WORKSHEET 7 AXIALLY LOADED MEMBERS

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WORKSHEET 7AXIALLY LOADED MEMBERS
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Q1
Are tension structures or compression
structures more efficient when loaded axially ?
tension structures
Q2
why ?
tension structures are not subject to
buckling they pull straight - can use thin
cables can use stress Force / Area
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Q3
What is meant by
(a) a short column
a column which will fail in true compression
(b) a long column
a column which buckles before full compressive
strength is reached
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Q4
What affects the buckling load (or buckling
stress)?
(a) the slenderness ratio - l/r (or l/B rect.
sections)
the slenderness ratio takes into account the
effective length, l and the stiffness (radius of
gyration) of the X-section r ? (I/A)
buckling load inversely proportional to
slenderness ratio i.e. greater the slenderness
ratio - more will tend to buckle
(b) the modulus of elasticity, E materials
with higher E will buckle less
(c) end fixing conditions - restraints but
included in slenderness ratio - effective length
free end Eff Length 2 x l, fixed ends Eff
Length 0.5 x l
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Q5
What are good sections for columns?
(i) sections which have similar radii of
gyration in all directions
(ii) sections in which the major part of the
material is a far from the Centre of
Gravity as possible
Q6
Why?
(i) so that they do not buckle in a weak
directions
(ii) to use the material efficiently
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Q7
What are two effects which can cause a pier to
overturn?
(a) a horizontal load
(b) an eccentric vertical load
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Q8
What is the middle-third rule?
the middle-third rule tells you that as long as
the resultant reaction falls in the middle-third
of the base of the pier then no tension will
develop in the pier.
if the middle-third rule holds the pier will not
lift off its base
there will be a factor of safety of gt3 if the
middle-third rule holds
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Q9 (a)
The diagram shows a heavy steel gate hung from a
hollow brick pier which weighs 8kN. Investigate
the stability of the pier.
(a) assume the pier is sitting on (but not stuck
to) a strong concrete footing. take
moments about the point X
(i) will the pier overturn?
No
Overturning Moment (clockwise)
1 kNm
M 1 x 1
Potential Stabilizing Moment (anticlockwise)
2.4 kNm
M 8 x 0.3
(ii) what is the margin of safety?
2.41
OTM can increase up to 2.4kNm before overturning
occurs
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Q9 (b)
(b) where is the resultant of the two loads?
155.6mm from X 144.4mm from centre
1 x 1000 R x h 8 x 300
9 x h 2400 -1000
h 1400 / 9
155.6
(i) is it within the middle third of the base?
No
(ii) is this what you would expect from (a)?
In (a) we assumed that there would be no crushing
of the leading edge of the pier. Under this
condition the middle-third rule gives a factor of
safety of gt3. For a factor of safety of 2.4 we
would expect the reaction to be just outside the
middle-third
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Q9 (c)
(c) calculate the stress distribution under the
pier
stress P/A (compressive part) M/Z (bending
part)
M P x e 1 x 1300 (or 9 x 144.4)
1300kNmm
Z bd2/6 600 x 6002 / 6
36 x 106 mm3
stress 9000 / (600 x 600) 1300000 / 36 x 106
0.025 0.036 MPa
(i) is it trying to develop tension on one side?
yes
on the gate side the stress is 0.061 MPa (61kPa)
- compression on the other side it would be
-0.011 MPa (11kPa) (tension)
since the interface cannot develop tension, a
redistribution would occur a different analysis
is required to find that the maximum compressive
stress would increase to 0.096 MPa
(ii) is this what you would expect from (b)?
yes
since the reaction is outside the middle third
you would expect tension to tend to develop
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Q9 (d)
(d) if you make the pier solid, it will be about
twice as heavy. Will this make it safer
against overturning?
yes
The potential stabilising moment would double
while the overturning moment remains the
same. No tension would develop (the reaction
would be within the middle third) and it would be
safer against overturning
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Q10(a)
A freestanding garden wall is 230mm thick and
1200mm high. The density of brick is 19kN/m3. The
wind load in this location is 0.5 kPa
(a) Find the location of the reaction on the base
weight of wall (of length 1m) 1.2 x 0.23 x 1 x
19
5.244 kN
0.6 kN
wind load on 1m length of wall 0.5 x 1 x 1.2
taking moments about A
overturning moment 0.6 x 600
360 kNmm
restraining moment 5.244 x 115
603.1 kNmm
5.244 x h 360 603.1
h 243.1/5.244
46.4 mm
(i) is it within the base?
yes
no
(i) is it within the middle third?
the reaction is 115 - 46.4 68.6mm from the
centre of the wall.
the middle third is 38.3mm from the centre of the
wall.
so the reaction is well outside the middle third.
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Q10(a)
A freestanding garden wall is 230mm thick and
1200mm high. The density of brick is 19kN/m3. The
wind load in this location is 0.5 kPa
(a) Find the location of the reaction on the base
weight of wall (of length 1m) 1.2 x 0.23 x 1 x
19
5.244kN
0.6kN
wind load on 1m length of wall 0.5 x 1 x 1.2
GRAPHICAL METHOD
X/600 0.6 / 5.244
X 0.6 x 600 / 5.244
X 68.6
the reaction is 68.6mm from the centre of the
wall.
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Q10(b, c)
(b) How wide would the footing have to be to
bring the reaction within the middle third?
Forgetting the weight and depth of the
footing, width of footing would have to be 6 x
68.6
412mm
We would probably make it 450mm wide. This is the
width of a common backhoe bucket.
(c) What other options are there for
increasing the stability of the wall?
(i) put a heavy coping on top (has to be wide
rather than high otherwise subject to wind)
(ii) make the wall thicker (expensive)
(iii) attached piers
(iv) zigzag plan (similar to (iii) but more
interesting