钢结构设计基本原理课后答案 肖亚明

合肥工业大学出版社出版 （肖亚明主编）第三章解：Q235

w160N/mm2N600kNf(1）采用侧面角焊缝hf

1.5

145.6mm14tmaxtmaxf

min

1.21012mmhf角钢肢尖和肢背都取 hf

t~2)10~2)9~8mm8mm3—2K1

0.65K2

0.35N K1 1

N0.65600390kN，N2

KN0.35600210kN2所需焊缝计算长度：N

390103l 120.7hfNl 2N

fw 20.78160f 210103 117.19mmw2 20.7hf

fw 20.78160f焊缝的实际长度为：l l

2hf

217.6328233.63mm240mm。l lw2

2hf

117.1928133.19mm140mm。（2）采用三面围焊缝，取hf正面角焊缝承担的内力为：

6mmN 0.7hf

l w3

fw621001.22160f侧面角焊缝承担的内力为：N K1 1

NN3

/20.65600163.97/2308.01kNN K2 2

NN3

/20.35600163.97/2128.02kN所需焊缝计算长度：l N1

308.01103 229.17mm20.7hfN

fw 20.76160f128.02103l 2w2 20.7hf

95.25mmfw 20.76160f焊缝的实际长度为：l l h1 f

229.176235.17mm240mm。mml l h 95.256101.25mm，取110 .mm2 w2 f解：Q235

w160N/mm2f（1）取d d1 2

170mm角焊缝受到轴力和剪力的共同作用，且均作用在角焊缝形心处1.5212角焊缝受到轴力为：N6001.5212

499.23kN1.5212角焊缝受到剪力为:V1.5212

332.82kNl 21702hw

3402hf N 499.23103

fw1.22160195.2N/mm2f 20.7hlfw

1.4hf

(3402h) f ff由上式求得：h 5.55mmfV 332.82103 fw160N/mm2f 20.7hlfw

hf

(3402h) ffhf最小焊脚尺寸hf

4.49mmtmaxtmax

1.5

206.71mm20故取焊脚尺寸为hf

7mmN 499.23103 156.26N/mm2

fw195.2N/mm2f 20.7hlfw

1.47(34027) f fV 332.82103 104.18fw160N/mm2f 20.7hlfw

1.47(34027) f// 22f f f156.26/1.222104.182

w，故取hf

165.10N/mm2f8mm可满足要求.

w160N/mm2f（2）改取d 150mm，d 190mm1 2角焊缝受到轴力、剪力和弯矩的共同作用1.51.5212角焊缝受到轴力为:N600 1.521211.5212角焊缝受到剪力为：1.5212

332.82kN角焊缝受到弯矩为：MNe499.23209984.6kNmm9.9846106Nmmh 0.785.6mm，l 1501902h 34028324mme w f5.63243wI 2 12 31.74106mm4w2IW

231.74106 195.96103mm3w最大正应力为：

324 324 N M

499.23103 9.9846106f 20.7hl Wfw w

20.78324 195.96103188.53N/mm21.22160195.2N/mm2V 332.82103 91.72fw160N/mm2f 20.7hl// 22f f f188.53/1.22291.722

20.78

f179.70N/mm2f

w160N/mm2f解:Q23512角焊缝①12

w160N/f

不满足要求。tmax最小焊脚尺寸:h tmaxf

1.5

5.2mm最大焊脚尺寸:h 1.2t 1.21214.4mmf min取h 6mmfNF角焊缝受到弯矩为:MNe100202kNmh 0.764.2mm,l 2002h 20026188mme w f4.21883I 2 4.65106mm4w 122I 24.65106W w 49.48103mm3w 188 188最大正应力为: N M

100103 2106f 20.7hl Wfw w

20.76188 49.48103103.74N/mm21.22160195.2N/mm2满足要求。（2）角焊缝②③角焊缝的有效截面如图所示xx取h 8xxf角焊缝有效截面形心位置：yy2

5.612255.45.621925.6192/2]/(1345.6255.45.621925.6)136.03mm剪力由腹板焊缝承担，腹板面积为:A 21925.62150.4mm2w全部焊缝对x轴的惯性矩为：I 1345.6136.03122.8)2255.45.6136.032.8)2w21925.6192/2)225.61923/1215.56106mm4翼缘焊缝最外边缘的截面模量：W Iw

15.56106 21.15104mm3h1

192136.03125.6翼缘和腹板连接处的截面模量:W Iw

15.56106 27.81104mm3w2 h2

192136.03腹板底边缘处的截面模量：I

15.56106W w3 y2

11.44104mm3136.03M10012012kNm由弯矩得最大应力为:M 12106 104.90N/mm23 Ww3腹板的剪应力为：

11.44104F/Aw

100103/46.50N/mm2 3 22f104.9021.22 46.502

97.75N/mm2f

w160N/mm2f解

满足要求。： Q235 钢 、 查 附 表 1-2 得fw185N/mm2,t

w125N/mm2,v

w215N/mm2c焊缝有效截面形心位置：yy 126)18812188/2]/(1261218812)134.13mm2焊缝对x轴的惯性矩为：I 1261212134.136)218812188/2)2121883/12x15.70106mm4翼缘焊缝边缘的截面模量：W Ix

15.70106 23.83104mm31 y 18812134.131翼缘和腹板连接处的截面模量:W Ix

15.70106 29.14104mm32 188y2

188134.13腹板底边缘处的截面模量:I

15.70106M

W x3 y2

11.70104mm3134.13由翼缘上边缘处焊缝拉应力M 120F ft W 23.83104 t1

185N/mm2F18523.83104/120367.38kN由腹板下边缘处焊缝压应力M 120F fc W 11.70104 c3

215N/mm2F21511.70104/120209.62kN由腹板焊缝单独承担剪力，腹板的剪应力F/Aw

F12)

w125N/mm2vF12518812腹板下端点正应力、剪应力均较大，由腹板下端点的折算应力222120F2211.70104 F18812c t得：F158.84kN

1.1185203.5N/mm2F。解：Q345B

w200N/mm2，hf

8mm角焊缝有效截面的形心位置：xx1

(21975.6197/2)/(21975.65005.6)截面的惯性矩：I 21975.62502wx5.65003/12196.23106mm4I 21975.6/243.41)225.61973/12wy5.650019.11106mm4JI Iwx wy

103215.34103mm4T(30020543.41)F461.59F由扭矩产生的最大应力Tf

TryJ

461.59F250215.34106

535.88106Ffwf

200N/mm2F200/535.88106373.22kNT

Trx

461.59F 329.23106Ff ff

J 215.34106w1.22200244N/mm2fF

F244/329.23106741.12kNF V 199.74106F fw244N/mm2F f A 21975.65005.6 f wF244/199.741061221.59kNT fV2f T)2ff329.23106F199.74106F21.22 (535.88106F)2689.32106Ff

w200N/mm2fF200/689.32106290.14kN综上得该连接所能承受的最大荷载为F290.14kN。解：Q235B

b140N/mm2，fv

b305N/mm2c单个螺栓的抗剪承载力设计值：d2

222Nbn fv v 4 v

2

140106.44kN4Nbd tfc

b2214305cNb min(Nb,Nb)93.94kNmin v c一侧所需的螺栓数目为:nN/Nb 700/93.947.45（个)，取n8min螺栓的布置如图所示：6N 888

10508045458050N净截面强度验算:螺栓群最外端净截面强度：N/An

700103/[(360423.5)14]187.97N/mm2f215N/mm2净截面强度满足要求。解：Q235

b140N/mm2，v

b305N/mm2,c

b170N/mm2t单个螺栓的抗剪承载力设计值：d2

222Nbn fv v 4 v

1

14053.22kN4Nbd tfc

b2218305cNb min(Nb,Nb)53.22kNmin v c单个螺栓的抗拉承载力设计值：d2Nbt

e fbAt

fb30317051.51kNt牛腿下支托承受剪力时由受力最大的螺栓承受的拉力MyN 1

F160320 0.133FN

51.51kN1 m y2i

2(802160224023202) t得：F386.32kN故支托承受剪力时该连接所能承受得最大荷载设计值为F386.32kN。牛腿下支托不承受剪力时MyN 1

F160320 0.133FN

51.51kNt m y2i

2(802160224023202) t得：F386.32kN由N F/nF/100.1FNb120.78kNc得:F1207.80kNNN2N2tNb vtNbv0.133F2 251.51 53.22

0.00319F1得:F313.15kN综上得支托承受剪力时该连接所能承受得最大荷载设计值为F313.51kN。解：Q345BM22，C螺栓的布置如图所示

b140N/mm2，fv

b385N/mm2c单个螺栓的抗剪承载力设计值:d2

222Nbn fv v 4 v

1

14053.22kN4Nbd tfc

b2210385cNb min(Nb,Nb)53.22kNmin v c螺栓群承受剪力及扭矩的共同作用TFe1200.30.050.105/2)48.3kNm受力最大的螺栓承受的应力为:TyN

48.3106200 42.45kN1Tx

x2 yi i

1052.52

4

2002)TxN

48.310652.5 11.14kN1Ty

x2i

y2 1052.52i

4

2002)N1Vy

F12010312kNn 102NN2NN21Tx1Ty42.45211.14122min

53.22kN8.8摩擦型连接

满足要求，故采用M22。预拉力P125kN，接触表面用喷丸处理，0.45单个螺栓的抗剪承载力设计值：Nb0.9nV f

P20.45125一侧所需的螺栓数目为:n N

6.9个,取n7Nb 101.3V承压型连接fb250N/mm2，fv

b470N/mm2c螺栓的布置如图所示单个螺栓的抗剪承载力设计值：d2

202Nbn fv v 4 v

2

250157.0kN4Nbd tfc

b2014470cNb min(Nb,Nb)131.6kNminn1010.9，M22摩擦型连接

NNbmin

v c 700131.6

5.3个，取n6预拉力P190kN，接触表面用喷丸处理,0.50①角钢肢与牛腿连接取螺栓的个数为n580mm,单个螺栓的抗剪承载力设计值：Nb0.9nv f

P20.50190T35055)43.75kNm则受力最大的螺栓承受的应力为：N N/n350/570kNvyTrN

43.75106160

109.38kNTx x22N2Tx Vy

yi

2

1602)109.38270109.382702v满足要求。②角钢肢与柱翼缘连接取螺栓的个数为n1080mm，此处连接承受剪力和弯矩的共同作用，弯矩M350180m受力最大的螺栓承受的拉力为:MyN 1

63106160 78.75kN0.8P0.8190152kNt m y2i

4(8021602)单个螺栓的抗剪承载力设计值：Nb0.9nv f

(P1.25Nt

)10.501.25(2)承压型连接

N N/n350/1035kNNb41.20kNv v满足要求。fb310N/mm2，fv

b590N/mm2，c

b500N/mm2t①角钢肢与牛腿连接取螺栓的个数为n480mm，单个螺栓的抗剪承载力设计值:Nbnv v

d2fb4 v

2

2224

310235.56kNNbdtfc

b2220590cNb min(Nb,Nb)235.56kNmin v cT35055)43.75kNm则受力最大的螺栓承受的应力为:N N/n350/487.5kNvy N Tx x2 y222N2Tx Vy

43.751061202(4021202)

164.06kN164.062164.06287.52min

235.56kN满足要求。②角钢肢与柱翼缘连接取螺栓的个数为n880mm，单个螺栓的抗剪承载力设计值：Nbnv v

d2fb4 v

1

2224

310117.78kNNbdtfc

b2220590cNb min(Nb,Nb)117.78kNmin v c此处连接承受剪力和弯矩的共同作用，弯矩M350180m受力最大的螺栓承受的拉力为：MyN 1

63106120 t m y2i

4(4021202)N N/n350/843.75kNNb/1.2216.33kNv cN2NN2N2tNb vtNbv82.032 43.752151.50 117.78三.计算题1.解：Q235截面Ⅰ净截面面积：

满足要求。第四章1002402A 2101002402n

45221.5)3094.06mm2由应力N/An

f，得：NAn

f3094.06215665.22kN截面Ⅱ净截面面积：

A 210(451004521.5)3370mm2n由应力N/An

f NAn

f3370215724.55kN综上得此拉杆所能承受的最大拉力为：N665.22kN查型钢表得：i 3.05cm,i 4.38cmx ymin查表4-2得：容许长细比250由长细比l /i，得：l i3.05250762.5cm0 0 x所以，此拉杆容许达到的最大计算长度为：l 762.5cm。02.：Q235Nl6mAB截面几何特性：A232016400813440mm284003I 2320162082485.69106mm4x 12163203I 2 87.38106mm4y 12I /Ax485.69I /Ax485.69106/13440x

190.1mmI /Ay87.38I /Ay87.38106/13440y

80.63mm长细比：

lox 31.566103

150x i 190.1xl 6103 y iy

80.6374.40

150x类）

0.930(b类y

0.723（bN 2400103 186.10/mm2f215N/mm2 A 0.96013440xN 2400103 247.10/mm2f215N/mm2 A 0.72313440yy轴整体稳定不满足要求；由以上计算结果知，此柱在y轴的整体稳定承载力不满足要求，可在柱长的中点加侧向支撑来满足稳定承载力的要求.3.：Q235l（1)截面a截面几何特性：A2320203201016000mm2103203xI 12 2320201702397.23106mm4x203203yI 2 12 109.23106mm4yi xI /Ax397.23106/16000157.56mmi yI /Ay109.23106/1600082.62mm长细比:

lox 63.4610103

150x i 157.56xl 10103 y iy

82.62 121.03

150由长细比查表得稳定系数为：x

0.788（b，y

0.375（c类）由整体稳定N fA得:N Af0.375160002051230kNmin故截面a的柱所能承受的最大轴心压力设计值为：N1230kN。b截面几何特性：A240016400816000mm284003xI 12 2400162082596.44106mm4x164003yI 2 12 170.67106mm4yI /AxI /AxxI /AyI /Ayy

193.07mm596.44106/16000170.67596.44106/16000170.67106/16000长细比：

lox 51.810103

150x i 193.07xl 10103 y iy

103.2896.8

150由长细比查表得稳定系数为:x由整体稳定N fA

0.848（b，y

0.476（c类）得：N Af0.476160002151637.44kNmin故截面b的柱所能承受的最大轴心压力设计值为：N1637.44kN。4.解：Q235钢,N，l 3m ,l 6m0x 0y取 80，x y

80查表得：x

0.688（b，y

0.688（b类）A

N 1000103 6760.41mm2f 0.688215i l /x ox x

3000/8037.5mmi l /y oy y

6000/8075mm由各截面回转半径的近似值查附表9—1得：i 0.28h,ix y

0.24b则 h/,b75/选取截面220012512截面验算：查型钢表得:A237.975.8cm2，i 3.57cm，i 9.54cmx y lox310 84.03

150x i 35.7xl ly iy

610395.4

62.9150查表得：x

0.661（b，yN 1000103

0.792（b类） 199.58N/mm2f215N/mm2 A 0.6617580x满足要求，故选用220012512。5.解：Q235钢，N，l 6m ，l 3m0x 0y（1)热轧工字钢取 80，x y

80查表得：x

0.783（a）,y

0.688（b类）A

N 1000103 6760.41mm2f 0.688215i l /x ox x

6000/8075mmi l /y oy y

3000/8037.5mm由各截面回转半径的近似值查附表9-1得：i 0.39h，ix y

0.20b则 h75/0.39b/选取截面45a(h=450mm，b=150mm）截面验算：b/h=0.333〈0.8A102cm2ix

17.7cm，iy

2.89cm lox 33.91506103x i 177xl 3103 y iy

28.9 103.8

150查表得：x

0.955（a类）,yN 1000103

0.530（b类） 184.98N/mm2f215N/mm2 A 0.53010200x满足要求,故选用45a。（2）3块剪切边的钢板焊成工字形截面取 80，x y

80查表得：x

0.688（b类)，y

0.578（c类）A

N 1000103 8047mm2f 0.578215i l /x ox x

6000/8075mmi l /y oy y

3000/8037.5mm由各截面回转半径的近似值查附表9-1得:i 0.43h,ix y

0.24b则 h75/，b/200mm，12mm，250mm,截面验算：截面几何特性:A220012250107300mm2102503xI 12 220012131295.39106mm4x122003yI 2 12 16106mm4yI /Ax95.39I /Ax95.39106/7300xI /AyI /Ayy

114.31mm16106/16106/7300长细比：

lox610 52.53

150x i 114.31xl ly iy

310346.82

64.1150由长细比查表得稳定系数为: 0.844（b类， 0.681（c类）x yN 1000103 201.15N/mm2f215N/mm2135/f135/fy

A 0.681x

满足要求b95t 12

7.92max

100.164.116.410h 25025(250t 10w

)max

250.564.157.05135/f135/fy刚度、整体稳定及局部稳定均满足要求，故选用此截面。C20707027+31+2101434327443f 9.6N/mm2，锚栓采用d20mm5000mm2c1）底板尺寸底板所需面积

N 1000103A A 5000109167mm2fc靴梁厚度取10mm

0 9.6底板宽度： B200210270360mm底板长度: LA/B109167/360,取采用BL360360,靴梁、肋板的布置如图所示基础对底板的压应力为：qN/An

1000103/(36025000)8.02N/mm2三边支承板：区格①b/a1 1

43/2000.2150.3,可按悬臂板计算区格②

M 1/2qb21/28.024327414.5Nmm1 1b/a1 1

70/2500.280.3，可按悬臂板计算M 1/2qb21/28.0270219649Nmm1 1四边支承板（区格③：b/a1 1

250/952.63，查表4-8得0.112M qa20.1128.029528131Nmm46Mmax/f6196496Mmax/f619649/2052)靴梁计算

23.98mm，取t24mm。靴梁与柱身的连接按承受柱的压力计算，为四条侧面角焊缝连接 ,取h 10mm，则焊缝的计算长度为fN 1000103l w 40.7hf

fw 410160f取靴梁高即焊缝长度260mm。靴梁与底板的连接焊缝传递柱压力，取hf度为

10mm，所需焊缝总计算长 l w

N 1.220.7h fwf f

10001031.220.710160

732mm焊缝的实际计算总长度超过此值。l度t，底板传给靴梁的荷载q1靴梁支座处最大剪力

Bq/23608.02/21443.6N/mm靴梁支座处最大弯矩

Vmax

ql1443.64362074.8N1Mmax1/2q1l21/21443.64321334608.2Nmm1.5

Vmax

62074.81.5 35.81N/mm2

125N/mm2ht 26010 vM 61334608.2 max 11.84N/mm2f215N/mm2W 102602靴梁强度满足要求。3)肋板计算将肋板视为支承于靴梁的悬臂梁，悬伸长度为l70mm取其厚度t10mm。其线荷载可偏安全假设为2q Lq/23608.02/21443.6N/mm2肋板与底板的连接为正面角焊缝，取hf

12mm，焊缝强度为 q2lw

1443.6 140.87N/mm2

w160N/mm2f 0.71.22hlfw

0.71.2212 f肋板与靴梁的连接为侧面角焊缝，所受肋板的支座反力为R70取h 7mm，所需焊缝长度为fl R 101052 64.45mmw

20.7hf

fw 20.77160f肋板支座处最大剪力V ql1443.670101052Nmax 2肋板支座处最大弯矩M 1/2ql21/21443.67023536820Nmmmax 21.5

Vmax

1010521.5 116.60N/mm2

125N/mm2ht 13010 vM 63536820 max 125.57N/mm2f215N/mm2W 101302肋板强度满足要求。前面柱脚板件区格弯矩相差较大，重新设置肋板如上图基础对底板的压应力为：qN/An

1000103/(36025000)8.02N/mm2三边支承板：区格①b/a1 1

43/2000.2150.3,可按悬臂板计算区格②

M 1/2qb21/28.024327414.5Nmm1 1b/a1 1

70/1200.58，0.0688M qa20.06888.0212027945.57Nmm3 1四边支承板（区格③：b/a1 1

250/952.63，查表4-8得0.112M qa20.1128.029528131Nmm4两边支承板(区格④：1102702a 11027021

11070/130.3859.06mmb/a1 1

59.06/130.380.45，0.049M qa20.0498.02130.3826680.24Nmm2 16Mmax/f68131/205底板厚度t 15.42mm6Mmax/f68131/2056.：Q235Nl6m(1）选取分肢截面尺寸(按实轴稳定条件确定）取 60y查表得：y

0.807（b类）N 2400103所需截面面积：A 13832mm2 f 0.807215y截面验算：

i l /y oy

6000/60100mmA268.09136.18cm2iyz 2.37cm,I 496.7cm40 1长细比：

13.63cm，i1

2.70cm， loy

610344.0

150y i 136.3y由长细比查表得稳定系数为：yN 2400103

0.882（b类） 199.82N/mm2f215N/mm2 A 0.88213618y满足要求,故选用2［36b。（2）确定分肢间距（按虚轴稳定条件确定)取缀条565A1

5.42cm2227yA2227yA2A144.0227136182542x

40.0i l /x ox x

6000/40.0150.00mm查附表9—1ix

0.44b，故bix

/0.44150.0/0.44340.91mm，取b。两槽钢翼缘间净距为340298100mm,满足构造要求。验算虚轴稳定： Ab 2 I 2I z2496.7104680923.7)2x 1

22

0301.41106mm4IxA301.4110613618i IxA301.4110613618x l /ix ox x

6000/148.7740.3mm227xA2227xA2A140.3227136182542ox

44.3150查得:xN 2400103

0.881（b类） 200.04N/mm2f215N/mm2 A 0.88113618x满足要求。(3）分肢稳定（只有斜缀条45o）l01

2(340223.7)21.670.7

0.744.331.011 i 1

max故分肢的刚度、强度和整体稳定无需进行验算,均满足要求。（4）斜缀条稳定柱剪力： V

13618215Af85fAf85fy235

34.44kN1斜缀条内力：N V1

V/234.44/224.35kN1 sin sin sin45ol1 01

/imin

[(340223.7)/sin45o]/11.037.62

150查表得：0.908（b）强度设计值折减系数1—5得：0.60.00150.60.001537.620.656N 24.351031 49.48N/mm2 f0.656215141.04N/mm21A 0.9085421满足要求.缀条无孔洞削弱，不必验算强度。缀条的连接角焊缝采用两面侧焊，按要求取hf

5mm；单面连接的单角钢按轴心受力计算连接时，0.85。则焊缝的计算长度：kN

0.724.35103l 1 10.7hf

w 0.750.85160fl k2N1

0.324.35103 15.34mmw2 0.7hff

w 0.750.85160f50mm。7.：Q235Nl（1)选取分肢截面尺寸(按实轴稳定条件确定)取 60y查表得：y

0.807（b类)N 1500103所需截面面积:A 8645mm2 f 0.807215yi l /y oy y

7500/60125mm9-1得iy

0.38h，故hiy

/0.38125/0.38328.95mm截面验算：y查型钢表得：A248.597cm12.44cm，z02.24cm，yI 304.7cm41长细比： loy

7.510360.3

150y i 124.4y由长细比查表得稳定系数为:yN 1500103

0.806（b类） 191.86N/mm2f215N/mm2 A 0.8069700y满足要求，故选用2[32a。（2）确定分肢间距(按虚轴稳定条件确定） ox y

60.30.5 0.560.330.2,取 30max 122y22y 160.32302x

52.3i l /x ox x

7500/52.3143.40mm查附表9-1ix

0.44b，故bix

/0.44143.40/0.44325.91mm，取b.两槽钢翼缘间净距为320288，满足构造要求。验算虚轴稳定：l io1 1

3025.1753mm,取缀板净距lo1

760mm Ab 2 I 2I z 2304.7104485022.4)2x 1

22

0189.75106mm4IxA189.751069700i IxA189.751069700x l /ix ox x

7500/139.8653.6mm2222x 1ox查得：x

15053.6230253.62302N 1500103 193.30N/mm2f215N/mm2 A 0.8009700x(3)分肢稳定

300.71

满足要求。0.561.430.7及40max故分肢的刚度、强度和整体稳定无需进行验算，均满足要求.(4）缀板设计2纵向高度h c2(320222.4)183.47mm，2b 3 3厚度t

c 320222.4 6.88mm,取h

200mm8mm.相邻缀板净b 40 40 b b距l 760mm，相邻缀板中心矩lo1 1

l ho1

760200960mm。缀板线刚度之和与分肢线刚度比值为： I /cb

22003/12)/(320222.4)

12.216I /l1 1

304.7104/960Af85fy235缀板刚度满足要求Af85fy235

970021585

24.54kNVl V l 24.54 960

11 1 5889.6kNmm2 2 2 2 2缀板剪力：V

Vl 24.54960 42.80kN1b1 c 2(320222.4)16Mb1

65889.6103 110.43N/mm2

f215N/mm2th2b b

82002b1

1.542.8103 40.12N/mm2

125N/mm2th 8200 vb b满足缀板的强度要求.缀板焊缝计算。采用三面围焊，计算时可偏安全地仅考虑端部纵向焊缝，取焊脚尺寸hf

7mm，lw

200mm。则A 0.7hlw fw

0.77200980mm20.7hl2

0.7720023W w 6

w 32666.67mm6 Mb1f Ww

5889.6103 180.29N/mm232666.67

fw1.22160195.2N/mm2f fV Vf Aw

42.80103 43.67N/mm2980

w160N/mm2f在弯矩和剪力共同作用下焊缝的折算应力为 f2 2ff180.2921.22 43.672焊缝强度满足要求。四.计算题1.解:Q235lqk

154.10N/mm2f第五章10.52434.5kN/m

w160N/mm2fq1.210.51.42446.2kN/m弯矩设计值：Mx

ql2 46.25.52174.69kNm1 8 81 由抗弯强度要求的截面模量为：W Mx

174.69106 773.82103mm3nx

f 1.05215xI36a,xq60.0kg/m强度验算：

878cm3，Ix

15796cm4，质量M 174.691060.61.255002/8x 192.44N/mm2f215N/mm2Wx nx

1.05878103满足要求。挠度验算：3 5 qkxl 5 (34.50.6)5500 1 13l 384 EIx故选用此截面.

384 2.0610515796104 428 l 250满足要求。按整体稳定确定梁截面假定工字钢型号在I45～I63之间，均布荷载作用在梁上翼缘，自由长度l 5.5m3-21

0.6600.6，所以1.070.2821.070.2820.643b 0.660bM 174.69106x所需毛截面抵抗矩:Wxnx

fb

1263.63103mm30.643215I45a，x量q80.4kg/m强度验算：

1433cm3，Ix

32241cm4，质M 174.691060.8041.255002/8x 118.52N/mm2f215N/mm2Wx nx

1.051433103满足要求。整体稳定验算：M 174.691060.8041.255002/8x 193.54N/mm2

f215N/mm2Wb x

0.6431433103满足要求。故选用此截面。(3）假设梁的跨度中点处受压翼缘设置一可靠的侧向支承,此梁的整体稳定不一定保证.按整体稳定确定梁截面I22～I40l1

5.5/22.75m，由附表3-2查整体稳定系数 2.10.6，所以b1.07

0.2821.070.2820.936b所需毛截面抵抗矩：Wnx

bxMxfb

2.1174.69106 868.07103mm30.936215查型钢表选用I36c，截面几何特性：Wxq71.3g/m强度验算：

964cm3，Ix

17351cm4,质量M 174.691060.7131.255002/8x 175.78N/mm2

f215N/mm2Wx nx

1.05964103满足要求.整体稳定验算:M 174.691060.7131.255002/8x 197.19N/mm2

f215N/mm2Wb x

0.936964103

满足要求.故选用此截面。2.解:Q235ll/400截面形心位置420201230320201012008620x 670mm420203202012008812003I 81200(670620)24202067010)2x 1232020(67010)26598.08106mm4（1)抗弯强度W Ix

6598.08106 11.576106mm3x1 1240670 570W Ix

6598.08106 9.848106mm3x2 670 6701M 3.215240052090kNm1x 8M 2090106x 202.12N/mm2

f205N/mm2Wx nx2

1.059.848106满足要求。(2）抗剪强度中和轴处截面的面积矩：S 4202067010)67020)28/25914103mm3xo上翼缘与腹板交界处的面积矩：S 4202067010)4704103mm3x1下翼缘与腹板交界处的面积矩：S 32020(67010)4224103mm3x2支座处剪力最大，所受最大剪应力为：VSxo

(4003.21035914103 47.50N/mm2

f 120N/mm2It 6598.08106xw

v满足要求.（3)局部承压强度取支撑长度a，则lz

a5hy

200520300mm1.0400103 166.67N/mm2f205N/mm2c ltzw

3008满足要求，无需设置支撑加劲肋。（4)折算应力在集中力作用处弯矩、剪力、局部压应力均较大集中力作用处:M 40053.27.553.252.52080kNmxV4005腹板与上翼缘交界处的应力为： Mx1 W

2080106 179.68N/mm211.576106nx1 VSx1

4081034704103 36.36N/mm21 Itxw

6598.081068 166.67N/mm2c腹板与上翼缘交界处的折算应力为：222321 c c 1 1179.682166.672166.67179.6836.362177.31N/mm（5)挠度

1.1f1.1205225.5N/mm2满足要求。Mkxl

(2090/1.2)10615000 1

11l 10EIx

102.061056598.08106 520 l 400满足要求。3.解：Q235Bl6mMmax

1(61.2301.4)673.8kNm4按整体稳定确定梁截面:假定工字钢型号在I22~I40之间,荷载作用在梁下翼缘，自由长度l 6m3—21

1.070.6，所以1.070.2821.070.2820.806b bM 73.8106

1.07所需毛截面抵抗矩:W x

x 425.88103mm3f 0.806215b考虑到葫芦轮子对轨道梁下翼缘的磨损，所需W 425.88103/0.9473.2103mm3x查型钢表选用I28a,截面几何特性：Wxq43.5kg/m强度验算：

508cm3，Ix

7115cm4，质量M 73.81060.4351.260002/8x 142.76N/mm2

f215N/mm2Wx nx

1.05508103满足要求。整体稳定验算：M 73.81060.4351.260002/8x 185.98N/mm2

f215N/mm2Wb x

0.806508103满足要求。故选用此截面.4.解：Q235Bl9m截面几何特性:A220012880011200mm288003I 22001240621132.55106mm4x 12122003I 2 16106mm4y 12W 1132.55106/4122.749106mm3xI /Ay16I /Ay16106/112001 1

37.80mmM 0.91.292 1101.29307.94kNmx 8 4（1）梁在跨中无侧向支承,集中荷载作用于梁上翼缘 l /iy y y

9000/37.80238.10h，t 12mm1l1t19000120.6552.0lbh 2008241查附表3—1得： 0.730.730.180.6550.8479b11t24.4hy1 b b

2W y x0.84790.276

432011200824 1238.10121238.10124.48242M 307.94106x 405.86N/mm2

f215N/mm2W 0.2762.749106b x整体稳定不满足要求。(2）材料改用Q345B钢 b b

4320Ah2W

23511t24.4hy10.8479

y x432011200824

23511238.10124.48242238.1022.749106 3450.188M 307.94106x 595.84N/mm2W 0.1882.749106b x整体稳定不满足要求。

f310N/mm2集中荷载悬挂于下翼缘3—1b

2.230.282.230.280.6552.0466114y1t2.4h b b

2W y x2.0466

432011200824 1238.10121238.10124.482420.6660.61.070.282/0.6660.646bxM 307.94106xWb x

173.40N/mm20.6462.749106整体稳定满足要求。

f215N/mm2跨度中点增设上翼缘侧向支承 l /iy y y

4500/37.80119.051查附表3-1得： 1b

h，t 12mm b b

4320Ah114y1t2.4hy x1.75

432011200824 1119.05121119.051224.48241.9250.61.070.282/1.9250.924bM 307.94106x 121.23N/mm2

f215N/mm2Wb x

0.9242.749106整体稳定满足要求。5.解:Q235l6ml/2000.750.75 12.52

2.5

0.808m选用[10，自重0.10kN/m，加拉条后取0。15kN/m截面几何特性：W 39.7cm3,I 198cm4，W ，i 3.94cm,i 1.42cmx x ymin x y檩条线荷载标准值为：q 0.750.8080.150.50.751.131N/mmk檩条线荷载设计值为：q 0.751.20.8080.151.20.51.40.751.432N/mm12.52q 1.43212.52x

1.330N/mm112.52

q 1.4321/y

0.532N/mm强度验算：

M 1/81.330625.985kNmxM 1/80.53232myMMx yM

5.985106 0.598106W Wx nx y ny

1.0539.7103 1.27.8103挠度验算：

207.46N/mm2f215N/mm2满足要求。垂直于屋面方向的挠度 5 q

l3 5

1 11.1312.5/ 12.5260001.1312.5/ 12.5260003l 384 EIx

384

2.06105198104不满足要求。

138 l 200故选用此截面强度满足要求，而挠度不能满足要求。6.解：Q235钢选择次梁截面将次梁设计为简支梁,受均布荷载作用次梁的荷载线标准值为：qk

(318)363kN/m次梁的荷载线设计值为:qd

(1.231.418)386.4kN/m

1/86362283.5kNmxk1/886.462388.8kNmx次梁的整体稳定能得到保证，故按强度计算所需净截面抵抗矩为W Mx

388.8106 1194.47103mm3nx

f 1.05310xHN44619981266xI 29000cm4x

1300cm3，强度验算:M

M 1/886.4621/81.20.66762392.4kNmx392.4106x 287.47N/mm2f310N/mm2W 1.051300103x nx

满足要求。挠度验算:2-1得l/250 5 qkxl 5 (630.667)6000 1 3 3

11l 384 EIx

384 2.0610529000104 334 l 200满足要求。主梁跨间次梁传递给主梁的集中力为:F (630.667)6382.0kNkF(86.41.20.667)6523.2kN则主梁的支座反力为：Rk

382.031146.0kN主梁的跨中最大弯矩为:

R3M 1146.09191.09382.06382.035157.0kNmxkM 1569.69261.69523.26523.237063.2kNmx主梁的整体稳定能得到保证，故按强度计算所需净截面抵抗矩为W Mx

7063.2106 22803103mm3nx x

f 1.05295①不考虑腹板屈曲后强度腹板高度hw主梁无净空要求，据刚度条件得梁的最小高度查附表2-1得l/400，故Tf l2 29518000400h 1585.07mmmin

1.34106 T

1.34106梁的经济高度为：h 0.42(22803103)0.41753.27mms x选取梁的腹板高度为1800mm。腹板厚度twhwt /3.5hww

/3.512.12mm,取t1800w1800

10mm翼缘尺寸

W 1 22803103 1A f hw

th6w

1018009668.33mm1800 6取翼缘宽度为460mm,厚度为22mm.截面几何特性：A18001024602238240mm21018003I 24602291122.1661010mm4x 122.1661010W 23.49106mm4x 922梁自重为78kN/m3，考虑到加劲肋等乘以增大系数1.2.g 1.278382403.58kN/mkg 1.21.278382404.30kN/md则主梁的支座反力为：Rk

382.031/23.58181178.22kNR31/24.3018主梁的跨中最大弯矩为：M 1146.09191.09382.06382.031/83.58182xk5301.99kNmM 1569.69261.69523.26523.231/84.30182x7237.35kNm强度验算：M 7237.35106x 293.43N/mm2

f295N/mm2Wx nx

1.0523.49106V 1608.3103

满足要求. 89.35kN/mm2f 170kN/mm2htww刚度验算:

180010

v满足要求。 M lT kx

5301.9910618000 1

1l 10EIx故选用此截面。

102.061052.1661010 468 l 400满足要求。②考虑腹板屈曲后强度截面尺寸取腹板:h 1800mm，t 8mm；翼缘：b,t24mmw w截面几何特性:A1800824802437440mm2818003xI 12 24802491222.3051010mm4x2.3051010xW 924 24.95106mm4x梁自重为78kN/m3，考虑到加劲肋等乘以增大系数1.2。g 1.278374403.5kN/mkg 1.21.278374404.2kN/md则主梁的支座反力为：Rk

382.031/23.5181177.5kNR31/218主梁的跨中最大弯矩为：M 1146.09191.09382.06382.031/83.5182xk5331.15kNmM 1569.69261.69523.26523.231/84.2182x7233.3kNm强度验算：M 7233.3106x 276.11N/mm2f295N/mm2Wx nx

1.0524.95106

满足要求.V 1607.4103 111.62kN/mm2

170kN/mm2ht 1800ww

v满足要求。刚度验算： M l

5331.1510618000

1T kx

l 10EIx

102.061052.3051010 495 l 400满足要求。腹板局部稳定计算：在支座处和每个次梁处设置支撑加劲肋，另在距梁端部较近范围内设置横向加劲肋，其构造如图所示。F/2FFF1239001050105010002000在支座处和每个次梁处设置支撑加劲肋，另在距梁端部较近范围内设置横向加劲肋，其构造如图所示。F/2FFF12390010501050100020003000对板段①h /t1 1

1, s

0 w 1.321.2，支座加414/414/900)2Vht fww v对板段②

/1.2s

18008170/1.321.2满足要求。

1754.38kNR1607.4kN左侧截面剪力V 1607.4523.23/24.24805.8kN2相应弯矩M 261.2)4523.211/24.2424828kNm2M 4802418242956198.68kNmfM M2 fa 2000mm，a/h1 1

1， s

h/t

2.271.20 w415.34/0 w415.34/2000)2ww v

/1.2s

18008170/2.271.2满足要求。

915.33kNV2

805.8kN对板段③右侧截面剪力V 1607.4523.25/24.29261.6kN3a 3000mm，a/h1 1

1, s

h /t

2.551.20 w415.34/0 w415.34/3000)2u ww v

/1.2s

18008170/2.551.2V 3 u

796.09kN相应弯矩 M M 7233.3kNm3 maxh /t0 w153h /t0 w153fy2351800/8 153 235b

1.781.25(10.2/b

)/b

(10.2/1.78)/1.780.50 1e

)h3tcw2Ix

10.50)900380.93622.3051010M W f1.050.93624.95106295eu x e x7236.97kNmM3

7233.3kNm其他板段可不验