Strength of Materials

1
Strength of Materials

• Study of the stress and deflection of structural
  and machine components.
• Required to ensure a safe design.
• Critical in design and selection of machine
  components.

2
Material Properties Tensile Test
3
Material Properties Shear Properties
Axial Strain Lateral Strain Poissons ratio
Modulus of Elasticity in Shear (G) stiffness of
a material in shear
4
Example

• Select a ductile steel, that will not permanently
  deform at a stress level of
• 45,000 psi.
• Also, determine its modulus of elasticity in
  shear.

5
Axial Loading

• Tension Stress
• Axial Deformation

• E, Modulus of Elasticity
• A, Cross-sectional Area

6
Example

• Compute the stress in the middle portion of the
  horizontal rod.

7
Direct Shear Loading

• Shear Stress

• A, Cross-sectional Area

8
Example

• Compute the stress in the bottom support pin.

9
Shafts

• Shafts are used to transmit rotary motion and
  torque.
• Rotational Power
• Formula for common U.S. units

• n, shaft speed (rpm)
• T, torque (in lbs)
• P, power (hp)

10
Torsional Loading Round Member

• Shear Stress
• Angular Deflection

11
Example

• Compute the torsional shear stress in a circular
  shaft, having a diameter of 1.25 in. The shaft is
  transmitting 110 hp at a speed of 560 rpm.

FD
12
Torsional Loading Non-Circular Member
T

• Shear Stress
• Angular Deformation

13
Bending Loads

• Normal Stress
• Flexural Deformation
• d charted,
• (based on load case)

14
Section Properties

• Moment of Inertia (I)
• complex shapes can be built from composite
  sections
• Section Modulus (SI/c)
• used when solving for shape
• Bending stress

15
Example

• Select an aluminum I-Beam to carry the load
  shown, with a maximum stress of 12000 psi.
• Also, calculate the deflection at the 400 lb load.

16
Example

• Calculate the bending stress at the top of the
  shaft at point B

17
Stress Concentrations

• Geometric discontinuities cause increased stress
  levels
• Compensated with a stress concentration factor.
• smax Kt snom
• Kt is charted based on geometry and load case

18
Example

• For the flat plate in tension, compute the stress
  at each hole.