CTC / MTC 222 Strength of Materials Chapter 3 Design for Direct Stress.
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Transcript of CTC / MTC 222 Strength of Materials Chapter 3 Design for Direct Stress.
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CTC / MTC 222Strength of Materials
Chapter 3Design for Direct Stress
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Chapter Objectives
• Define design stress and design factor and select appropriate values for them
• Understand the relationship between design stress, allowable stress and working stress
• Understand the relationship between design factor, factor of safety and margin of safety
• List the conditions which affect the choice of design factor
• Design members subject to direct stress• Determine when stress concentrations occur,
and specify suitable values for stress concentration factors
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Direct Normal Stress
• Stress – force per unit area• Stress = force / area = F / A
• Normal Stress – a stress which acts perpendicular (or normal) to the cross section of the member
• Direct Normal Stress – a normal stress which is also uniform across the resisting area
• Units in US Customary system• Pounds / in2 (psi), kips / in2 (ksi)
• Units in SI system• Newtons / m2 , Newtons / mm2 , Kilonewtons / m2 • Also expressed in pascals (Pa), or more commonly,
megapascals (MPa) • 1 Pa = 1 N / m2
• 1MPa = 1x 106 N / m2 = 1x 103 KN / m2 = 1 N / mm2
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Direct Normal Stress
• σ = Applied Force/Cross-sectional Area = F/A
• Area A is perpendicular to the line of action of the force
• Conditions• Member is straight• Uniform cross section over length considered• Material is homogeneous• Load applies along centroidal axis (no bending)• No buckling (compression members)
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Design Normal Stresses
• Design stress – level of stress in a member that is considered safe
• Also called allowable stress, or working stress• Design factor, N – factor by which reported strength
(usually the yield strength or the ultimate strength) is divided to obtain the design stress
• Also called factor of safety
• Design stress, σd
• Sometimes based on sy, yield strength - σd = sy / N• Sometimes based on su, ultimate strength - σd = su / N
• Margin of safety• Margin of safety = (yield strength / max stress) – 1 , based on
yield stress• Margin of safety = (ultimate strength / max stress) – 1 , based
on ultimate strength
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Design Factor
• Design factor – based on judgment and experience, considering the following factors:
• Codes and Standards• Type of material – ductile or brittle• Type of loading – static, dynamic or repeated• Possible misuse of part• Precision of analysis• Environment• Size effect• Quality control• Importance of part• Cost• Market segment in which part is used
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Design Factor Guidelines for Direct Normal Stresses
• Design stress, σd
• σd = sy / N – based on yield strength• σd = su / N – based on ultimate strength
• Ductile Materials - >5% elongation before failure• Static loads - σd = sy / N , N = 2• Repeated loads - σd = su / N , N = 8• Impact or shock load - σd = su / N , N = 12
• Brittle Materials - <5% elongation before failure• Static loads - σd = su / N , N = 6• Repeated loads - σd = su / N , N = 10• Impact or shock load - σd = su / N , N = 15
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Design Shear Stress, d
• Design shear stress for ductile materials is based on yield strength in shear, d = sys / N
• sys – the level of shear stress at which material would exhibit the phenomenon of yield
• sys - sometimes estimated as approximately ½ sy
• Recommended design factors same as for direct stress
• Design shear stress for brittle materials is based on ultimate strength in shear, d = sus / N
• sus – the level of shear stress at which material would actually fracture
• Data on acceptable design factors is lacking
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Design Bearing Stress, σbd
• Bearing Stress – created when two load-carrying parts are placed in contact
• Actually a compressive stress, but due to localized nature, different allowable stresses are used• For steel – σbd = 0.90 sy
• For aluminum – σbd = 0.65 sy
• For other materials see specific codes and specifications
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Stress Concentration Factors
• Changes in cross-section of a member can cause stress concentrations
• Stress concentration factor KT
• Depends on geometry of the member• Can be measured experimentally, or by
computerized analyses• KT = σmax / σnom
• See Section 3-11 and Appendix A-22
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Design or Analysis for Direct Stress
• Three basic types of problems• Calculate actual stress
• σ = F / A
• Calculate allowable load• F = σd A
• Calculate required area • A = F / σd