Intro to Structural Member Properties.ppt

Report
Introduction to Structural Member
Properties
Structural Member Properties
Moment of Inertia (I) is a mathematical property
of a cross section (measured in inches4) that gives
important information about how that crosssectional area is distributed about a centroidal axis.
Stiffness of an object related to its shape
In general, a higher moment of inertia produces a
greater resistance to deformation.
©iStockphoto.com
©iStockphoto.com
Moment of Inertia Principles
Joist
Plank
Beam
Material
A
Douglas Fir
B
Douglas Fir
Length Width Height Area
8 ft
1 ½ in. 5 ½ in. 8 ¼ in.2
8 ft
5 ½ in. 1 ½ in. 8 ¼ in.2
Moment of Inertia Principles
What distinguishes beam A from beam B?
Will beam A or beam B have a greater resistance to
bending, resulting in the least amount of deformation,
if an identical load is applied to both beams at the
same location?
Moment of Inertia Principles
Why did beam B have greater deformation than
beam A?
Difference in moment of inertia due to the
orientation of the beam
Calculating Moment of Inertia – Rectangles
Calculating Moment of Inertia
Calculate beam A moment of inertia
=
=
=
 1 .5 in .   5 .5 in . 
3
12
 1 .5
in .   1 66 .3 7 5 in .
12
249.5625 in.
12
= 21 in.
4
4
3

Calculating Moment of Inertia
Calculate beam B moment of inertia
=
=
=
 5 .5 in .   1 .5 in . 
3
12
 5.5
in.   3.375 in.
12
1 8 .5 6 2 5 in .
12
= 1 .5 in .
4
4
3

Moment of Inertia
14Times
Stiffer
Beam
A
Beam
B
IA = 21 in.
4
IB = 1.5 in.
4
Moment of Inertia – Composite
Shapes
Why are composite
shapes used in
structural design?
Non-Composite vs. Composite Beams
Doing more with less
Area = 8.00in.2
Area = 2.70in.2
Structural Member Properties
Chemical Makeup
Modulus of Elasticity (E) The ratio of the
increment of some specified form of stress to the
increment of some specified form of strain. Also
known as coefficient of elasticity, elasticity modulus,
elastic modulus. This defines the stiffness of an
object related to material chemical properties.
In general, a higher
modulus of elasticity
produces a greater
resistance to
deformation.
Modulus of Elasticity Principles
Beam
Material
Length Width Height Area
I
A
Douglas Fir
8 ft
1 ½ in. 5 ½ in. 8 ¼ in.2 20.8 in.4
B
ABS plastic
8 ft
1 ½ in. 5 ½ in. 8 ¼ in.2 20.8 in.4
Modulus of Elasticity Principles
What distinguishes beam A from beam B?
Will beam A or beam B have a greater resistance to
bending, resulting in the least amount of deformation,
if an identical load is applied to both beams at the
same location?
Modulus of Elasticity Principles
Why did beam B have greater deformation than
beam A?
Difference in material modulus of elasticity –
The ability of a material to deform and return to
its original shape
Characteristics of objects that affect deflection
(ΔMAX)
Applied force or load
Length of span between supports
Modulus of elasticity
Moment of inertia
Calculating Beam Deflection
3
ΔMAX =
FL
48EI
Beam
Material
Length
(L)
Moment Modulus of Force
of Inertia Elasticity
(F)
(I)
(E)
A
Douglas Fir
8.0 ft
B
ABS Plastic
8.0 ft
20.80 in.4 1,800,000 250 lbf
psi
20.80 in.4 419,000 250 lbf
psi
Calculating Beam Deflection
3
ΔMAX =
FL
48EI
Calculate beam deflection for beam A
ΔMAX =
 2 5 0 lb f   9 6 in . 
3
4 8  1 ,8 0 0 ,0 0 0 p si   2 0 .8 0in .
4

Δ M A X = 0 .1 2 in .
Beam
A
Material
Douglas Fir
Length
8.0 ft
I
20.80
in.4
E
Load
1,800,000 250 lbf
psi
Calculating Beam Deflection
3
ΔMAX =
FL
48EI
Calculate beam deflection for beam B
3
ΔMAX =
 2 5 0 lb f   9 6 in . 
4 8  4 1 9 ,0 0 0 p si   2 0 .8 0
in .
4

Δ M A X = 0 .5 3 in .
Beam
B
Material
ABS Plastic
Length
I
8.0 ft 20.80 in.4
E
419,000
psi
Load
250 lbf
Douglas Fir vs. ABS Plastic
4.24 times
less
deflection
Δ M A X A = 0 .1 2 in .
Δ M A X B = 0 .5 3 in .

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