Esfuerzos

1. Stress

CHAPTER OBJECTIVES • Review important principles of statics • Use the principles to determine internal resultant loadings in a body • Introduce concepts of normal and shear stress • Discuss applications of analysis and design of members subjected to an axial load or direct shear

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CHAPTER OUTLINE 1. 2. 3. 4. 5. 6. 7.Introduction Equilibrium of a deformable body Stress Average normal stress in an axially loaded bar Average shear stress Allowable stress Design of simple connections

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1.1 INTRODUCTION Mechanics of materials • A branch of mechanics • It studies the relationship of – External loads applied to a deformable body, and – The intensity ofinternal forces acting within the body • Are used to compute deformations of a body • Study body’s stability when external forces are applied to it

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1.1 INTRODUCTION Historical development • Beginning of 17th century (Galileo) • Early 18th century (Saint-Venant, Poisson, Lamé and Navier) • In recent times, with advancedmathematical and computer techniques, more complex problems can be solved

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1.2 EQUILIBRIUM OF A DEFORMABLE BODY External loads • Surface forces – Area of contact – Concentrated force – Linear distributed force – Centroid C (or geometric center) • Body force (e.g., weight)

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1. Stress1.2 EQUILIBRIUM OF A DEFORMABLE BODY Support reactions • for 2D problems

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1.2 EQUILIBRIUM OF A DEFORMABLE BODY Equations of equilibrium • For equilibrium – balance of forces – balance of moments • Draw a free-body diagram to account for all forces acting on the body • Apply the two equations to achieve equilibrium state
∑F=0 ∑ MO =0

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1.2 EQUILIBRIUM OF A DEFORMABLE BODY Internal resultant loadings • Define resultant force (FR) and moment (MRo) in 3D: – Normal force, N – Shear force, V – Torsional moment or torque, T – Bending moment, M

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1.2 EQUILIBRIUM OF A DEFORMABLE BODY Internal resultantloadings • For coplanar loadings: – Normal force, N – Shear force, V – Bending moment, M

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1.2 EQUILIBRIUM OF A DEFORMABLE BODY Internal resultant loadings • For coplanar loadings: – Apply ∑ Fx = 0 to solve for N – Apply ∑ Fy = 0 to solve for V – Apply ∑ MO = 0 to solve for M

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1.2 EQUILIBRIUM OF A DEFORMABLE BODY Procedure for Analysis • Method of sections 1. Choose segment to analyze 2. Determine Support Reactions 3. Draw free-body diagram for whole body 4. Apply equations of equilibrium

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1.2 EQUILIBRIUM OF A DEFORMABLE BODY Procedure for analysis • Free-body diagram 1. Keep all externalloadings in exact locations before “sectioning” 2. Indicate unknown resultants, N, V, M, and T at the section, normally at centroid C of sectioned area 3. Coplanar system of forces only include N, V, and M 4. Establish x, y, z coordinate axes with origin at centroid
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1.2 EQUILIBRIUM OF A DEFORMABLE BODY Procedure for analysis •Equations of equilibrium 1. Sum moments at section, about each coordinate axes where resultants act 2. This will eliminate unknown forces N and V, with direct solution for M (and T) 3. Resultant force with negative value implies that assumed direction is opposite to that shown on free-body diagram

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EXAMPLE 1.1 Determine resultant...