Transcript No Slide Title

WORKSHEET1
Loads, Supports, Moments
and Equilibrium
A. loads
Q1. a) what is the main force acting on and in buildings?
gravity
b) in what direction does it act?
vertically downwards
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
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
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
A. loads
Q4. What makes up the total load on a structure
Total Load = Dead Load + Live Load + Self-Weight
A. loads
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 )
A. loads
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)
B. supports
Q7. Draw and name the reactions that can be produced by:
a) a fixed support
b) a simple support
M
H
3 - V, H & M
V
1-V
V
c) a roller support
1-V
V
d) a pinned support
H
2-V&H
V
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
C. moments
W
W1
200N
Q9. Given the beam loaded as shown,
calculate the weight, W required
for equilibrium
W2
100N
A
4m
2m
4m
Taking moments about A
clockwise moments
=
200*2 + 100*6
=
400 + 600 =
1kNm
For equilibrium ∑M = 0
anticlockwise moments =
W*4
=
W
=
1kNm
1000
250N
C. moments
4kN 8kN 10kN6kN
Q10. Given the simply supported beam
loaded as shown:
calculate the reactions, RL and RR
RL
RR
1m 1.5m 2m 1.5m
For equilibrium ∑M = 0
0.5m
taking moments about RL
clockwise moments
= 4*1 + 8*2.5 + 10*4.5 + 6*6
= 4 + 20 +
45
+ 36
= 105 kNm
RR
=
16.15 kN
RL
=
11.85 kN
anticlockwise moments = RR * 6.5
For equilibrium ∑M = 0
RR * 6.5
=
105
For equilibrium ∑V = 0
RR + RL =
28 kN
RL =
28 - 16.15
C. moments
Q11. Given a cantilever beam 8m long loaded
with a Uniformly Distributed Load
M
(UDL) of 3 kN / m
3 kN/m UDL
8m
determine the moment reaction
at the support
total load on beam
W
=
3*8 =
24 kN
can be taken to act at centre of beam
4m
moment M =
24 * 4 =
96 kNm
4m
C. moments
2kN
1.5kN/m
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.
2kN/m
RL
RR
4m 4m
6m 2m
6kN 16kN 2kN
What are the values of the reactions, a) RL, b) RR
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
RL
RR
2m 2m
Anticlockwise moments = RR*6
∑M = 0
RR*6 = 92
RR = 15.3 kN
∑V = 0
RR+ RL = 6 + 16 + 2 = 24
RL = 8.7 kN
4m
C. moments
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.
Weight
20kN
16kN
2m
A
3m
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
C. moments
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.
Weight
20kN
16kN
2m
A
3m
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
e) will the building overturn?
yes since 32 > 30
C. moments
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.
Weight
20kN
16kN
2m
A
3m
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
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
D. equilibrium
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)