同濟大學鋼結構基本原理(第二版)習題參考解答第五章

鋼結構基本原理（第二版）習題參考解答第五章：軸心受壓構件鋼結構基本原理（第二版）習題參考解答第五章：軸心受壓構件第第6頁共6頁某車間工作平臺柱高2.6m,軸心受壓,兩端鉸接.材料用I16,Q235f 215N/mm2.求軸心受壓穩(wěn)定系數(shù)d如改用Q345鋼fd

310N/mm2解答:P3353-6,知I16ix

6.57cm,iy

A柱子兩端較接,x y

1.0故柱子長細比為

x

l1.0260039.6,

yl26001.0137.6x i 65.7x

y i 18.9y因為x

,故對于Q235鋼相對長細比為 137.62352.06137.62352.06105fyE

1.48242422 31 22

2

2 1 21.482

0.9650.3001.481.482

0.9650.3001.481.482

41.4820.354fy235fy235y

137.64-40.354)

crd

Afd

0.35426.11102215198.7kN當改用Q365鋼時,同理可求得1.792。fy235由式5-34b計算得0.257 (或fy235y

166.7,查表得0.257)

crd

Afd

0.25726.11102310208.0kN5-25E/Q235.10m,截面為三塊鋼板焊接而成,翼緣為剪切邊,材料為Q235,強度設計值fd

205N/mm2,承受軸心壓力設計值3000kN(包括自重).如采用圖5-26所示的兩種截面,計算兩種情況下柱是否安全. 圖5-26 題5.5解答:截面特性計算:對a)截面:1 I 2( 500203205002602) 850031.436109mm41 1 x 12 1 I 2 205003 500834.167108mm4y 12 12A250020500824000mm2IxAIyAi IxAIyAx y

131.8mm對b)截面:1 1I 2( 40025340025212.52) 1040039.575108mm41 x 12 1 I 2 254003 4001032.667108mm4y 12 12A4002524001024000mm2IxAIyAi IxAIyAx y

105.4mm整體穩(wěn)定系數(shù)的計算:鋼柱兩端鉸計算長度l lox oy

10000mm對a)截面:

ox1000040.88

l ox

75.87lx i 244.6lx

y i 131.8y對b)截面:

kx 50.08

l ox

94.88lx lx

y i 105.4y根據(jù)題意,查P106表5-4(a),知鋼柱對x軸為b類截面,對y軸為c類截面.對a)截面:x

fyE2352.06105 x

0.440 1

2

222x 2x

22

3 x x

3 x x x 0.9650.30.440.442240.9650.30.440.442240.44220.442 0.895(或計算x對y軸:

40.884-4f235f235yffyyE2352.06105

0.896) y

0.8162222 3 y y y2222 3 y y yy 2y

22

y y 1 0.9060.5950.8160.8162 0.9060.5950.8160.8162240.816220.8162 0.604(或計算y

75.874-5f235f235y

0.604)故取該柱的整體穩(wěn)定系數(shù)為0.604對b)截面,同理可求得x整體穩(wěn)定驗算:

0.852,y

0.489,故取該柱截面整體穩(wěn)定系數(shù)為0.489對a)截面N

crd

Afd

0.604240002052971.68kN 3000kN 不滿足。對b)截面N

crd

0.489240002052405.88kN 3000kN 不滿足。5-27l 8m,l0x 0

4m(x軸為強軸).截面采用焊接組合工字形,翼緣采用I28a型鋼.鋼材為Q345,強度設計值fd

310N/mm2.5-28l0x30ml0y15mx軸為虛軸),材料為Q235,fd205N/mm2. 解答:截面及構件幾何性質(zhì)計算A286.07172.14cm2I40a單肢慣性:I 659.9cm41

圖5-28 題5.7110繞虛軸慣性矩:Ix

2[659.986.07(

)2]522043.3cm42繞實軸慣性矩:Iy

221714回轉(zhuǎn)半:i x

55.07cm iIxAIxA522043.3172.14

15.88cml 3000 l 1500長細比:

ox 54.48 oy 94.46x i 55.07x

y i 15.88y綴條用L756,A1x

28.79717.594cm2P1115-5ox構件相對長細比,因oxffyyE

227 AxA1227 AxA1x54.48227172.1417.594y y

56.85 y

1.0142352.06105P1065-4(a2352.061051

2 22

0.9650.32

0.9650.32

42

0.591235fy235fyy

94.464-40.591)

crd

Afd

0.591172.141022052085.6kN5-29N2000kN(包括自重),計算長度l0x

20m,l0y

10m(x軸為虛軸),材料為Q235,f 205N/mm2,fd

125N/mm2. 解答:一、整體穩(wěn)定驗算截面及構件幾何性質(zhì)計算:A286.07172.14cm2I40a單肢慣性:I 659.9cm41

圖5-29 題5.8110繞虛軸慣性矩:Ix

2[659.986.07(

)2]522043.3cm42繞實軸慣性矩:Iy

221714回轉(zhuǎn)半:i x

55.07cm iIxAIxA522043.3172.14

15.88cml 2000 l 1000長細比:

ox 36.32 oy 62.97x i 55.07x

y i 15.88y36.32228.882綴板采用3036.32228.882計算知K /Kb 1

6，由P111表5-5得 22x 1

46.40(其中1

80 28.88)2.77構件相對長細: 因2352.062352.06105

只需計算 :y yfyyEfyyEy

62.97

0.677P1065-4(a)可知應采用b0.9650.2240.9650.224222

0.791235fy235fyy

62.974-40.791)故Ncrd

Afd

0.791172.141022052791.34kN，滿足。二、局部穩(wěn)定驗算:單肢截面板件的局部穩(wěn)定單肢采用型鋼,板件不會發(fā)生局部失穩(wěn).受壓構件單肢自身穩(wěn)定單肢回轉(zhuǎn)半徑i1

2.77cma長細比滿足： a1 i1

802.77

28.880.5max

0.562.9731.49,且滿足1

40故單肢自身穩(wěn)定滿足要求.綴板的穩(wěn)定軸心受壓構件的最大剪:V max

172.14102205 41516NAff85dAff85d235y235235綴板剪力:TV1綴板彎矩:MV

a41516110020758Nc 2 1100a41516 1100a 1.142107Nmm12 2 21100綴板厚度滿:t 30bM 1.142107

40 27.5mm 25.4N/mm2 f 205N/mm2W 30