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CM 197 Mechanics of Materials Chap 9: Strength of Materials Simple Stress. Professor Joe Greene CSU, CHICO Reference: Statics and Strength of Materials , 2 nd ed., Fa-Hwa Cheng, Glencoe/McGraw Hill, Westerville, OH (1997). CM 197. Chap 9: Strength of Materials Simple Stress. Objectives

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Cm 197 mechanics of materials chap 9 strength of materials simple stress
CM 197Mechanics of Materials Chap 9: Strength of Materials Simple Stress

Professor Joe Greene

CSU, CHICO

Reference: Statics and Strength of Materials, 2nd ed., Fa-Hwa Cheng, Glencoe/McGraw Hill, Westerville, OH (1997)

CM 197


Chap 9 strength of materials simple stress
Chap 9: Strength of Materials Simple Stress

  • Objectives

    • Introduction

    • Normal and Shear Stresses

    • Direct Normal Stresses

    • Direct Shear Stresses

    • Stresses on an Inclined Plane


Introduction
Introduction

  • Introduction

    • Statics: first 8 chapters

    • Strength of Materials: Rest of book

      • Relationships between external loads applied to an elastic body

      • Intensity of the internal forces within the body

      • Statics: all bodies are rigid.

      • Strength of materials: all bodies are deformable

    • Terms

      • Strain: deformation per unit length

      • Stress: Force per unit area from an external source

      • Strength: Amount of force per unit area that a material can support without breaking.

      • Stiffness: A material’s resistance to deformation under load


Mechanical test considerations
Mechanical Test Considerations

P

P

A

P

P

P

P

shear

  • Normal and Shear Stresses

    • Force per unit area

      • Normal force per unit area

        • Forces are perpendicular (right angle) to the surface

      • Shear force per unit area

        • Forces are parallel (in same direction) to the surface

  • Direct Normal Forces and Primary types of loading

    • Prismatic Bar: bar of uniform cross section subject to equal and opposite pulling forces P acting along the axis of the rod.

    • Axial loads: Forces pulling on the bar

    • Tension= pulling the bar; Compression= pushing; torsion=twisting; flexure= bending; shear= sliding forces

compression

tension

torsion

flexure


Stress
Stress

  • Stress: Intensity of the internally distributed forces or component of forces that resist a change in the form of a body.

    • Tension, Compression, Shear, Torsion, Flexure

  • Stress calculated by force, P, per unit area. Applied force divided by the cross sectional area of the specimen.

    • Note: P is sometimes called force, F. Eqn 9-1

  • Stress units

    • Pascals = Pa = Newtons/m2; MegaPascal=MPa= Newton/mm2

    • Pounds per square inch = Psi Note: 1MPa = 1 x106 Pa = 145 psi

    • 1 kPa = 1x103 Pa, 1 MPa = 1x106Pa, 1GPa = 1x109 Pa

    • 1 psi = 6.895kPa, 1ksi = 6.895MPa, 1 psf = 47.88 Pa

  • Example

    • Wire 12 in long is tied vertically. The wire has a diameter of 0.100 in and supports 100 lbs. What is the stress that is developed?

    • Stress = P/A = P/r2 = 100/(3.1415927 * 0.052 )= 12,739 psi = 87.86 MPa


Stress1
Stress

0.1 in

1 in

10in

1 cm

5cm

10cm

  • Example

    • Tensile Bar is 10in x 1in x 0.1in is mounted vertically in test machine. The bar supports 100 lbs. What is the stress that is developed? What is the Load?

      • Stress = F/A = F/(width*thickness)= 100lbs/(1in*.1in )= 1,000 psi = 1000 psi/145psi = 6.897 MPa

      • Load = 100 lbs

    • Block is 10 cm x 1 cm x 5 cm is mounted on its side in a test machine. The block is pulled with 100 N on both sides. What is the stress that is developed? What is the Load?

      • Stress = F/A = F/(width*thickness)= 100N/(.01m * .10m )= 100,000 N/m2 = 100,000 Pa = 0.1 MPa= 0.1 MPa *145psi/MPa = 14.5 psi

      • Load = 100 N

100 lbs


Allowable axial load
Allowable Axial Load

  • Structural members are usually designed for a limited stress level called allowable stress, which is the max stress that the material can handle.

    • Equation 9-1 can be rewritten

  • Required Area

    • The required minimum cross-sectional area A that a structural member needs to support the allowable stress is from Equation 9-1

    • Eqn 9-3

    • Example 9-1

    • Internal Axial Force Diagram

      • Varaition of internal axial force along the length of a member can be detected by this

      • The ordinate at any section of a member is equal to the value of the internal axial force of that section

      • Example 9-2


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