第六章-框架在豎向荷載作用下的內(nèi)力分析

1、第六章 框架在豎向荷載作用下的內(nèi)力分析（采用彎矩二次分配法）6.1計算方法和荷載傳遞路線1.計算方法框架結(jié)構(gòu)在豎向荷載作用下的內(nèi)力計算采用力矩分配法，因為框架結(jié)構(gòu)對稱，荷載對稱；又屬于奇數(shù)跨，故在對稱軸上梁的截面只有豎向位移（沿對稱軸方向）沒有轉(zhuǎn)角。對稱截面可取為滑動端。彎矩二次分配法是一種近似計算方法，即將各節(jié)點的不平衡彎矩同時作分配和傳遞，并以兩次分配為限。(取一榀橫向框架)2.荷載傳遞路線對于邊跨板，為7.2m×4.5m,由于7.2/4.5<3.0 所以按雙向板計算對于中跨板，為4.5m×2.7m,由于4.5/2.73.0 所以按雙向板計算6.2豎向荷載計算5.

2、2.1 A-B(C-D)軸間框架梁板傳至梁上的三角形或梯形荷載等效為均布荷載。1.屋面板傳載恒載：5.0×4.5/2×(1-2×0.312+0.313) ×2=18.85kN/m活載：0.5×4.5/2×(1-2×0.312+0.313) ×2=1.89kN/m2.樓面板傳荷載恒載：3.99×4.5/2×(1-2×0.312+0.313) ×2=15.08kN/m活載：2.0×4.5/2×(1-2×0.312+0.313) ×2=7.5

3、6kN/m3.梁自重：5.46 kN/mA-B(C-D) 軸間框架梁均布荷載為：屋面梁：恒載=梁自重+板傳荷載=5.46 kN/m+18.85 kN/m=24.31 kN/m 活載=板傳荷載=1.89 kN/m樓面梁：恒載=梁自重+板傳荷載=5.46 kN/m+15.08 kN/m=20.54 kN/m活載=板傳荷載=7.56 kN/m B-C軸間框架梁1.屋面板傳載恒載：5.0×2.4/2×5/8 ×2=8.44kN/m活載：0.5×2.7/2×5/8 ×2=0.84kN/m2.樓面板傳荷載恒載：3.99×2.7/2

4、15;5/8×2=6.73kN/m活載：2.0×2.7/2×5/8×2=4.22kN/m3.梁自重：3.9kN/mB-C 軸間框架梁均布荷載為：屋面梁：恒載=梁自重+板傳荷載=3.9 kN/m+8.44kN/m=12.34kN/m 活載=板傳荷載=0.84kN/m樓面梁：恒載=梁自重+板傳荷載=3.9 kN/m+6.73kN/m=10.63kN/m活載=板傳荷載=4.22kN/m6.3 框架計算簡圖6.4.梁固端彎矩梁端彎矩以繞桿端順時針為正，反之為負(fù)。固端彎矩=（均布荷載×跨度²）/12=ql2/12荷載部位邊跨中跨跨度均布荷載固端

5、彎矩跨度均布荷載固端彎矩左右左右恒荷載頂層7.224.31-105.02105.022.712.34-7.50-7.50其它層7.220.54-88.7388.732.710.63-6.46-6.46活荷載頂層7.21.89-8.168.162.70.84-0.51-0.51其它層7.27.56-32.6632.662.74.22-2.56-2.56豎向荷載作用下框架梁的固端彎矩6.5框架節(jié)點分配系數(shù) 如下表邊柱節(jié)點中柱節(jié)點頂層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/（i

6、b左+iz下+ib右）=0.281c下= ic下/（ib右+ib下+ib右）=0.401標(biāo)準(zhǔn)層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底層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/（i

7、z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恒載產(chǎn)生彎矩分配與傳遞方法：首先將各點的分配系數(shù)填在相應(yīng)方框內(nèi)，將梁的固端彎矩填寫在框架橫梁相應(yīng)位置上，然后將節(jié)點放松，把各節(jié)點不平衡彎矩同時進(jìn)行分配。假定遠(yuǎn)端固定進(jìn)行傳遞（不向滑動端傳遞），右（左）梁分配彎矩向左（右）梁傳遞，上（下）分配彎矩向下（上）柱傳遞（傳遞系數(shù)均為0.5）。第一次分配彎矩傳遞

8、后，再進(jìn)行第二次彎矩分配。 梁彎矩的調(diào)幅（由于鋼筋混凝土結(jié)構(gòu)具有塑性內(nèi)力重分布性質(zhì)，因此在重力荷載作用下對梁端彎矩進(jìn)行調(diào)幅,調(diào)幅系數(shù)為0.8;對跨中彎矩進(jìn)行調(diào)幅,調(diào)幅系數(shù)1.2.）1、恒載作用下的彎距樓層AB跨BC跨左端中間右端左端中間右端MMMMMMMMMMMM5-74.28-59.42-73.60-88.3293.5874.86-38.11-30.49-26.87-32.2438.1130.494-85.73-68.58-48.78-58.5486.91369.53-19.24-15.39-9.55-11.4619.2415.393-81.94-65.55-49.56-59.4785.14

9、68.11-20.80-16.64-11.11-13.3320.8016.642-82.25-65.80-49.33-59.2085.3068.24-20.66-16.53-10.97-13.1620.6616.531-73.46-58.77-55.34-66.4182.0665.65-24.18-19.34-14.49-17.3924.1819.34注: 1）M為調(diào)幅后的彎距。2）彎矩符號逆時針為正2、活載作用下的彎距樓層AB跨BC跨左端中間右端左端中間右端MMMMMMMMMMMM5-7.82-6.26-7.40-8.888.346.67-1.96-1.57-1.19-1.431.961.5

10、74-28.14-22.51-19.55-23.4630.7424.59-8.37-6.70-4.52-5.428.376.703-29.16-23.33-18.73-22.4831.3725.10-7.81-6.25-3.96-4.757.816.252-29.28-23.42-17.14-20.57344327.54-7.76-6.21-3.91-4.697.766.211-27.02-21.62-20.36-24.4330.2524.20-9.05-7.24-5.2-6.249.057.24注: 1）M為調(diào)幅后的彎距。2）彎矩符號逆時針為正6.7梁端剪力：均布荷載下: V=Vq×

11、;b/21、 恒載作用下梁端剪力樓層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512.342.716.660.0016.6616.6612.9612.96410.632.714.35

12、0.0014.3514.3511.1611.16310.632.714.350.0014.3514.3511.1611.16210.632.714.350.0014.3514.3511.1611.16110.632.714.350.0014.3514.3511.1611.16注：就采用調(diào)幅前的值 2、活載作用下梁端剪力層次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

13、.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：就采用調(diào)幅前的值6.8柱軸力和剪力1.恒載作用下的柱軸力剪力（1） 邊柱層截面橫梁剪力（

14、kN）縱向荷載（kN）柱 重（kN）（kN）邊柱軸力（kN）邊柱剪力（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說明： 假定外縱墻受力荷載完全由

15、縱梁承受。為本層荷載產(chǎn)生的軸力。柱重：首 層：0.6 ×0.6×26×4.43=41.46kN 頂 層：0.6×0.6×26×3.6=33.7kN其他層：0.6×0.6×26×3.6=33.7kN a 頂層荷載：女兒墻：0.8×0.24×10×4.5=8.06kN連系梁 ：3.25×4.5=14.625kN屋面荷載：5.0×0.5×4.5×5/8×0.5×4.5×2=31.64kN =54.33kN b 標(biāo)

16、準(zhǔn)層荷載樓面荷載：3.99×0.5×4.5×5/8×0.5×4.5×2=25.25kN連系梁：3.25×4.5=14.625kN墻重：6.29×3.6×（4.5-3.3）=27.17kN窗： 3.3×0.3×2.1=2.07kN =69.13kN(2) 中柱：層截面橫梁剪力橫梁剪力縱向荷載柱 重（kN）中柱軸力中柱剪力（kN）（kN）（kN）（kN）（kN）（kN）51190.2016.6671.99533.70178.86178.8625.8922212.56213.70543374

17、.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. 頂層荷載 屋面荷載：=12×(2.7/2/4.5)2+(2.7/2/4.5)3=0.8475.0×0.5×4.5×5/8×0.5×4.5×2+5.0×2.7/2×0.847×0.5×4.5×2=57.37kN 連系梁 ：3.25×4.5=14.625kN =71.995kN. 標(biāo)準(zhǔn)層荷載樓面荷載3.99×0.5×4.5×5/8×0.5×4.5×2+3.99×2.7/2×0.847×0.5×4.5×2=45.78kN連系梁 ：3.25×4.5=14.625kN =60.405kN2. 活載作用下的柱軸力剪力邊