基本氯习 拉(压)扭转 平面弯曲 omao max mNYo]rms可] 强度条件 N M max nImax min W≥ [o] [a] Nm≤4a] M≤W[ Imax Mmx swol /m|「f7 0m6 度条件变形能 0x <61 N(x M(x U=rA dx MA(x 2EA UFJ QGI U L JL 2EL
拉 （压） 扭 转 平面弯曲 强度条件刚度条件变形能 [ ] s max s [ ] max min s N A [ ] Nmax A s [ ] max t t [ ] | | max tn t M W max [ ] M W n t t [ ] s max s [ ] max t t [ ] max s M Wz [ ] Mmax Wz s [ ] q max q q max [q] Lf L |f max | x EA N x U L d 2 ( ) 2 = x GI M x U L n d 2 ( ) 2 = x EI M x U L d 2 ( ) 2 =
Review of basic deformations The internal-force calculation Take the left part of point a as the study object, the internal forces of point a are calculated by the following formulas: (where Pi Pi are the external forces of the left part of point A) Tension and Compress ion NA=∑()∑P(少 Torsion Mn=∑m(←)∑m(→) Plane Bending Q=(∑1)(∑4) M4=(∑m2(P)(∑m(P))
Tension and Compression Torsion Plane Bending The internal-force calculation Take the left part of point A as the study object, the internal forces of point A are calculated by the following formulas: (where “ Pi , Pj” are the external forces of the left part of point A). = ( ) − ( ) MAn mi mj =( ( ) )−( ( ) ) MA mA Pi mA Pj =( )−( ) QA Pi Pj = ()− (→) NA Pi Pj
基本氯习 内力计算 以A点左侧部分为对象,A点的内力由下式计算: (其中“P、P”均为A点左侧部分的所有外力) 拉 压 N4=∑P()∑P(少 扭 转 Mn=∑m1(←)-∑m(→) 平 Q=(∑1)(∑4) 面 M-(m2()(∑m(P))
拉 压 扭 转 平 面 弯 曲 内力计算 以A点左侧部分为对象，A点的内力由下式计算： (其中“Pi、Pj ”均为A 点左侧部分的所有外力) = ( ) − ( ) MAn mi mj =( ( ) )−( ( ) ) MA mA Pi mA Pj =( )−( ) QA Pi Pj = ()− (→) NA Pi Pj
Review of basic deformations Relations among the shearing force bending moment and external forces do(x) dx =g(x) dM() o(x) ax dm(x)=g() Applications of symmetry and antisymmetry For the symmetric structure under the action of symmetric loads the diagram of its shearing stress Q is antisymmetric and the diagram of the bending moment M is symmetric For the symmetric structure under the action of antisymmetric loads the diagram of its shearing stress Q is symmetric and the diagram of the bending moment M is antisymmetric
Relations among the shearing force, bending moment and external forces. ( ) q(x) x Q x = d d ( ) d d ( ) Q x x M x = ( ) d d ( ) 2 2 q x x M x = Applications of symmetry and antisymmetry： For the symmetric structure under the action of symmetric loads the diagram of its shearing stress Q is antisymmetric and the diagram of the bending moment M is symmetric .For the symmetric structure under the action of antisymmetric loads the diagram of its shearing stress Q is symmetric and the diagram of the bending moment M is antisymmetric
基本氯习 弯曲剪力、弯矩与外力间的关系 do(x) dM()=o(x) ax dm(x)=g() 对称性与反对称性的应用: 对称结构在对称载荷作用下,Q图反对称,M图对称;对称 结构在反对称载荷作用下,Q图对称,M图反对称
弯曲剪力、弯矩与外力间的关系 ( ) q(x) x Q x = d d ( ) d d ( ) Q x x M x = ( ) d d ( ) 2 2 q x x M x = 对称性与反对称性的应用： 对称结构在对称载荷作用下，Q图反对称，M图对称；对称 结构在反对称载荷作用下，Q图对称，M图反对称