第三章1. 解：Q235钢、2/160mm N f w f =、kN N 600= （1）采用侧面角焊缝最小焊脚尺寸：mm t h f 6.5145.15.1max =⨯=≥角钢肢背处最大焊脚尺寸：mm t h f 12102.12.1min =⨯=≤ 角钢肢尖处最大焊脚尺寸：mm t h f 8~9)2~1(10)2~1(=-=-≤ 角钢肢尖和肢背都取 mm h f 8=查表3-2得：65.01=K 、35.02=KkN N K N 39060065.011=⨯==，kN N K N 21060035.022=⨯==所需焊缝计算长度：mm f h N l wf f w 63.21716087.02103907.02311=⨯⨯⨯⨯=⨯= mm f h N l w f f w 19.11716087.02102107.02322=⨯⨯⨯⨯=⨯= 焊缝的实际长度为：mm h l l f w 63.2338263.217211=⨯+=+=，取240mm 。
mm h l l f w 19.1338219.117222=⨯+=+=，取140mm 。
（2）采用三面围焊缝，取mm h f 6= 正面角焊缝承担的内力为：kN f l h N w f f w f 97.16316022.1100267.07.033=⨯⨯⨯⨯⨯==∑β侧面角焊缝承担的内力为：kN N N K N 01.3082/97.16360065.02/311=-⨯=-=kN N N K N 02.1282/97.16360035.02/322=-⨯=-=所需焊缝计算长度：mm f h N l w f f w 17.22916067.021001.3087.02311=⨯⨯⨯⨯=⨯= mm f h N l wff w 25.9516067.021002.1287.02322=⨯⨯⨯⨯=⨯= 焊缝的实际长度为：mm h l l f w 17.235617.22911=+=+=，取240mm 。
mm h l l f w 25.101625.9522=+=+=，取110mm 。
2. 解：Q235钢、2/160mm N f w f = （1）取mm d d 17021==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角焊缝受到轴力为：kN N 23.49915.15.160022=+⨯=角焊缝受到剪力为：kN V 82.33215.1160022=+⨯=f f w h h l 234021702-=-⨯=23/2.19516022.1)2340(4.11023.4997.02mm N f h h l h N w f f f f w f f =⨯=≤-⨯=⨯=βσ由上式求得：mm h f 55.5≥23/160)2340(4.11082.3327.02mm N f h h l h V w f f f w f f =≤-⨯=⨯=τ由上式求得：mm h f 49.4≥最小焊脚尺寸mm t h f 71.6205.15.1max =⨯=≥ 故取焊脚尺寸为mm h f 7=223/2.195/26.156)72340(74.11023.4997.02mm N f mm N l h N w f f w f f =≤=⨯-⨯⨯=⨯=βσ23/16018.104)72340(74.11082.3327.02mm N f l h V w f w f f =≤⨯-⨯⨯=⨯=τ()()222222/160/10.16518.10422.1/26.156/mm N f mm N w f f ff=>=+=+τβσ由于折算应力较接近w f f ，故取mm h f 8=可满足要求。
（2）改取mm d 1501=，mm d 1902= 角焊缝受到轴力、剪力和弯矩的共同作用 角焊缝受到轴力为：kN N 23.49915.15.160022=+⨯=角焊缝受到剪力为：kN V 82.33215.1160022=+⨯=角焊缝受到弯矩为：mm N mm kN Ne M ⋅⨯=⋅=⨯==6109846.96.99842023.499 mm h e 6.587.0=⨯=，mm h l f w 324823402190150=⨯-=-+=4631074.31123246.52mm I w ⨯=⨯⨯=3361096.1953241074.3123242mm I W w w ⨯=⨯⨯==最大正应力为：22363/2.19516022.1/53.1881096.195109846.932487.021023.4997.02mm N mm N W M l h N w w f f =⨯<=⨯⨯+⨯⨯⨯⨯=+⨯=σ 23/16072.9132487.021082.3327.02mm N f l h V w f w f f =≤=⨯⨯⨯⨯=⨯=τ()()222222/160/70.17972.9122.1/53.188/mm N f mm N w f f ff=>=+=+τβσ不满足要求。
3. 解：Q235钢、2/160mm N f w f = （1）角焊缝①最小焊脚尺寸：mm t h f 2.5125.15.1max =⨯=≥ 最大焊脚尺寸：mm t h f 4.14122.12.1min =⨯=≤取mm h f 6=角焊缝①受到轴力和弯矩的共同作用 角焊缝受到轴力为：kN F N 100== 角焊缝受到弯矩为：m kN Ne M ⋅=⨯==220100mm h e 2.467.0=⨯=，mm h l f w 188622002200=⨯-=-=4631065.4121882.42mm I w ⨯=⨯⨯=3361048.491881065.421882mm I W w w ⨯=⨯⨯==最大正应力为：22363/2.19516022.1/74.1031048.4910218867.02101007.02mm N mm N W M l h N w w f f =⨯<=⨯⨯+⨯⨯⨯⨯=+⨯=σ 满足要求。
（2）角焊缝②③角焊缝的有效截面如图所示 取mm h f 8=角焊缝有效截面形心位置：mm y y 03.136)6.519226.54.5526.5134/(]2/1926.51922)8.2192(6.54.552)8.212192(6.5134[2=⨯⨯+⨯⨯+⨯⨯⨯⨯+-⨯⨯⨯+++⨯⨯==剪力由腹板焊缝承担，腹板面积为：24.21506.51922mm A w =⨯⨯=全部焊缝对x 轴的惯性矩为：4632221056.1512/1926.52)2/19203.136(6.51922)8.203.136192(6.54.552)8.21203.136192(6.5134mm I w ⨯=⨯⨯+-⨯⨯⨯+--⨯⨯⨯+++-⨯⨯=翼缘焊缝最外边缘的截面模量：346111015.216.51203.1361921056.15mm h I W w w ⨯=++-⨯==翼缘和腹板连接处的截面模量：346221081.2703.1361921056.15mm h I W w w ⨯=-⨯== 腹板底边缘处的截面模量：346231044.1103.1361056.15mm y I W w w ⨯=⨯== 弯矩：m kN M ⋅=⨯=12120100由弯矩得最大应力为：24633/90.1041044.111012mm N W M w =⨯⨯==σ腹板的剪应力为：23/50.464.2150/10100/mm N A F w =⨯==τ翼缘和腹板连接处的折算应力；2222223/160/75.9750.4622.190.104mm N f mm N w f f=<=+⎪⎭⎫ ⎝⎛=+⎪⎪⎭⎫ ⎝⎛τβσ 满足要求。
4. 解：Q235钢、查附表1-2得2/185mm N f w t =，2/125mm N f w v =，2/215mm N f w c =焊缝有效截面形心位置：mm y y 13.134)1218812126/(]2/18812188)6188(12126[2=⨯+⨯⨯⨯++⨯⨯==焊缝对x 轴的惯性矩为：463221070.1512/18812)2/18813.134(12188)613.13412188(12126mm I x ⨯=⨯+-⨯⨯+--+⨯⨯= 翼缘焊缝边缘的截面模量：346111083.2313.134121881070.15mm y I W x ⨯=-+⨯==翼缘和腹板连接处的截面模量：346221014.2913.1341881070.15188mm y I W x ⨯=-⨯=-=腹板底边缘处的截面模量：346231070.1113.1341070.15mm y I W x ⨯=⨯==弯矩：F M 120=由翼缘上边缘处焊缝拉应力241/1851083.23120mm N f F W M w t t =≤⨯==σ 得：kN F 38.367120/1083.231854=⨯⨯≤由腹板下边缘处焊缝压应力243/2151070.11120mm N f F W M w c c =≤⨯==σ 得：kN F 62.209120/1070.112154=⨯⨯≤由腹板焊缝单独承担剪力，腹板的剪应力2/125)12188/(/mm N f F A F w v w =≤⨯==τ得：kN F 00.28212188125=⨯⨯≤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()222422/5.2031851.11.1121881070.11120mm N f F F w t c =⨯=≤⎪⎭⎫ ⎝⎛⨯+⎪⎭⎫ ⎝⎛⨯=+τσ 得：kN F 13.182≤5. 解：Q345B 钢、/200N f w f=角焊缝有效截面的形心位置：x x .43)6.55006.51972(/)2/1976.51972(1=⨯+⨯⨯⨯⨯⨯==截面的惯性矩：46321023.19612/5006.52506.51972mm I wx ⨯=⨯+⨯⨯⨯=462321011.1941.435006.512/1976.52)41.432/197(6.51972mmI wy ⨯=⨯⨯+⨯⨯+-⨯⨯⨯=4331034.21510)11.1923.196(mm I I J wy wx ⨯=⨯+=+=扭矩：F F T 59.461)41.43205300(=-+= 由扭矩产生的最大应力266/2001088.5351034.21525059.461mm N f F F Jr T w f y T f =≤⨯=⨯⋅=⋅=-τ 得：kN F 22.3731088.535/2006=⨯≤-266/24420022.11023.3291034.215)41.43197(59.461mm N f F F J r T w f f x T f =⨯=≤⨯=⨯-⋅=⋅=-βσ得：kN F 12.7411023.329/2446=⨯≤-由力F 产生的应力26/2441074.1996.55006.51972mm N f F FA F w f f w V f =≤⨯=⨯+⨯⨯==-βσ 得：kN F 59.12211074.199/2446=⨯≤-由最大应力点的折算应力262626622/2001032.689)1088.535(22.11074.1991023.329)(mm N f F F F F w f T f f Vf T f =≤⨯=⨯+⎪⎪⎭⎫ ⎝⎛⨯+⨯=+⎪⎪⎭⎫ ⎝⎛+----τβσσ 得：kN F 14.2901032.689/2006=⨯≤-综上得该连接所能承受的最大荷载为kN F 14.290=。