1、Shaoxing QuInstitute of Mechanics, Zhejiang UniversityEmail: Tel.: 87952024Mechanics of Materials & Mechanics of Materials & ExperimentsExperiments（甲）（甲）I IAxial tension, compression and the internal force and stresses on both cross section and inclined section Mechanical behavior of materia

2、ls subjected to tension and compression, as well as Hookes lawDeformation and strain energy under axial tension and compression, stress concentrationStatistically indeterminate problems with tension and compression (including thermal stress and assembly stress)Direct shear and bearingHistorical pers

3、pective of architects and engineersIndustrial RevolutionTimber, Brick, & MortarMetals, Polymers, Plastics, etcCompressive LoadsTensile LoadsHistorical perspective of architects and engineersZhao Zhou BridgeHydraulic JacksPPmmInternal force on cross sectionThree steps:1. Cut2. Replace with Result

4、ant force and resultant moment3. Equilibrium equationsF1F3F2FnF1FRF3M00FMPPmmSign convention for resultant forceN: axial forcePmmAxial force diagram (軸力圖軸力圖)P2P1mmP3PPmmIf a bar is subjected to external forces P1, P1 , , Pn and n2, then N=N(x). Axial force diagram (軸力圖軸力圖) Problem. A bar is subjecte

5、d to the force system as shown in the following Fig . Plot the axial force diagram of the bar.P1=2kNP2=3kNP3=1kNABCN2P1 =2kNP2 =3kNACP1=2kNAN1 P1=2kNP2=3kNP3=1kNABCPPmmStress on cross sectionPN P ACmmCmmp mPpA00limlimmAAPppA : normal stress: shear stressPN ANdAPlane cross-section assumption. If the

6、cross section is plane at first, it still remains plane after deformed and perpendicular to the axial line.ANdAANA :Unit: Pa=N/m2 1MPa=106N/m2( )( )( )N xxA x1. Bar with varying cross-sectionsFixedPA(x)x2. Bar with varying axial forceFixedPp(x)xAxial force diagram3. Saint-Venants Principle for axial

7、 tension/compressionPP/2 P/2Problem. Try to determine the maximum normal stress of the screw bar(P=800kN).3max22min44( 800 10 )208MPa3.1470SSAd Solution. 1. Calculate axial force and plot axial force diagramAxial force diagram800kNSP 2. Calculate maximum compressive stressPPkkInternal force on incli

8、ned section. It is observed from experiments that during tensile or compressive loading, a bar may break along inclined section instead of cross-section.PANormal stress on cross section.PPkk kkPP kkPPp kkPP kkPPp cosAAPPcoscosPPPpAAA2coscospsin2sin2pkkPP 2coscospsin2sin2pDiscussion:1. If =0, takes t

9、he greatest value.2. If =45, takes the greatest value.maxmax23. If =90maxmax0Mechanical properties? Strength, hardness, toughness, elasticity, plasticity, brittleness, and ductility and malleability are mechanical properties used as measurements of how metals behave under a load. These properties ar

10、e described in terms of the types of force or stress that the metal must withstand and how these are resisted. Tension & compression experiments to obtain the following properties: elasticity, plasticity, strength and malleability.PAllLow-Carbon Steel in TensionE1. Hookes Law:E: Elastic modulus

11、or Youngs modulus same unit as stress2. Proportional limit p3. Elastic limit e1. Upper yielding limit2. Lower yielding limit sUnstableStable3. Yielding is related to the maximum shearing stress. s reflects the strength of materials.1. have to be increased when it is elongated further (or increasing)

12、2. Ultimate strenth b b also reflects the strength of materials.2. Permanent relative reduction of area1. Residual relative elongation1100%lll1100%AAA5%Brittle materials: cast iron, glass, ceramics5%Ductile materials: carbon steel, copper, aluminum alloyBoth and reflect plasticity of materials1. Unloading along a straight line with the slope as E2. Reloading will follow the unloading path, but elastic limit (proportional limit is enhanced)Cold hardeningShortcoming: plastic deformation or elongation is