mechanics of material, stress ,strain, axial loading......you will know about stressstrain diagram, elongation, plastic and elastic deformation .......................................................................................................................................................
MAE005-Mechanics of Solids Mechanics of solids Mechanics of solids is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation under the action of forces, temperature changes, phase changes, and other external or internal agents Classification of Engineering Mechanics Engineering Mechanics Mechanics of rigid bodies Statics Mechanics of deformable bodies Mechanics of fluids Dynamics Mechanics of Solids Ideal fluid Kinematics Theory of elasticity Viscous fluid Kinetics Theory of plasticity Incompressible fluid Objectives Understand different methods that used to analyze stress and strain in solid body Apply various principles to solve problems in solid mechanics Analyze forces of solid body cause by external force Analyze the result of solid mechanics experiments Apply the concepts of stress, strain, torsion and bending and deflection of bar and beam in engineering field Explain the stress, strain, torsion and bending Calculate and determine the stress, strain and bending of solid body that subjected to external and internal load Learning outcome Apply the concepts of stress, strain, torsion and bending and deflection of bar and beam in engineering field Explain the stress, strain, torsion and bending Calculate and determine the stress, strain and bending of solid body that subjected to external and internal load Use solid mechanic apparatus and analyze the experiments result Work in-group that relates the basic theory with application of solid mechanics Topics Stress and Strain Mechanical properties Axial load Torsion Bending Stress transformation Deflection of Beams and Shaft Text books and References Text books: Ferdinand Beer and E Russell Johnston, “Mechanics of Materials”, 7th edition, Mc-Graw-Hill, New York, 2012 Russell C Hibbeler, “Mechanics of Materials”, 8th edition, Prentice Hall, 2010 Reference books: Roy R Craig, “Mechanics of Materials”, 3rd edition, John Wiley & Sons, 2011 Grading distribution Attendance: 10% Homework: 10% Quizzes: 20% (5% for each) Midterm exam: 20% Final exam: 40% Contents Chapter 1: Introduction-Concept of stress Chapter 2: Stress and Strain Chapter 3: Mechanical properties Chapter 4: Axial load Chapter 5: Torsion Chapter 6: Bending Chapter 7: Combined loadings Chapter 8: Stress transformation Chapter 9: Deflection of Beams and Shaft Chapter 10: Bulking of columns CHAPTER Introduction – Concept of Stress 10 1.8 Stress in two force members • Normal and shearing stresses on an oblique plane: P P cos ; sin cos A0 A0 • The maximum normal stress occurs when the reference plane is perpendicular to the member axis: P m ; A0 • The maximum shear stress occurs for a plane at + 45o with respect to the axis: P P m sin 45 cos 45 A0 A0 55 1.9 Allowable stress • When designing a structural member or mechanical element, the stress in it must be restricted to safe level • Choose an allowable load that is less than the load the member can fully support • One method used is the factor of safety (F.S.) Ffail F.S = Fallow 1.9 Allowable stress If load applied is linearly related to stress developed within member, then F.S can also be expressed as: σfail F.S = σallow τfail F.S = τallow • In all the equations, F.S is chosen to be greater than 1, to avoid potential for failure • Specific values will depend on types of material used and its intended purpose 57 1.9 Allowable stress Cross-sectional area of a tension member Condition: The force has a line of action that passes through the centroid of the cross section 58 1.9 Allowable stress Cross-sectional area of a connecter subjected to shear Assumption: If bolt is loose or clamping force of bolt is unknown, assume frictional force between plates to be negligible 59 1.9 Allowable stress Required area to resist bearing Bearing stress is normal stress produced by the compression of one surface against another Assumptions: (σb)allow of concrete < (σb)allow of base plate Bearing stress is uniformly distributed between plate and concrete 60 1.9 Allowable stress Although actual shear-stress distribution along rod difficult to determine, we assume it is uniform Thus use A = V / τallow to calculate l, provided d and τallow is known 61 1.9 Allowable stress Procedure for analysis When using average normal stress and shear stress equations, consider first the section over which the critical stress is acting Internal Loading Section member through x-sectional area Draw a free-body diagram of segment of member Use equations of equilibrium to determine internal resultant force Required Area Based on known allowable stress, calculate required area needed to sustain load from A = P/τallow or A = V/τallow 62 1.10 Chapter review The internal loadings in a body consist of a normal force, shear force, bending moment, and torsional moment 63 1.10 Chapter review Average normal stress Average shear stress Factor of safety (F.S.) 64 Stress analysis & design example • Would like to determine the stresses in the members and connections of the structure shown • From a statics analysis: FAB = 40 kN (compression) FBC = 50 kN (tension) • Must consider maximum normal stresses in AB and BC, and the shearing stress and bearing stress at each pinned connection 65 Stress analysis & design example • The rod is in tension with an axial force of 50 kN • At the rod center, the average normal stress in the circular cross-section (A = 31410-6 m2) is BC = +159 MPa • At the flattened rod ends, the smallest crosssectional area occurs at the pin centerline: A 20 mm 40 mm 25mm 300 106 m BC , end N BC FBC 50 103 N 167 MPa 6 A A 300 10 m • The boom is in compression with an axial force of 40 kN and average normal stress of –26.7 MPa • The minimum area sections at the boom ends are unstressed since the boom is in compression 66 Stress analysis & design example • The cross-sectional area for pins at A, B, and C 25 mm 6 A r2 491 10 m V • The force on the pin at C is equal to the force exerted by the rod BC C , avg V 50 10 N 102 MPa 6 A 491 10 m • The pin at A is in double shear with a total force equal to the force exerted by the boom AB, V V A , avg V 20 kN 40.7 M Pa 6 A 491 10 m 67 Stress analysis & design example • Divide the pin at B into sections to determine the section with the largest shear force: VE 15kN VG 25kN (largest) VE • Evaluate the corresponding average shearing stress: B , avg VG 25kN 50.9 MPa 6 A 491 10 m VG 68 Stress analysis & design example • To determine the bearing stress at A in the boom AB, we have t = 30 mm and d = 25 mm, N AB FAB 40 kN b 53.3MPa td td 30 mm 25mm • To determine the bearing stress at A in the bracket, we have t = 2(25 mm) = 50 mm and d = 25 mm, NAB FAB 40kN b 32.0MPa td td 50mm 25mm 69 ... 40% Contents Chapter 1: Introduction-Concept of stress Chapter 2: Stress and Strain Chapter 3: Mechanical properties Chapter 4: Axial load Chapter 5: Torsion Chapter 6: Bending Chapter 7: Combined... loadings Chapter 8: Stress transformation Chapter 9: Deflection of Beams and Shaft Chapter 10: Bulking of columns CHAPTER Introduction – Concept of Stress 10 The bolts used for the connections of this...Mechanics of solids Mechanics of solids is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation under the action of forces,