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Introduction to Structural Member Properties

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Properties of Structural Members

  1. Moment of Inertia
    • beam shapes/strengths

2. Modulus of Elasticity

    • material properties

3. Maximum Deflection

- How much bending is okay?

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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 cross-sectional area is distributed about a centroidal axis.

In general, a higher Moment of Inertia produces a greater resistance to deformation.

Stiffness of an object related to its shape

©iStockphoto.com

©iStockphoto.com

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Moment of Inertia Principles

Beam

Material

Length

Width

Height

Area

A

Douglas Fir

8 ft

1 ½ in.

5 ½ in.

8 ¼ in.2

B

Douglas Fir

8 ft

5 ½ in.

1 ½ in.

8 ¼ in.2

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Moment of Inertia Principles

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?

What distinguishes beam A from beam B?

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Calculating Moment of Inertia - Rectangles

Why did beam B have greater deformation than beam A?

Moment of Inertia Principles

Difference in Moment of Inertia due to the orientation of the beam

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Calculating Moment of Inertia

Calculate beam A Moment of Inertia

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Calculating Moment of Inertia

Calculate beam B Moment of Inertia

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Moment of Inertia

.

13.42 Times Stiffer

Beam “A”

Beam “B”

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Moment of Inertia – Composite Shapes

Why are composite shapes used in structural design?

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Non-Composite vs. Composite Beams

Doing more with less

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Economics of Materials

Steel = $1/pound

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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. Stiffness of an object related to material chemical properties

In general, a higher modulus of elasticity produces a greater resistance to deformation.

Structural Member Properties

Chemical Makeup

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Modulus of Elasticity - Bikes

  • Steel
    • Flexible (elastic)
    • Heavy
  • Carbon
    • Inflexible (not elastic)
    • Light

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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

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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?

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Why did beam B have greater deformation than beam A?

Modulus of Elasticity Principles

Difference in material Modulus of Elasticity – The ability of a material to deform and return to its original shape

Applied force or load

Length of span between supports

Modulus of elasticity

Moment of inertia

Characteristics of objects that affect deflection (ΔMAX)

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Modulus of Elasticity

  • Can be more important than strength
    • Shaky floors
    • Feeling Unsafe

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Calculating Beam Deflection

Beam

Material

Length

(L)

Moment of Inertia

(I)

Modulus of Elasticity

(E)

Force (F)

A

Douglas Fir

8 ft

20.8 in.4

1,800,000 psi

250 lbf

B

ABS Plastic

8 ft

20.8 in.4

419,000 psi

250 lbf

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Designing around deflection

  • L/180 is typical,
    • Prevent cracking in concrete

  • L/500 is stringent
    • Prevent cracking in brittle flooring

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Calculating Beam Deflection

Beam

Material

Length

I

E

Load

A

Douglas Fir

8 ft

20.8 in.4

1,800,000 psi

250 lbf

Calculate beam deflection for beam A

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Calculating Beam Deflection

Beam

Material

Length

I

E

Load

B

ABS Plastic

8 ft

20.8 in.4

419,000 psi

250 lbf

Calculate beam deflection for beam B

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Douglas Fir vs. ABS Plastic

.

4.24 Times less deflection

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Activity

  • Calculate Moment of Inertia
  • Calculate Modulus of Elasticity
  • Calculate weight of items using the above values and the following formulas.