Ch.1 INTRODUCTION LIU Jiemin @SJZU 2008 1 Ch.1 INTRODUCTION LIU Jiemin @SJZU 2008 2 1.1 Tasks and Objects of M.M 1.2 Elementary Assumptions of solid deformable bodies 1.3 External forces and Internal forces 1.4 Stresses 1.5 Strains Chapter 1 Introduction Chapter 1 Introduction Ch.1 INTRODUCTION LIU Jiemin @SJZU 2008 3 1.1 Tasks and Objects of M.M 1.2 Elementary Assumptions of solid deformable bodies 1.3 External forces and Internal forces 1.4 Stresses 1.5 Strains Chapter 1 Introduction Chapter 1 Introduction Ch.1 INTRODUCTION LIU Jiemin @SJZU 2008 4 1.1.1 Parts (Members) a. Uniform-section rod b. Non-uniform section Block Shell Plate Middle surface Middle surface 1.1 Tasks and Objects of M.M Ch.1 INTRODUCTION LIU Jiemin @SJZU 2008 5 Axle Cross-Section \ue000 Strength, Stiffness and Stability of Members under External Forces \ue000 Rods 1.1.2 Tasks and Objects of M.M Centroid 1.1 Tasks and Objects of M.M Ch.1 INTRODUCTION LIU Jiemin @SJZU 2008 6 材料破坏的形式\ue002强度、刚度和稳定性的概念 1.1 Tasks and Objects of M.M1.1 Tasks and Objects of M.M Ch.1 INTRODUCTION LIU Jiemin @SJZU 2008 7 构件保持原有平衡状态的能力构件保持原有平衡状态的能力 1.1 Tasks and Objects of M.M1.1 Tasks and Objects of M.M Ch.1 INTRODUCTION LIU Jiemin @SJZU 2008 8 Ch.1 INTRODUCTION LIU Jiemin @SJZU 2008 9 Under conditions of satisfying strength, stiffness and stability, provide necessary theoretical foundation and calculating method for design of economic and safe members. Task of M.M: 1.1 Tasks and Objects of M.M Ch.1 INTRODUCTION LIU Jiemin @SJZU 2008 10 \ue000 Internal force\ue002内力\ue003 \ue000 Stress\ue000应力\ue001 \ue000 Deformation\ue000变形\ue001 \ue000 Strain\ue000应变\ue001 \ue000 Failure characteristics\ue000破坏\ue001 1.1.3 Basic conceptions of M.M What’s investigated in M.M? Mechanics response of materials (rods) under external loads : 1.1 Tasks and Objects of M.M What’s investigated in M.M? Ch.1 INTRODUCTION LIU Jiemin @SJZU 2008 11 1.1 Tasks and Objects of M.M 1.2 Elementary Assumptions of solid deformable bodies 1.3 External forces and Internal forces 1.4 Stresses 1.5 Strains Chapter 1 Introduction Chapter 1 Introduction Ch.1 INTRODUCTION LIU Jiemin @SJZU 2008 12 \ue015\ue011\ue011\ue011\ue016\ue011\ue011\ue011\ue017\ue015\ue011\ue011\ue011\ue016\ue011\ue011\ue011\ue017Elementary AssumptionsRestraints Elementary Assumptions AlFCBABlC x\ue003F1.2 Elementary Assumptions of solid deformable bodies \ue000 Homogeneity (均匀性 \ue000 Continuity(连续性假设 \ue000 Isotropy(各向同性 \ue000 Elasticity (弹性) \ue000 Small deformation(小变形) Ch.1 INTRODUCTION LIU Jiemin @SJZU 2008 13 1.1 Tasks and Objects of M.M 1.2 Elementary Assumptions of solid deformable bodies 1.3 External forces and Internal forces 1.4 Stresses 1.5 Strains Chapter 1 Introduction Chapter 1 Introduction Ch.1 INTRODUCTION LIU Jiemin @SJZU 2008 14 External force Internal force intensity 1.3 External forces and Internal forces 1.3.1 Internal forces: Resultant of the distributed force system in members, caused by external forces. Ch.1 INTRODUCTION LIU Jiemin @SJZU 2008 15 Axial force-FN, Shearing force-Fs, Torque-T(Mx), Bending moment-My, Mx Method of finding internal forces: Method 1: Cross-section method 1.3 External forces and Internal forces 1.3.2 Components of internal forces Ch.1 INTRODUCTION LIU Jiemin @SJZU 2008 16 1.3.2 Simple cross-section method of finding internal forces M 2'RRFM = -M '= -F'''''([)()]()RRiiciciMM\ue002 \ue001\ue002 \ue001\ue002 \ue001 \ue001\ue002 \ue001 \ue001\ue002\ue002\ue00d\ue00d\ue00dF\ue00dFMFM 'FFFM’ FR’ '1F'2F'3FFR 0F1FF3F0\ue002\ue000\ue002(\ue000\ue00d\ue00d)c'R'i'iMMFF)(MM)(MM)(MTFFFFFF'izz'iyy'ix'z , iz ,s'y , iy ,s'x , iN\ue00d\ue00d\ue00d\ue002\ue00d\ue00d\ue00d\ue002\ue002\ue002\ue002\ue002FFF1.3 External forces and Internal forces Ch.1 INTRODUCTION LIU Jiemin @SJZU 2008 17 Ex.1.1 The uniform-section rod is subjected to F at the free end. Determine the internal forces on the cross-section m-m. Solution: Method 1 FFFF:FNNy\ue002\ue002\ue001\ue002\ue00d00Method 2 FFF'y , iN\ue002\ue002\ue00dy 1.3 External forces and Internal forces Ch.1 INTRODUCTION LIU Jiemin @SJZU 2008 18 1.1 Tasks and Objects of M.M 1.2 Elementary Assumptions of solid deformable bodies 1.3 External forces and Internal forces 1.4 Stresses 1.5 Strains Chapter 1 Introduction Chapter 1 Introduction Ch.1 INTRODUCTION LIU Jiemin @SJZU 2008 19 261P a=1N /m1M Pa=10 PapN orm al stressShearing stress:: \ue007\ue008Intensityinternal forceofFAdFdAplimA\ue003\ue003\ue002\ue002\ue003\ue009 0\ue007\ue008\ue002\ue0002221.4 Stresses 1.4.1 Normal stress and shearing stress Ch.1 INTRODUCTION LIU Jiemin @SJZU 2008 20 (a) (b) NFA\ue007 \ue002\ue0071.4 Stresses 1.4.2 One-dimensional stress, Pure shearing stress Ch.1 INTRODUCTION LIU Jiemin @SJZU 2008 21 (d) (c) '0':0\ue008\ue008\ue008\ue008\ue002\ue002\ue00c\ue001\ue00c\ue002\ue00ddxddydzdydxdzMz1.4 Stresses 1.4.3 Theory of conjugate shearing stress Ch.1 INTRODUCTION LIU Jiemin @SJZU 2008 22 1.1 Tasks and Objects of M.M 1.2 Elementary Assumptions of solid deformable bodies 1.3 External forces and Internal forces 1.4 Stresses 1.5 Strains Chapter 1 Introduction Chapter 1 Introduction Ch.1 INTRODUCTION LIU Jiemin @SJZU 2008 23 1.5 Strains Normal strain and Shearing strain N orm al strainShearing strain:: \ue004\ue005u\ue003S\ue003klimslimkbus\ue001 \ue00bdudsakb\ue004\ue003\ue003\ue002\ue002\ue003 \ue009 000'2ka\ue006\ue00f\ue005\ue009\ue009\ue00e\ue010\ue012\ue013\ue002\ue014'b Ch.1 INTRODUCTION LIU Jiemin @SJZU 2008 24 Ex. 1.1 Deformation of a plate ABCD is shown in Fig.a. Determine: \ue0021\ue003Average normal strains of AB and AD; \ue0022\ue003Shearing strain of the right angle BAD at point A. Solution\ue004 0Edge AD: 2(0.1-0.05) +0.1 -0.1-4.99,\ue002AD 'avx\ue0042-510 muAD\ue003\ue002\ue002\ue002\ue001\ue00a1.5 Strains Edge AB: Ch.1 INTRODUCTION LIU Jiemin @SJZU 2008 25 \ue0022\ue003Shearing strain of the right angle BAD at point A. -3tan0.1100110 radG D 'AD\ue00a\ue005\ue005\ue002\ue002\ue002\ue002Under condition of small deformation: 1.5 Strains Ch.1 INTRODUCTION LIU Jiemin @SJZU 2008 26 Ch.1 INTRODUCTION fW3C$UVFR*T!!u8Hzt0!N2E$Kx(TAXn LvkYQ E+J847 Z)4SMwQ7gP emL$KBabe# WL1CXCiLo*5 ry1 ZG1Bwe9I2SaFv6 %iB4jz9C5a7nd4mmw5GoO 4UhVZR#Gkn 6*hrQ Y(SY# wfVW$M TWvj&2gasIuxpPc5B-XubtB !#Zel AdRB$i)7GH TQ7CI0mdg5q PRp3d8g!wn Zusb5-J1SyWqV PSCOHWTZu ZBU3K-5cvx %sD+qj 6e!Av4 S!VG* py&ooD ZoQsO3UkFtq49e !XWz3X gIq L6290lY#G tNU6BNDOVwaz ren9Bif+g !Yv47$KcXe* UuXprf4m Ev ZWiD4nhWM1Ph -l*o4O Ec-o Ki)J!9 Z8lQH w$$stm0dqakr+1k&FH 4JN$S0bg1%h 3KUQ0 -y-MkqqWVRdy*DItBZck*ax(EekA#lHoa)3pTW321 I*izekG1cxp nSA4sp!&$0i WX%RI)J*e0TUl)1KN hHj1NnOll18 L)Doj%Ndfk (CLiYgt(z7mC51 fbQW ))Ipt8!y 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