Transcript WORKSHEET 2 FORCES, MOMENTS, LOADS & SUPPORTS

WORKSHEET 2
FAILURE, STRESS AND STRAIN
Q1
What happens to an element under:
a) tension?
material tends to be pulled apart
element stretches - becomes longer and thinner
finally breaks
b) compression? particles pushed against each other
element shortens - becomes squatter
finally breaks
slender elements may buckle first
Q1
What happens to an element under:
c) shear?
particles slide relative to each other
material tears
d) bending?
side closest to load shortens and comes under
compression
side furthest from load lengthens and comes
under tension
neutral axis remains same length
Q2
When does buckling occur
when a slender element is put under compression
Q3
Can a compression member carry more or less load before
it buckles (i.e. is the buckling load greater or smaller if:
a) the member is longer?
carries less load - buckling load is smaller
b) the member is more slender?
carries less load - buckling load is smaller
buckling load is a function of the slenderness ratio
(the slenderness ratio is the ratio between the
effective length and the width of the member)
Q3
Can a compression member carry more or less load before
it buckles (i.e. is the buckling load greater or smaller if:
c) it is rigidly restrained at its ends?
carries more load - buckling load is greater
reduces the effective length by 1/2
d) one of its ends is free?
carries less load - buckling load is smaller
increases the effective length by 2
Q4
Timber studs in a timber-framed wall are usually 100 x 50 mm.
The framing includes one or two rows of noggings.
What do the noggings do?
The studs would tend to buckle in the weaker direction
The noggings support the studs in the weaker direction
This results in a slenderness ratio roughly equal in
both directions
Q5
What happens to an unreinforced concrete beam when loaded?
a) the beam bends - the bottom face
comes under tension due to bending
concrete is weak in tension
the beam cracks due to bending
b) the beam bends - shear produces
diagonal tension
concrete is weak in tension
the beam cracks due to shear
Q6
Name the three basic states of stress:
a) tension
state of stress where material pulled apart
b) compression
state of stress where material crushed
c) shear
state of stress where parts of material slide
relative to each other
Q7
Name another very important state of stress:
bending
state of stress where compression and tension
exist in different fibres of same element
(producing a moment effect)
C
T
Q7
Name another very important state of stress:
buckling
state of stress where compression acts
on slender member
Q8
What happens to an element that is stressed:
it deforms
changes in shape or dimensions or both
results in strain
change may be reversible or irreversible
(elastic or inelastic)
Q9
Give units where applicable
a) what is stress?
internal force intensity as result of external forces
force per unit area
b) what are the units of stress?
Pa, kPa, MPa
1Pa = 1 N / m2 1MPa = 1 N / mm2
Q9
Give units where applicable
c) what is strain?
change in size or shape relative to original state,
e.g. change in length relative to original length
d) what are the units of strain?
e = DL / L - dimensionless
Q10
a 20mm dia. high-strength steel cable 5 m long has a weight of 50 kN
added to its end. Neglecting the self-weight of the cable and given that the
cable lengthens by 4mm:
a) what is the stress in the cable?
area of cable = p x 20 x 20 / 4 = 314.16 mm2
stress = F / A
stress = 50 / 314.16
(keep units to Newtons, MPa and mm2 for simplicity)
stress = 50000 / 314.16 = 159.2 N/mm2
= 159.2 MPa
b) what is the strain in the cable?
strain = DL / L
strain = 4 / 5000
= 0.0008 (8 x 10-4)
Q10
c) Given that the maximum allowable tensile stress for
high-strength steel is 1000MPa, is the cable strong enough?
stress in cable = 159.2 MPa
maximum allowable stress of steel = 1000 MPa
stress in cable < maximum allowable stress
yes - the cable is strong enough
Q11
When a column is under load:
a) What factors do we have to take into consideration?
(i) whether buckling will occur
(the slenderness ratio of the column)
(ii) whether it is strong enough to take the load w.r.t
its compressive strength
(material strength and x-sectional area)
b) What is the first means of failure we should check for?
whether buckling will occur
Q12
A reinforced concrete column 400 x 400 mm and 3.5 m high
is subject to a load 160 kN.
Given that the column shortens by 0.07 mm:
a) What is the stress in the column?
stress = Force / Area
= 160 / (0.4 x 0.4)
= 1000 kN/m2
= 1000 kPa (1 MPa)
Q12
Given that the column shortens by 0.07 mm:
b) What is the strain in the column?
strain = DL / L = 0.07 / 3500
= 0.00002
= 2 x 10 -5
c) Given that the maximum allowable stress of the concrete
is 20MPa, is the column strong enough?
max allowable stress
= 20 MPa
actual stress
= 1 MPa
since actual stress < max allowable stress
yes column is strong enough as regards compressive strength
Q12
d) Could you reduce the area of the column?
Considering strength only - max allowable stress = 20 MPa
Min Area = Force / Max Allow stress
= 160 (kN) / 20 (MPa)
(keep units to Newtons, MPa and mm2 for simplicity)
= 160,000 (N) / 20 (MPa = N / mm2 )
= 8000 mm2
e.g 90 x 90 mm
However a 90 x 90 mm column, apart from being difficult to build,
would be very slender and subject to buckling