Bending Stressmi@see.cn
Bending Stress mi@seu.edu.cn
Contents·PureBendingvs.NonuniformBending（纯弯曲与横力弯曲）·AssumptionsforPureBending（纯弯曲基本假设）·NeutralSurface&NeutralAxes（中性层与中性轴）·Kinematics（几何关系）Hooke'sLaw（物理关系）·StaticEquivalency（静力等效关系）·PureBendingNormalStressFormula（纯弯曲正应力公式）·NormalStressStrengthCondition（正应力强度条件）·StressConcentrations（应力集中）·Bendingof a Composite Beam（复合梁弯曲）·Bending of a Curved Beam（曲梁弯曲）2
• Pure Bending vs. Nonuniform Bending（纯弯曲与横力弯曲） • Assumptions for Pure Bending（纯弯曲基本假设） • Neutral Surface & Neutral Axes（中性层与中性轴） • Kinematics（几何关系） • Hooke’s Law（物理关系） • Static Equivalency（静力等效关系） • Pure Bending Normal Stress Formula（纯弯曲正应力公式） • Normal Stress Strength Condition（正应力强度条件） • Stress Concentrations（应力集中） • Bending of a Composite Beam（复合梁弯曲） • Bending of a Curved Beam（曲梁弯曲） Contents 2
Contents·Shearing Stresses in a RectangularBeam（矩形梁切应力）·EffectofShearingStress/Strain（切应力和切应变效应）·ShearingStresses inaWide-flangeBeam（宽翼缘梁切应力）·ShearFlowinaThin-walledBeam（薄壁梁剪力流）·ShearingStressesinaCircularBeam（圆截面梁切应力）·Shearing Stresses in an Equilateral Triangular Beam（等边三角梁切应力）·ShearingStress StrengthCondition（切应力强度条件）·Rational DesignofBeams（梁的合理设计）·Nonprismatic and Constant-strength Beams（非等直梁和等强度梁）: Unsymmetric Loading of Thin-Walled Members and Shear Center（薄壁梁的非对称弯曲与剪力中心）3
• Shearing Stresses in a Rectangular Beam（矩形梁切应力） • Effect of Shearing Stress/Strain（切应力和切应变效应） • Shearing Stresses in a Wide-flange Beam（宽翼缘梁切应力） • Shear Flow in a Thin-walled Beam（薄壁梁剪力流） • Shearing Stresses in a Circular Beam（圆截面梁切应力） • Shearing Stresses in an Equilateral Triangular Beam（等边三角梁 切应力） • Shearing Stress Strength Condition（切应力强度条件） • Rational Design of Beams（梁的合理设计） • Nonprismatic and Constant-strength Beams（非等直梁和等强度梁） • Unsymmetric Loading of Thin-Walled Members and Shear Center （薄壁梁的非对称弯曲与剪力中心） Contents 3
Pure Bending vs. Nonuniform BendingP/PB? Pure bending (CD)DC9LPaaFs = O, M = constFsPNonuniform bending (AC & DB)F≠0，M≠0PMPa4
S F M 0 const ， • Pure bending (CD) S F M ≠ ， ≠ 0 0 • Nonuniform bending (AC & DB) Pure Bending vs. Nonuniform Bending 4 P B P P C D A P a a l P P FS Pa M
Deformation Characteristics: Before:MM·After:: Straight longitudinal lines turns into curves.: Longitudinal lines get shortened under compression and lengthenedundertension: Cross-section lines remain straight and perpendicular to longitudinalcurves.5
M M • Before: • After: Deformation Characteristics • Straight longitudinal lines turns into curves. • Longitudinal lines get shortened under compression and lengthened under tension. • Cross-section lines remain straight and perpendicular to longitudinal curves. 5