《材料力学》课程PPT教学课件（双语版）基本变形复习

Mechanics of materials Review of basic deformations

Mechanics of Materials

基本形复习

Review of basic deformations Tension( Compression T orson Plane bending A Interna N MAN M O M>0 for N>0 M>0 x-Axle of the x— Axle of the x-Parallel to the axle of the>0 pole dle Stress Mi (x y OS p)= b A B x Deforma tio f 0= d △E d DAB EA ABG f(x er o-f

Tension( Compression) Torsion Plane bending Internal force Stress Deforma tion N N > 0 x— Axle of the pole A Mn > 0 x— Axle of the pole A Mn A M Q M > 0 x—Parallel to the axle of the Q > 0 pole x s A N(x) s= L ( ) d ( ) L N x L x EA x  =  O t r p n I M r t (r)= z x I My s = s t x y z z y bI QS t = A B x GI M LAB p n AB d   = q u f x q= f´ u= f EI M x f x ( ) ( )=−

基本氯习 拉(压)扭转 平面弯曲 A N MAN M 内力 N>0 M>0 x平行于杆额。 O M x杆轴 0 x杆轴 x 应 力 N(x) My p)= A b A B 变 L x 形a=(N(x)dx f 0= (P AB JLAB ULP d M(x) E4(x) f"(x) E B=f

拉 （压） 扭 转 平面弯曲 内力应力变形 N N > 0 x—杆轴A Mn > 0 x—杆轴A Mn A M Q M > 0 Q > 0 x—平行于杆轴 xs AN(x ) s = L x EA x N x L L d ( ) ( ) d  = O t r pn I M r t ( r) = z x I My s = s t x y zz y bI QS  t = A B x GI M LAB pn AB d   = q u f x q= f ´ u= f EI M x f x ( )  ( ) = −

Review of basic deformations Tension( Compression) Torsion Plane bending Strength max mNYo]rms可] conditions max A0 N M max nImax min W≥ [o] [a] Nm≤ M≤W[ Imax Mmx swol Rigidity conditions U/mL「f 0m6 0x <61 Strain energy =/M2(x MA(x M(x Lx UFJ QGI U L 2EA JL 2EL

Tension( Compression) Torsion Plane bending Strength conditions Rigidity conditions Strain energy [ ] s max  s [ ] max min s N A  [ ] Nmax A s [ ] max t  t [ ] | | max t n 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]        L f 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  =

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