CTC / MTC 222Strength of Materials

Chapter 3Design for Direct Stress

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

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

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)

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

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

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

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

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

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

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