H V
Q7. Draw and name the reactions that can be produced by: M
a) a fixed support
3 - V, H & M H V
b) a simple support
1 - V V
c) a roller support
1 - V V
d) a pinned support
2 - V & H H V

10. B. supports
Q8. Draw the reactions that can be produced by the following
structural systems. State whether the system is a mechanism,
statically determinate or statically indeterminate
(a)
(b)
(c)
(d)
(e)
(f)
a) statically determinate
d) statically indeterminate
b) statically indeterminate
e) statically determinate
c) statically indeterminate
f) mechanism

11. C. moments 1kNm W * 4 = 1000 W = 250N A W1 200N W2 100N W 4m 2m
Q9. Given the beam loaded as shown,
calculate the weight, W required
for equilibrium
Taking moments about A
clockwise moments =
200* *6
1kNm
= =
For equilibrium ∑M = 0
anticlockwise moments = kNm
W * 4 =
W =
250N

12. C. moments R L = 105 kNm RR * 6.5 = 105 RR = 16.15 kN RR + RL = 28 kN
Q10. Given the simply supported beam
loaded as shown: R L 1m 2m
1.5m
0.5m
4kN
8kN
10kN
6kN
calculate the reactions, RL and RR
For equilibrium ∑M = 0
taking moments about RL
clockwise moments
= 4*1 + 8* * *6
= 105 kNm =
anticlockwise moments = RR * 6.5
RR * 6.5 =
RR = kN
For equilibrium ∑M = 0
For equilibrium ∑V = 0
RR + RL = 28 kN
RL =
RL = kN

13. C. moments M 24 kN 96 kNm Q11. Given a cantilever beam 8m long loaded
with a Uniformly Distributed Load
(UDL) of 3 kN / m 8m
3 kN/m UDL M
determine the moment reaction
at the support
total load on beam W =
24 kN
3 * 8 =
can be taken to act at centre of beam 4m
moment M = * 4 =
96 kNm

14. C. moments = 92 kNm RR = 15.3 kN RL = 8.7 kN 2kN/m 1.5kN/m 2kN R 4m 6m
Q12. Beam loadings in real structures are
often complex.
Consider a beam with a point load of 2kN on the end of an
overhang with a UDL of 1.5 kN/m distributed over 2/3 of the
main span. The beam also carries its own self-weight of 2kN/m.
What are the values of the reactions, a) RL, b) RR
6kN
2kN R L 2m 4m
16kN
Take moments about one of the reactions, e.g. RL (or RR )
Clockwise moments = (1.5*4)*2 + (2*8)*4 + 2*8
= 92 kNm
Anticlockwise moments = RR*6
∑M = 0
RR*6 = 92
RR = 15.3 kN
∑V = 0
RR+ RL = = 24
RL = kN

15. C. moments = 32 kNm Weight 20kNA
Q13. The drawing on the right shows a lightweight
prefabricated building. The total weight of the
(empty) building is 20kN. The line of action of the
wind load is 2m above the ground.
Given a wind load of 16kN as shown:
a) what is tending to overturn the building?
the wind load of 16kN causes an overturning moment
b) what is the overturning moment?
in this case the overturning moment is the clockwise moment about A caused by the wind
= 32 kNm
overturning moment = 16 * 2

16. C. moments = 30 kNm yes since 32 > 30 Weight 20kNA
Q13. The drawing on the right shows a lightweight
prefabricated building. The total weight of the
(empty) building is 20kN. The line of action of the
wind load is 2m above the ground.
Given a wind load of 16kN as shown:
c) what is restraining the building?
The weight of the building, 20kN, causes a restraining moment
d) what is the restraining moment?
the restraining moment is the anticlockwise moment as a result of the weight of the building
= 30 kNm
restraining moment = 20 * 1.5
yes since 32 > 30
e) will the building overturn?

17. C. moments 3m 2m
16kN
Weight
20kN A
Q13. The drawing on the right shows a lightweight
prefabricated building. The total weight of the
(empty) building is 20kN. The line of action of the
wind load is 2m above the ground.
Given a wind load of 16kN as shown:
f) suggest two options that will make the building safer
(i) increase the weight of the building to at least 32/1.5 = 21.4kN
(ii) lower the height of the building so that the action of the wind is
lowered by at least 125 mm (to 1.875m above ground)
(iii) make the building base wider - at least 3.2 m wide
(iv) tie the building down - fix it to the ground. It will act as a cantilever

18. D. equilibrium Q14. What are the three equations of equilibrium and
what do they mean? a)
SV = 0
the sum of all the vertical forces is equal to zero (at any point)
the total downward forces equal the total upward forces
the structure doesn’t move up or down b)
SH = 0
the sum of all the horizontal forces is equal to zero (at any point)
the total forces acting to the right equal the total forces
acting to the left
the structure doesn’t move to the left or right c)
SM = 0
the sum of all the moments (about any point)
the total clockwise moments equal the total anticlockwise moments
the structure does not rotate/spin

19. D. equilibrium a) cross-bracing b) knee-bracing c) rigid joints
Q15. Given the post-and beam arrangement as shown, describe
three ways of stabilising it. Draw and name them.
a) cross-bracing
b) knee-bracing
c) rigid joints
d) solid infill (shear panels)
e) build-in posts
(rigid joints)