第六章-框架在竖向荷载作用下内力分析.doc

第六章 框架在竖向荷载作用下的内力分析（采用弯矩二次分配法）6.1计算方法和荷载传递路线1.计算方法框架结构在竖向荷载作用下的内力计算采用力矩分配法，因为框架结构对称，荷载对称；又属于奇数跨，故在对称轴上梁的截面只有竖向位移（沿对称轴方向）没有转角。对称截面可取为滑动端。弯矩二次分配法是一种近似计算方法，即将各节点的不平衡弯矩同时作分配和传递，并以两次分配为限。(取一榀横向框架)2.荷载传递路线对于边跨板，为7.2m4.5m,由于7.2/4.53.0 所以按双向板计算对于中跨板，为4.5m2.7m,由于4.5/2.73.0 所以按双向板计算6.2竖向荷载计算5.2.1 A-B(C-D)轴间框架梁板传至梁上的三角形或梯形荷载等效为均布荷载。1.屋面板传载恒载：5.04.5/2(1-20.312+0.313) 2=18.85kN/m活载：0.54.5/2(1-20.312+0.313) 2=1.89kN/m2.楼面板传荷载恒载：3.994.5/2(1-20.312+0.313) 2=15.08kN/m活载：2.04.5/2(1-20.312+0.313) 2=7.56kN/m3.梁自重：5.46 kN/mA-B(C-D) 轴间框架梁均布荷载为：屋面梁：恒载=梁自重+板传荷载=5.46 kN/m+18.85 kN/m=24.31 kN/m 活载=板传荷载=1.89 kN/m楼面梁：恒载=梁自重+板传荷载=5.46 kN/m+15.08 kN/m=20.54 kN/m活载=板传荷载=7.56 kN/m5.2.2 B-C轴间框架梁1.屋面板传载恒载：5.02.4/25/8 2=8.44kN/m活载：0.52.7/25/8 2=0.84kN/m2.楼面板传荷载恒载：3.992.7/25/82=6.73kN/m活载：2.02.7/25/82=4.22kN/m3.梁自重：3.9kN/mB-C 轴间框架梁均布荷载为：屋面梁：恒载=梁自重+板传荷载=3.9 kN/m+8.44kN/m=12.34kN/m 活载=板传荷载=0.84kN/m楼面梁：恒载=梁自重+板传荷载=3.9 kN/m+6.73kN/m=10.63kN/m活载=板传荷载=4.22kN/m6.3 框架计算简图6.4.梁固端弯矩梁端弯矩以绕杆端顺时针为正，反之为负。固端弯矩=（均布荷载跨度）/12=ql2/12荷载部位边跨中跨跨度均布荷载固端弯矩跨度均布荷载固端弯矩左右左右恒荷载顶层7.224.31-105.02105.022.712.34-7.50-7.50其它层7.220.54-88.7388.732.710.63-6.46-6.46活荷载顶层7.21.89-8.168.162.70.84-0.51-0.51其它层7.27.56-32.6632.662.74.22-2.56-2.56竖向荷载作用下框架梁的固端弯矩6.5框架节点分配系数 如下表边柱节点中柱节点顶层b右= ib右/（ ib右+iz下）=0.442c下= iz下/（ib右+ib下）=0.558b左= ib左/（ib左+iz下+ib右）=0.318b右= ib右/（ib左+iz下+ib右）=0.281c下= ic下/（ib右+ib下+ib右）=0.401标准层b右= ib右/（ ib右+iz下+iz上）=0.284c上下= iz上/（ ib右+iz下+iz上）=0.358b左= ib左/（ib左+iz下+ iz上+ib右）=0.227b右= ib右/（ib左+iz下+ iz上+ib右）=0.201c上= iz上/（ib左+iz下+ iz上+ib右）=0.286c下= iz下/（ ib左+iz下+ iz上+ib）=0.286底层b右= ib右/（ ib右+iz下+iz上）=0.304c上= iz上/（iz下+ iz上+ib右）=0.384c下= iz下/（iz下+ iz上+ib右）=0.312b左= ib左/（ib左+iz下+ iz上+ib右）=0.240b右= ib右/（ib左+iz下+ iz上+ib右）=0.212c上= iz上/（ib左+iz下+ iz上+ib右）=0.303c下= iz下/（ib左+iz下+ iz上+ib右）=0.2466.6恒载产生弯矩分配与传递方法：首先将各点的分配系数填在相应方框内，将梁的固端弯矩填写在框架横梁相应位置上，然后将节点放松，把各节点不平衡弯矩同时进行分配。假定远端固定进行传递（不向滑动端传递），右（左）梁分配弯矩向左（右）梁传递，上（下）分配弯矩向下（上）柱传递（传递系数均为0.5）。第一次分配弯矩传递后，再进行第二次弯矩分配。 梁弯矩的调幅（由于钢筋混凝土结构具有塑性内力重分布性质，因此在重力荷载作用下对梁端弯矩进行调幅,调幅系数为0.8;对跨中弯矩进行调幅,调幅系数1.2.）1、恒载作用下的弯距楼层AB跨BC跨左端中间右端左端中间右端MMMMMMMMMMMM5-74.28-59.42-73.60-88.3293.5874.86-38.11-30.49-26.87-32.2438.1130.494-85.73-68.58-48.78-58.5486.91369.53-19.24-15.39-9.55-11.4619.2415.393-81.94-65.55-49.56-59.4785.1468.11-20.80-16.64-11.11-13.3320.8016.642-82.25-65.80-49.33-59.2085.3068.24-20.66-16.53-10.97-13.1620.6616.531-73.46-58.77-55.34-66.4182.0665.65-24.18-19.34-14.49-17.3924.1819.34注: 1）M为调幅后的弯距。2）弯矩符号逆时针为正2、活载作用下的弯距楼层AB跨BC跨左端中间右端左端中间右端MMMMMMMMMMMM5-7.82-6.26-7.40-8.888.346.67-1.96-1.57-1.19-1.431.961.574-28.14-22.51-19.55-23.4630.7424.59-8.37-6.70-4.52-5.428.376.703-29.16-23.33-18.73-22.4831.3725.10-7.81-6.25-3.96-4.757.816.252-29.28-23.42-17.14-20.57344327.54-7.76-6.21-3.91-4.697.766.211-27.02-21.62-20.36-24.4330.2524.20-9.05-7.24-5.2-6.249.057.24注: 1）M为调幅后的弯距。2）弯矩符号逆时针为正6.7梁端剪力：均布荷载下: V=Vqb/21、 恒载作用下梁端剪力楼层q(kn/m)L(m)ql/2M/LV左V右V左V右AB跨梁端剪力524.317.287.522.9384.8490.2077.5582.91420.547.273.940.5773.7874.1067.6267.94320.547.273.940.8673.5074.3867.3468.22220.547.273.940.8473.5274.3667.3668.20120.547.273.941.2772.7575.1366.5968.97BC跨梁端剪力512.342.716.660.0016.6616.6612.9612.96410.632.714.350.0014.3514.3511.1611.16310.632.714.350.0014.3514.3511.1611.16210.632.714.350.0014.3514.3511.1611.16110.632.714.350.0014.3514.3511.1611.16注：就采用调幅前的值 2、活载作用下梁端剪力层次Q(kn/m)L(m)Ql/2M/LV左V右V左V右A B跨51.897.26.8040.0726.7326.8766.176.3147.567.227.220.36126.85927.58124.5925.3137.567.227.220.30726.91327.52724.6525.2627.567.227.220.71526.50527.93524.2425.6717.567.227.220.44926.77127.66924.5025.40跨50.842.71.130.0001.131.130.880.8844.222.75.700.0005.705.704.434.4334.222.75.700.0005.705.704.434.4324.222.75.700.0005.705.704.434.4314.222.75.700.0005.705.704.434.43注：就采用调幅前的值6.8柱轴力和剪力1.恒载作用下的柱轴力剪力（1） 边柱层截面横梁剪力（kN）纵向荷载（kN）柱 重（kN）（kN）边柱轴力（kN）边柱剪力（kN）51184.8454.3333.70139.17139.1734.4022172.87172.8743373.7869.1333.70142.91315.7821.4344176.61349.4835573.5069.1333.70142.63492.1122.6466176.33525.8127773.5269.1333.70142.65668.4624.8288176.35702.1619972.7569.1341.46141.88844.048.741010183.34885.50说明： 假定外纵墙受力荷载完全由纵梁承受。为本层荷载产生的轴力。柱重：首 层：0.6 0.6264.43=41.46kN 顶 层：0.60.6263.6=33.7kN其他层：0.60.6263.6=33.7kN a 顶层荷载：女儿墙：0.80.24104.5=8.06kN连系梁 ：3.254.5=14.625kN屋面荷载：5.00.54.55/80.54.52=31.64kN =54.33kN b 标准层荷载楼面荷载：3.990.54.55/80.54.52=25.25kN连系梁：3.254.5=14.625kN墙重：6.293.6（4.5-3.3）=27.17kN窗： 3.30.32.1=2.07kN =69.13kN(2) 中柱：层截面横梁剪力横梁剪力纵向荷载柱 重（kN）中柱轴力中柱剪力（kN）（kN）（kN）（kN）（kN）（kN）51190.2016.6671.99533.70178.86178.8625.8922212.56213.70543374.1014.3560.40533.70148.86361.4217.2544182.56395.1235574.3814.3560.40533.70149.14544.2617.8266182.84577.9627774.3614.3560.40533.70147.61725.5719.4188181.31759.2719975.1314.3560.40541.46149.89909.167.001010191.35950.62. 顶层荷载 屋面荷载：=12(2.7/2/4.5)2+(2.7/2/4.5)3=0.8475.00.54.55/80.54.52+5.02.7/20.8470.54.52=57.37kN 连系梁 ：3.254.5=14.625kN =71.995kN. 标准层荷载楼面荷载3.990.54.55/80.54.52+3.992.7/20.8470.54.52=45.78kN连系梁 ：3.254.5=14.625kN =60.405kN2. 活载作用下的柱轴力剪力边柱中柱层截面VA(kN)A 柱轴力(kN)A柱剪力(