材料力學(xué)課件 2

PPPPPPbachhExample2-1Awoodentenonjointisshowninthefigure.Knowingthatthequantitiesarea=b=12cm，h=35cm，c=4.5cmandP=40KN.Trytodeterminetheshearingstressandbearingstressforthejoint.[例2-1]

木榫接頭如圖所示，a=b

=12cm，h=35cm，c=4.5cm,P=40KN，試求接頭的剪應(yīng)力和擠壓應(yīng)力。1

Freebodydiagramisshowninthefigure

受力分析如圖∶

Shearingstressandbearingstress

剪應(yīng)力和擠壓應(yīng)力Shearingforceis剪切面和剪力為∶Bearingforceis擠壓面和擠壓力為：PPPPPPbachhSolution：

解：2mExample2-2

Agearandashaftareconnectedbyakey（b×h×L=20×12×100).Thetorquethatthekeycantransmitism=2KNm.Knowingthediameteroftheshaftisd=70mm，thepermissibleshearingstressandthepermissiblebearingstressofthekeyarerespectively[

]=60MPaand[

jy]=100MPa.Trytocheckthestrengthofthekey.[例2-2]

齒輪與軸由平鍵（b×h×L=20×12×100）連接，它傳遞的扭矩m=2KNm，軸的直徑d=70mm，鍵的許用剪應(yīng)力為[

]=60MPa，許用擠壓應(yīng)力為[

jy]=100MPa，試校核鍵的強(qiáng)度。

3

Freebodydiagramofthekeyisshowninthefigure

鍵的受力分析如圖mbhLmdP

Checkthestrengthofshearandbearing

剪應(yīng)力和擠壓應(yīng)力的強(qiáng)度校核Solution：

解：4Accordingtotheabovecalculation,strengthconditionsofthekeyaresatisfied.綜上，鍵滿足強(qiáng)度要求。bhLdmQ5mm[Example2-3]

Agearandashaftareconnectedbyakey（b=16mm,h=10mm).Thetorquethatthekeycantransmitism=1600Nm.Knowingthediameteroftheshaftisd=50mm，thepermissibleshearingstressandthepermissiblebearingstressofthekeyarerespectively[

]=80MPaand[

jy]=240MPa.Trytodesignthelengthofthekey.[例2-3]

齒輪與軸由平鍵（b=16mm，h=10mm，）連接，它傳遞的扭矩m=1600Nm，軸的直徑d=50mm，鍵的許用剪應(yīng)力為[

]=80MPa，許用擠壓應(yīng)力為[

jy]=240MPa，試設(shè)計(jì)鍵的長度。

6

Freebodydiagramofthekeyisshowninthefigure

鍵的受力分析如圖bhLmmmdP

Strengthconditionsoftheshearingstressandthebearingstress

剪應(yīng)力和擠壓應(yīng)力的強(qiáng)度條件Solution：解：7bhLdmQ

Accordingtotheabovecalculation

綜上8bPPttdPP[Example2-4]

Arivetedtie-inactedbyforceP=110kNisshowninthefigure.Knowingthethicknessist=1cm，widthofitisb=8.5cm.Thepermissiblestressis[

]=160MPa.Diameteroftherivetisd=1.6cmandthepermissibleshearingstressis[

]=140MPa，thepermissiblebearingstressis[

jy]=320MPa.Trytocheckthestrengthoftheriveting.(Assumetheforceactedoneachrivetisequal.）

[例2-4]

一鉚接頭如圖所示，受力P=110kN，已知鋼板厚度為t=1cm，寬度

b=8.5cm，許用應(yīng)力為[

]=160MPa；鉚釘?shù)闹睆絛=1.6cm，許用剪應(yīng)力為[

]=140MPa，許用擠壓應(yīng)力為[

jy]=320MPa，試校核鉚接頭的強(qiáng)度。（假定每個(gè)鉚釘受力相等。）

9

Freebodydiagramisshowninthefigure

受力分析如圖ttdPPP112233P/4bPPSolution：

解：10

Thestrengthconditionsofshearandbearing

剪應(yīng)力和擠壓應(yīng)力的強(qiáng)度條件ttdPPP112233P/411

Thesections2—2and3—3ofthesteelplatearethecriticalsections.

鋼板的2--2和3--3面為危險(xiǎn)面ttdPPP112233P/4Therefore，thetie-inissafe.綜上，接頭安全。12[Example2-5]Forces5P,8P,4PandPareactedatpointsA,B,CandDontherodrespectively，theirdirectionsareshowninthefigure.Trytoplottheaxial-forcediagramoftherod.

[例2-5]圖示桿的A、B、C、D點(diǎn)分別作用著5P、8P、4P、P的力，方向如圖，試畫出桿的軸力圖。ABCDO5P4PP8PNx–3P5PP2P⊕⊕⊕○13[Example2-6]TherodsAB、CD、EFandGHinthestructureareshowninthefigureEachofthemconsiststwoofrolledunequal-legssteels.Knowing[

]=170MPa，E=210GPa.RodsACandEGmaybeseenasrigidrod.TrytoselectthesectiondimensionofeachrodandtodeterminethedisplacementsofpointsA、DandC.

[例2-6]結(jié)構(gòu)如圖，AB、CD、EF、GH都由兩根不等邊角鋼組成，已知材料的[

]=170MPa，E=210GPa。AC、EG可視為剛桿，試選擇各桿的截面型號和A、D、C點(diǎn)的位移。

ACP=300kN0.8m3.2m1.8m1.2m2m3.4m1.2mBDFHq0=100kN/mEG14①Determinetheinternalforce.Thefreebodydiagramisshowninthefigure.

求內(nèi)力，受力分析如圖P=300kN0.8m3.2m1.8m1.2m2m3.4m1.2mABCDFHq0=100kN/mEGSolution：解：15NG=NDDq0=100kN/mEGACNCNANENDP=300kN②Determinetheareabystrengthcondition

由強(qiáng)度條件求面積16③Determinethetypesoftherodsreferencetothetable

試依面積值查表確定型鋼號④Determinethedeformation

求變形17⑤Determinethedisplacement.Thedeformationisshowninthefigure.

求位移,變形圖如圖ABDFHEGCC1A1E1D1G118ABCDP=100kN1.5m3m2.5mF[Example2-7]DiametersofrodACandBDinthestructureshowninthefigurearerespectivelyd1=25mm,d2=18mm.Knowing[

]=170MPa，E=210GPa.RodABmaybeseenasarigidrod.Tryto(1)checkthestrengthofeachrodandtodeterminethedisplacements△Aand△BofpointsAanB.(2)determinethedisplacement△F′ofpointFwhentheforcePisactedonpointA.△F′=△Aisagenerallaw,whichiscalledtheoremofconjugatedisplacement.[例2-7]

結(jié)構(gòu)如圖，AC、BD的直徑分別為:d1=25mm,d2=18mm,已知材料的[

]=170MPa

，E=210GPa,AB可視為剛桿，試校核各桿的強(qiáng)度;求A、B點(diǎn)的位移△A和△B。(2)求當(dāng)P作用于A點(diǎn)時(shí),F點(diǎn)的位移△F′，△F′=△A是普遍規(guī)律：稱為位移互等定理。19BNBP=100kNNAAABCDP=100kN1.5m3m2.5mF①DeterminetheinternalforceThefreebodydiagramisshowninthefingure.

求內(nèi)力，受力分析如圖

Solution：解：20②Checkthestrength

校核強(qiáng)度③Determinethedeformationandthedisplacement

求變形及位移21④Determinedisplacement△F′ofpointFwhenforcePisactedonpointA

求當(dāng)P作用于A點(diǎn)時(shí),F點(diǎn)的位移△F′BDP=100kN1.5m3m2.5mAFC22P=100kN12m12mA[Example2-8]Thestructureisshowninthefigure.Knowing[

]=2MPa，E=20GPa,unitweightofconcrete

=22kN/m3.Trytodesigntheareasofthetwopartsandtodeterminethedisplacement△AofpointA[例2-8]結(jié)構(gòu)如圖，已知材料的[

]=2MPa，E=20GPa,混凝土容重

=22kN/m3，試設(shè)計(jì)上下兩段的面積并求A點(diǎn)的位移△A。23Determinetheareainaccordancewiththestrengthcondition.由強(qiáng)度條件求面積P=100kN12m12mASolution：解：242.Knowingtherelationbetweentheallowableshearingstress[τ]andtheallowabletensilestress[σ]oftheboltmaterialis[τ]=0.6[σ]，Trytodeterminethereasonableratioofthediamete