Bending Internal Forcesmi@se.eol.cn
Bending Internal Forces mi@seu.edu.cn
Contents·Introduction（弯曲变形筒介）·The Forms ofInternal Forces in Beams（梁中内力的形式·Symmetric Bending（对称弯曲）·Types of Beams（静定梁的分类）·Types of Supports and Reactions（梁的支撑种类及相应的支座反力形式）·InternalReleases（内力释放器）·Determinacy of Beams（梁的静定性）? Sign Convention of Shearing Forces and BendingMoments（剪力和弯矩的符号规则）·DirectCalculationof ShearingForces（剪力简易计算法）2
• Introduction（弯曲变形简介） • The Forms of Internal Forces in Beams（梁中内力的形式） • Symmetric Bending（对称弯曲） • Types of Beams（静定梁的分类） • Types of Supports and Reactions（梁的支撑种类及相应 的支座反力形式） • Internal Releases（内力释放器） • Determinacy of Beams（梁的静定性） • Sign Convention of Shearing Forces and Bending Moments（剪力和弯矩的符号规则） • Direct Calculation of Shearing Forces（剪力简易计算法） Contents 2
·Direct Calculation of Bending Moments（弯矩简易计算法）· Diagram of Shearing Forces & Bending Moments （剪力图与弯矩图）? Differential Relations among Loads, Shearing Forces andBendingMoments（弯矩、剪力和荷载之间的微分关系）·Diagram of Internal Forces for Plane Frames（平面刚架的内力图）·Diagram of Internal Forces for Curved Beams（曲梁的内力图）3
• Direct Calculation of Bending Moments（弯矩简易计算 法） • Diagram of Shearing Forces & Bending Moments（剪力 图与弯矩图） • Differential Relations among Loads, Shearing Forces and Bending Moments（弯矩、剪力和荷载之间的微分关系） • Diagram of Internal Forces for Plane Frames（平面刚架 的内力图） • Diagram of Internal Forces for Curved Beams（曲梁的内 力图） 3
Introduction4
Introduction 4
IntroductionChessSTOPPontoonWindloadBalk
Introduction 5
IntroductionPlanksJoists6
Introduction 6
IntroductionzhntoucomOriginal GridDeformed Grid
Introduction 7
Introduction1600N/m900N/m1400mmc)1.0m2.6m2.6m-350mmBR←8
Introduction 8
IntroductionCompressionFreeBodyDiagram,leftpartRTensioncut hereEnlargedViewofStresses9
Introduction 9
The Form of Internal Forces in Beams. Internal forces onBCcross-sections ofbending beams11AOmCFBBmAmMThe internal forces on cross-sectionFsm-m can be simplified as shearingmforces and bending moments atFmBcross-sectional centroidMBFSm10
• Internal forces on cross-sections of bending beams m m F A B FS m m A M FA m m F B FS M FB The internal forces on cross-section m-m can be simplified as shearing forces and bending moments at cross-sectional centroid. The Form of Internal Forces in Beams 10