习题答案第一章绪论1-1(a)I-I 截面；II-II 截面；III-III 截面kN 20=N F kN 10−=N F kN50−=N F (b)I-I 截面；II-II 截面；III-III 截面kN 40=N F kN 10=N F kN 20=N F 1-2(a)（I ）截面，；（II ）截面，0=M 0=S F Pa M =PF S −=(b)（I ）截面，；（II ）截面，θsin 61Pl M =θsin 31P F S =θsin 92Pl M =θsin 32P F S =(c)（I ）截面，；（II ）截面，021M M =l M F S 0−=031M M =lM F S 0−=1-3(2)1-1截面，；2-2截面，；m kN 5⋅−=M kN 10=S F 0=M kN 10=S F 3-3截面，m kN 5⋅−=M kN10=S F 1-41-1截面，；2-2截面，P F N 32=Pa M 43=P F S 32=Pa M 32=1-5；1-1截面kN ，，kN kN 100=NBC F 6.86−=N F m kN 25⋅=M 50−=S F 1-6；1-1截面kN ，，kNkN 33.13=NCD F 2.20=N F m kN 5.2⋅−=M 667.1−=S F 1-7I-I 截面，，；II-II 截面，P F N 23−=2P F S =4PaM =P F N 2887.0−=，P F S 5.0−=PM 25.0−=1-81-1截面，，；2-2截面，，P F N 32=P F S 2=PR M 23=P F N =0=S F ；3-3截面，，PR M =0=N F P F S =PRM =1-9（1），，；（2），，4P R A =813P R B =8P R C =P F SD 43=左P F SD 43−=右0==右左D D M M 第二章拉伸与压缩2-1(2)，；（3），a MP 5.2−=AC σa MP 5.6−=CB σ6105.2−×−=AC ε；（4）6105.6−×−=CB εm1035.15−×−=∆AB 2-2amax MP 9.388=σ2-3；，a max MP 66.63=τa 30MP 49.950=σa 30MP 13.550=τ2-4,,m a 1MP 6.254=σa 2MP 3.127=σ310546.2−×=∆C 2-5aMP 7.32=σ2-622cm 828.2,cm 414.1==b a 2-7cm0376.0=∆l 2-8cm 58.0≥D 2-9kN369≤P 2-10(1)m ；（2）kN 6.0=x 200=P 2-11kgf 14140≤P 2-13mm 6.22≥d 2-14mm80=d 2-15(1)；（2）mm a a MP 8.64,MP 102===CD CE BC σσσ1018.0=∆l 2-16)(mm 83.1↓=∆B 2-17mm 175.0=∆2-19mm61.2=∆C 2-20mm ，mm46.1=∆CH 024.4=∆CV2-21Ebt Pl l /694.0=∆2-22(1)；（2）；（3）)8(24)(33221h y h d y f F N −==πγ)8(24)(232y yh y f πγσ==，h d F N 2max 1213πγ=h γσ2712max =2-2344540′=θ2-24)22(+=EA Paδ2-29)243(21222a ax x a EA Pl +−=δ2-3221212E E E E b e +−=2-332221cm 4,cm 2==A A 2-34P F P F N N 455.0,606.021==2-35P F F N N 828.021==2-372321cm 2472===A A A 2-3823221cm 57.3,cm 68.4===A A A 2-39kN ，kN 33.531==N N F F 66.102−=N F 2-40kN ，kN56.841−=N F 28.522−=N F 2-41(1);(2)a 2a 1MP 78.18,MP 8.14−==σσCt 0628.59=∆2-42(1)kN ;(2);(3)kN 6021=−=N N F F 0kN,8021=′=′N NF F 5.1021=′′−=′′N N F F 2-43kN,kN71.2=B R 25.19=NCD F 2-44598.3,197.7,155.431542∆=⋅⋅∆==⋅⋅∆===C N N N N N l A E F F l A E F F F δ第三章剪切实用计算3-1aMP 58.86=τ3-2mm4.15=d 3-367.1:22.1:1::=h D d 3-4m,mm,mm9=δ90=l 48=h 3-5,a MP 8.34=τa MP 8.22=jy σ3-6]a MP 979.3=τ3-7mm127=l 3-8d =5.95mm 3-9d =3.4cm,t =1.04cm3-10mm,h =63.8mm,x =16.75mm 5.10=δ3-11P =246.2kN3-12a2a 1MP 14.24,MP 07.379==ττ第四章扭转4-3a max a MP 75.40,MP 59.32==ττA 4-4a max MP 28.28=τ4-6cm,cm50.41≥D 699.42=D 4-721029.4−×=ϕ4-8,a max MP 4.26=τ41023.5−×=AB ϕ4-11,m kN 781.4⋅=n M amax MP 56.47=τ4-138.65cm,=2d 210423.0−×=AD ϕ4-14 2.57倍4-167/21=M M4-17d =53mm4-18m N 84.477⋅=n M 4-20kW 9345=N 4-21nr l M F n S 202π=4-23ml M ml M C A 41,43==4-24内管:;外管:;a MP 2.147=τa MP 4.164=τm/48.20=θ4-26,a 1MP 98.16=τa 25MP 8.26=τ4-27mN 1454⋅≤M 4-28amax MP 6.18=τ4-30716.0:886.0:1::321=n n n I I I 4-31降低62.5%4-33amax MP 2.405=τ4-34d =6mm,n =6圈4-35[P ]=3.086kN4-36=0.293cmδ4-38(1);(2)a max 1MP 85.3=τa max 1MP 0.4=τ4-39,rada max MP 22.15=τ0679.0=ϕ第五章弯曲内力5-1(a)aMF a M F F S S S 2,2,003021===2/,,030201M M M M M M −=−=−=(b)qlF ql F ql F S S S ===321,,23222121,21,23ql M ql M ql M −=−=−=(c)qaF qa F qa F S S S 43,,321=−=−=23221,,0qa M qa M M −=−==(d)l q F l q F l q F S S S 03020131,241,61−===,161,032021===M l q M M (e)kN5,kN 5,kN 5321−=−==S S S F F F 0,0,0321===M M M (f)kN10,kN 10,kN 10321===S S S F F F mkN 10,m kN 5,m kN 5321⋅−=⋅=⋅=M M M 5-2(a)000/3)(,/3)(M l x M x M l M x F S −==0max0max 2,/3M Ml M F S ==(b)pax M x F S ==)(,0)(11)()(,)(12a x p pa x M p x F S −−=−=paMp F S ==maxmax ,(c)pxx M p x F S −=−=)(,)()(23)(,2/)(a x p px x M p x F S −−−==paMp F S ==maxmax ,5-7x =0.207l5-842a l x −=第六章弯曲应力6-1(a)amax a MP 2.38,MP 37.30==σσA (b)a max a MP 2.104,MP 73.61==σσA (c)a max a MP 2.128,MP 67.38==σσA 6-2a max MP 26.55=σ6-4cm30≥D 6-5h =0.416m,b =27.7cm 6-6[P ]=56.88kN6-10(1)b =0.5774D ,h =0.8165D ;(2)b =0.50D ,h =0.866D6-11b=27cm6-12a max MP 120=σ6-130,MP 379.0,MP 93.12,MP 03.6a a a ====b a b a ττσσ6-14(在跨中点上,下边缘),(在梁端,中性轴上)a max MP 86.101=σa max MP 397.3=τ6-15amax MP 12.22=τ6-16h =25.6cm,b =12.8cm 6-18x =4.833m6-19h y C 43=6-20232Ebh ql l =∆6-282max 43bh Pl =σ6-29a =1.8m6-30a =1.7322m,q =37.503kN/m6-31,a max MP 46.71=σa max MP 57.3=τ6-322/max =b σσ第七章弯曲变形7-1(a),,EI x M y 220=EI l M y B 220=EIl M B 220=θ(b),,)2464(14322x q x ql x ql EI y −+−=EI ql y B 84−=EIql B 63−=θ(c),,)51010(120322320x lx x l l lEI x q y −+−−=EI l q y B 3040−=EIl q B 2430−=θ(d),,)3(632x ax EI P y −=EI Pa y B 653=EI Pa B 22=θ(e),)0()29(1221a x x a EIqax y ≤≤−−=)2()166438412816(3844322342a x a a a x a ax x EIqy ≤≤+−+−−=,EI qa y B 24414−=EIqa B 673−=θ(f),)0()830(2443221a x x ax x a EIqy ≤≤+−−=)2(241)661(433222a x a a x a ax x a EI q y ≤≤+−−−=,EI qa y B 24714−=EIqa B 6133−=θ7-2(a),,)(6)(30lx l x EI M x y −−=EI l M l y 162(20−=3(3920max lx EI l M f =−=,EI l M A 60−=θEIl M B 30=θ(b),,4(6)(30lx l x EI M x y −=02(=l y )32(37220max lx EI l M f =−=EIlM B A 240−==θθ(c),)1073(360)(22440x l l x lEIxq x y −−−=)5193.0(15340maxl x EIl q f =−=,EI l q A 360730−=θEIl q B 4530=θ(d),)2/()82417(384)()2/0()16249(384)(322323231l x l x lx x l l EI qlx y l x x lx l EIqxx y ≤≤+−+−−=≤≤+−−=,,EI ql l y 7685)2(4−=EI ql A 12833−=θEIql B 38473=θ7-3(a)])2(!32)(!312[1)(332a x Pa x P x Pa EI x y −+−−=,,,EI Pa y C 433−=EI Pa C 12112−=θEI Pa y D 123=EIPa D 122=θ(b)])2(4)(!4)(2!3216[1)(442233a x qaa x q a x qa x qa x qa EI x y −+−−−−×−−=,,,EI qa y C 484=EI qa C 1633=θEI qa y D 48174−=EIqa D 48193−=θ(c)])2(!323)(!4)(!349!348474839[1)(343334a x qa a x q a x qa x qa x qa qa EI x y −×+−−−×+−+−=,,,EI qa y C 48394−=EI qa C 48473=θEI qa y D 4874=EI qa D 4833−=θ(d)])2(!4)(!3!4!337639[1)(43433a x qa x qa x q x qa x qa EI x y −+−−−×−−=,,,EI qa y C 721154−=EI qa C 18174−=θEI qa y D 18294−=EIqa D 983=θ(e)])2(!2)(!4)(!3!23!24[1)(243322a x qaa x q a x qa x qa x qa EI x y −−−−−−+−=,,,EI qa y C 241014−=EI qa C 383−=θEI qa y D 47−=EIqa D 6173−=θ7-4(a),(b),(c),(d)EI a M y C 320−=EI qa y C 344−=EI Pa y C 3−=EIPa y C 3103−=7-5=3.77cmC y 7-6d =0.28m7-7(a)(b)EIPl EI Pl y B B 185,9223−=−=θEIqa b qa qa EI y B B 668(1334−=+−=θ7-83611a EIP y C −=7-9EIqb EI qab EI a b qb f C 863)(433−−+=7-10(a)EIqa EI qa y C C 24,24534−=−=θ(b))44(24),43(24332323l a l a EIql l a a EI qa y C C −+−=−−−=θ7-11EIql y EI ql y C B 76897,6144239944−=−=7-12ql P 43=7-13a /b =1/27-1426,282334k ql EI ql kql EI ql y +=−−=θ7-15EIPl k P y C 243493−−=7-16EIPl y A 33−=7-17(1),(b),(c)20161l q M =20max 064.0l q M =lx q q 0=7-18EIPx y 33=7-20l a 32=7-2122275Ebh Pl x A =7-22小挠度下：221dx y d ≈ρ7-23Ebhtl h Q Ebh tl x EI thl y A A A 23322,6−⋅=−=7-242121h h =σσ7-25EI Pa y F 48173−=7-263/2l x =7-27(a)(b)EIqa y C 44=EI Pa GI Pal EI Pl y n C 3333++=7-28mN 85.51⋅=n M 7-293334Eah Pl y C −=7-30(a)(b)EIPa f 33−=EIPa f 233−=第八章应力和应变分析基础8-3(a),,,a MP 75.13=ασa MP 825.10=ατa max MP 5.12=τ045=α(b),,,a MP 606.5−=ασa MP 606.10−=ατa max MP 15=τ045=α(c),,,a MP 5.17=ασa MP 0.13−=ατa max MP 0.20=τ045=α(d),,,a MP 20=ασ0=ατa max MP 5.13=τ045=α8-4(a)，，a 1MP 426.52=σa 3MP 426.32−=σ05.22=α(b)，，a 1MP 37=σa 3MP 27−=σ04700′−=α(c)，，a 1MP 4.62=σa 2MP 6.17=σ71580′=α(d)，，a 1MP 7.120=σa 3MP 7.20−=σ05.22−=α8-5(a)，，，3.881=σ02=σ3.283−=σ3.58max =τ(b)，，，511=σ02=σ413−=σ6.4max =τ(c)，，，1201=σ5.722=σ5.223−=σ2.71max =τ(d)，，，301−=σ302−=σ303−=σ0max =τ(e)，，，521=σ502=σ423−=σ47max =τ8-7，，a MP 15=τ=1σ02=σa3MP 30−=σ8-9，=1σa 2MP 7.135−=σa3MP 150−=σ8-10，，a 1MP 60−=σ02=σa3MP 8.19−=σ8-12m N M n ⋅=6.1258-13kN 56.125=P 8-14cm31007.94−×=∆bc l 8-15,01=σδδµσ∆−=E 28-16,,a MP 33.213−=σa MP 69.301−=τa MP 49.369=p 8-186105.288−×−=θ8-19，，，611025.627−×=ε621025.166−×−=ε008.16=α6max 105.793−×=γ8-20，，a 1MP 889.88−=σa 3MP 44.124=σ030=α8-21a MP 29.8=p 8-22,E qt t µ2−=∆)2(21q Eµθ−=第九章强度理论9-1（1）按第一强度理论，(a)危险；（2）按第二强度理论，(b )危险9-2（1）按第三强度理论，(a)危险；（2）按第四强度理论，全部不危险9-3a 4MP 138=xd σ9-4a 3MP 72.179=xd σ9-6aMP 5.1=p9-7cm 0.1≥t 9-8(1)(2)安全a 2MP 4.18=xd σ9-9，更小[]σσ==a 3MP 300xd 4xd σ9-10kN/m24.415=q 9-11aMP 4.42=M xd σ9-12tHdxd 43γσ=第十章组合变形时的强度计算10-1（a ）斜弯曲(b)平面弯曲(c)平面弯曲(d)斜弯曲(e)斜弯曲(f)弯扭组合(g)平面弯曲(h)斜弯曲10-2（2）（3）cm a max MP 84.9=σ602.0=f 10-3(1)b =9cm ,h =18cm (2)cm,21097.1−×=f 01.81=α10-4a max MP 69.150=σ10-5,,a MP 2.146−=A σa MP 56.120=B σa MP 42.36−=C σ10-6)(MP 1.91a max 压=σ10-7kN []108.8=P 10-8(2)(3)a max MP 42.158=σ)(117→=EI P f B 10-9amax MP 083.7=σ10-10αtan 82d l S +=10-12a max MP 130=σ10-13amax MP 75.160=σ10-14a max MP 72.25=σ10-16a max MP 6.135=σ10-18,[]+<=σσa MP 85.26内[]+−<−=σσa MP 38.32外10-19d =3.38cm 10-20d =5.95cm 10-21d =5.11cm 10-22a 4MP 4.54=xd σ10-23a max MP 2913=σ10-24m-m 截面：；n-n 截面：a 3MP 1.89=xd σa 3MP 11.47=xd σ10-25a 4MP 48.269=xd σ10-26a 3MP 4.142=xd σ第十一章变形能法11-1（a ）,(b)EA l P U 62=EAl P U 672=11-2716=b a U U 11-3EAl P U 2957.0=11-4(a)(b)4126.9d G l m U π=EIl m U 182=11-5EIql EI Pl B 8322+=δ11-6(a),)(42向上EI Ma A −=δ)(125顺时针EIMa B −=θ(b),EI qa A 24−=δEIqa B 853=θ(c),EI qa A 24714=δEIqa B 353=θ(d),EI qa A 324=δEIqa B 83=θ11-7(a),EI Pa B 343=δEIPa A 2=θ(b),EI PL B 9653=δEIPL A 1652=θ11-8222122)1()(3a b k P ak Pb b a EI Pb A ++++=δ11-9EIqL 2473=θ11-10(a),EI qa A 323=θEIqa y A 854=(b),EI qa B 123−=θEIqa y A 2474=(c),,EI qa A 243=θEI qa x B 124=EI qa x C 38454=(d)EIqa y C 48514=(e),EI Ma A 34=θEIMa y C 652=11-11(a),(b)EI a h Ph X AB3)32(2+=EI Pl X AB 33=11-1218.3mm=A f 11-13EA Pa EI Pa f C 28323+=11-14,,)()221(←+=EA Pl x A )(↑−=EA Pl y A )()221(逆时针+=EA P AB θ11-15,)(3726↓=EA Pb y A 。