Introduction to Structural Member Properties
Properties of Structural Members
2. Modulus of Elasticity
3. Maximum Deflection
- How much bending is okay?
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
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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 |
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?
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
Calculating Moment of Inertia
Calculate beam A Moment of Inertia
Calculating Moment of Inertia
Calculate beam B Moment of Inertia
Moment of Inertia
.
13.42 Times Stiffer
Beam “A”
Beam “B”
Moment of Inertia – Composite Shapes
Why are composite shapes used in structural design?
Non-Composite vs. Composite Beams
Doing more with less
Economics of Materials
Steel = $1/pound
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
Modulus of Elasticity - Bikes
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?
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)
Modulus of Elasticity
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 |
Designing around deflection
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
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
Douglas Fir vs. ABS Plastic
.
4.24 Times less deflection
Activity