某四層建筑豎向荷載作用下框架結構的內力計算過程案例目錄TOC\o"1-3"\h\u4329某四層建筑豎向荷載作用下框架結構的內力計算過程案例 1154011.1計算單元的選擇確定 136431.2荷載計算 2177261.2.1恒載作用下柱的內力計算 2241891.2.2活載作用下柱的內力計算 4179511.2.3恒荷載作用下梁的內力計算 5272761.2.4活荷載作用下梁的內力計算 8191941.3內力計算 10249651.4梁端剪力和柱軸力的計算 16213941.4.1恒載作用下 1612301.4.2活載作用下 1686131.5橫向框架內力組合: 1795851.5.1.結構抗震等級: 1718641.5.2.框架梁內力組合: 171.1計算單元的選擇確定取⑦號軸線橫向框架進行計算，如圖1.1所示：圖1.1框架計算簡圖計算單元寬度為8.4米，如圖6-1所示，由于房間內布置有次梁，故直接傳給框架的樓面荷載如圖中的水平陰影所示，計算單元范圍內的其余樓面荷載則通過次梁和縱梁以集中的形式傳給橫梁框架，作用于個節點上，由于縱向框架的中心線與柱的中心線不重合，因此在框架節點上還作用有集中力矩。1.2荷載計算1.2.1恒載作用下柱的內力計算各層框架梁上的恒荷載分布如圖6-2所示：1.2各層梁上作用的恒荷載對于第4層，q1、q1：均布荷載形式橫梁自重q1=6.566q1，=2.304q2、q2：屋面板和走道板傳給橫梁的梯形荷載與三角形荷載q2=1.72×2.1×2=24.024q2，=1.72×3=17.16P1、P2：由邊縱梁、中縱梁傳給柱的恒載，包括主梁自重+次梁自重+樓板重+女兒墻重等重力荷載，計算如下：P1=[（4.2×2.1）+（4.2+8.4）×2.1/2]×1.72+3.946×8.4/2++6.353×8.4+7.94×0.08×8.4+2×1.42×8.4=226.785P2=[（4.2×2.1）+（4.2+8.4）×2.1/2]×1.72+（2.7+4.2）×1.5×1.72+6.535×8.4+3.946×8.4/2=251.079集中力矩M1=P1e1=226.785×（0.1.0.35）/2=17.009M2=P2e2=251.079×（0.1.0.35）/2=19.131對于3層，q1：橫梁自重極其橫墻自重均布荷載q1=6.566+1.82×2.55=11.207q1，=2.304q2，q2：樓面板和走道板傳給橫梁的梯形荷載與三角形荷載q2=4.2×2.1×2=17.64q2，=4.2×3=12.6P1、P2分別由邊縱梁、中縱梁傳遞給柱的恒載，它包括主梁自重+次梁自重+樓板重等重力荷載，計算如下：P1=[（4.2×2.1）+（4.2+8.4）×2.1/2]×4.2+3.946×8.4/2+6.535×8.4+2.54×（8.4×2.51.1.5×1.8×2）+0.4×1.5×1.8×2=206.928P2=[（4.2×2.1）+（4.2+8.4）×2.1/2]×4.2+3.946×8.4/2+6.535×8.4+1.82×8.4×2.55+（2.7+4.2）×1.5×4.2=246.531集中力矩M1=P1e1=206.928×0.075=11.52M2=P2e2=246.531×0.075=18.45（3）、對于第2-1層，q1=6.566+1.82×2.5=11.116q1，=2.304q2=4.2×2.1×2=17.64q2，=12.6P1=[4.2×2.1+（4.2+8.4）×2.1/2]×4.2+3.946×8.4/2+6.535×8.4+2.54×（8.4×2.1.1.5×1.8×2）+0.4×1.5×1.8×2=201.861P2=[4.2×2.1+（4.2+8.4）×2.1/2]×4.2+3.946×8.4/2+6.535×8.4+1.82×8.4×2.5+（2.7+4.2）×1.5=241.767集中力矩M1=P1e1=201.861×0.075=11.440M2=P2e=241.767×0.075=18.4331.2.2活載作用下柱的內力計算各層框架梁上的活荷載分布如圖1.3所示：圖6-3各層梁上作用的活荷載對于第4層，q2=4.2×0.5=2.1q2，=3×0.5=1.5P1=P2=集中力矩M1=P1e1=11.025×0.075=0.827M2=P2e2=16.2×0.075=1.215對于第3-1層，q2=4.2×2=8.4q2，=2.5×3=7.5P1=10.5×2.1×2=44.1P2=10.5×2.1×2+6.9×1.5×2.5=69.975集中力矩M1=P1e1=44.1×0.075=3.308M2=P2e2=69.975×0.075=1.248將上述計算的荷載匯總到表6-1、6-2表6-1橫向框架恒載層次q2q2，P1P2M1M2層次q246.5662.30424.02417.16226.785251.07917.00919.131311.2072.30417.6412.6206.928246.53111.5218.451-211.1162.30417.6412.6201.861241.76711.4418.433表1.2橫向框架活載層次q2q2，P1P2M1M242.11.511.02516.20.8271.2151-38.47.544.169.9753.3081.2481.2.3恒荷載作用下梁的內力計算各層框架梁上的恒荷載分布如圖6-4所示：圖1.4各層梁上作用的恒荷載梯形荷載和三角形荷載轉化為等效均布荷載對于第4層：梯形荷載轉化為均布荷載=三角形荷載轉化為均布荷載為：對于第1-3層：梯形荷載轉化為均布荷載為：三角形荷載轉化為均布荷載為：計算豎向荷載作用下各跨梁的固端彎矩對各節點編號見圖6-5圖1.5框架節點第四層：第三層：第二層(第一層)：1.2.4活荷載作用下梁的內力計算各層框架梁上的活荷載分布如圖6-6所示：圖1.6各層梁上作用的活荷載等效均布荷載與梯形、三角形荷載的轉化。（1）、對于第4層，梯形荷載轉化為均布荷載=三角形荷載轉化為均布荷載為：（2）、對于第1-3層，梯形荷載轉化為均布荷載為：三角形荷載轉化為均布荷載為：計算活荷載作用下各跨梁的固端彎矩第四層：第三層：第二層(第一層)：1.3內力計算梁端、柱端彎矩采用彎矩二次分配法計算，由于結構和荷載均對稱，故計算時可用半框架，彎矩計算如下圖所示，梁端剪力可根據梁豎向荷載引起的剪力相疊加而得，柱軸力可由梁端剪力和節點集中力疊加得到。計算柱底軸力區需考慮柱的自重。計算各節點處梁柱的彎矩分配系數節點處彎矩分配系數為具體計算如下：節點Q節點R節點M節點N節點I節點J節點E節點E圖6-7恒載作用下橫向框架彎矩的二次分配圖1.8恒載作用下彎矩圖圖1.9活載作用下橫向框架彎矩的二次分配圖6-10活載作用下彎矩圖1.4梁端剪力和柱軸力的計算1.4.1恒載作用下例：第4層：AB跨荷載剪力：VA=-VB=27.962×8.4/2=117.440彎矩剪力：VA=-VB=BC跨：荷載剪力：VB=VC=13.029×3/2=19.544彎矩剪力：VB=-VC=0A柱：N頂==226.785+117.440+0.846=341.071柱重：0.5×0.5×3.3×25=20.625N底=391.217+20.625=361.696B柱：N頂==251.079+117.440-0.846+19.544=391.217N底=391.217+20.625=411.842恒載作用下梁端剪力及柱軸力表6-3層次荷載引起的剪力彎矩引起剪力總剪力柱軸力AB跨BC跨AB跨BC跨AB跨BC跨A柱B柱VA=VBVB=VCVA=-VBVB=VCVAVBVB=VCN頂=N底N頂=N底4117.44019.5440.8460118.286-116.5919.544391.217411.8423113.05611.2690.9970114.053-112.0611.269761.076781.7012112.67311.2690.9350113.608-111.7411.2691137.851158.4751112.67311.2690.9630113.636-111.7111.2691510.5961536.2211.4.2活載作用下例：第4層：AB跨荷載引起的剪力：VA=-VB=1.87×8.4/2=7.854彎矩引起的剪力：VA=-VB=BC跨：荷載引起的剪力：VB=VC=0.938×3/2=1.407彎矩引起的剪力：VB=-VC=0A柱：N=11.025+7.854+0.29=19.169B柱：N=16.2+7.854-0.29+1.407=21.171恒載作用下梁端剪力及柱軸力表6-4層次荷載引起的剪力彎矩引起剪力總剪力柱軸力AB跨BC跨AB跨BC跨AB跨BC跨A柱B柱VA=VBVB=VCVA=-VBVB=VCVAVBVB=VCN頂=N底N頂=N底47.8541.4070.29008.144-7.5641.40719.16921.171331.4207.0320.149031.569-31.2717.03294.838133.449231.4207.0320.215031.635-31.2057.032170.052241.727131.4207.0320.144031.635-31.2767.032241.721350.0051.5橫向框架內力組合:1.1.1.結構抗震等級:結構的抗震等級可根據結構類型,地震烈度,房屋高度等因素確定,本工程的框架為三級抗震等級1.1.2.框架梁內力組合:本工程考慮了三種內力組合,即1.2,1.35,1.2,此外,對于本設計,與考慮地震作用組合相比較小,對結構設計不起控制作用,故不予考慮1.2組合。圖6.6均布、梯形、三角形、集中力作用下的計算簡圖梁上設計值:=1.239.83=47.80KN/mKN/m左震時:=47.24KN>0則發生在X處=47.24KN>0右震時:＝211.91KN>0則發生在X處X=1.63m表6-4框架梁內力組合表層

次截

面內

力恒

SGk活

SQk地震

SEkγRE[1.2(SGk+

0.5SQk)+1.3SEk]1.35SGk

+SQk1.2SGk

+1.4SQk→←一層AM-159.7-8.0949.07-99.53-191.21-223.69-202.97V161.617.5421.9173.79131.09231.11209.29B左M-161.85-6.6282.32-68.38-228.91-221.12-203.49V166.18.0421.9174.46131.76232.28210.58B右M-1.1-1.41270.6167.22-70.47-2.90-3.30V-3.120.958.8454.97-59.77-3.31-2.48二層三層AM-144.15-8.0931.25-102.91-163.84-202.69-184.31V143.757.5621.37157.51108.04201.62183.08B左M149.616.62120.95251.5519.70208.59188.80V143.758.0421.37157.73108.26202.10183.76B右M-10.5-1.41103.0490.38-110.55-11.59-14.57V3.130.981.8786.95-80.501.131.02四層AM-30.37-7.3912.78-18.20-43.12-48.39-46.79V13.217.567.1922.308.2821.3926.44B左M22.571.9230.3352.55-6.5936.3931.37V14.518.047.1923.699.6727.6328.67B右M-0.58-2.0921.8423.73-26.66-2.87-3.62V6.010.921.5326.81-11.189.018.47注：1、M下部受拉為正，V向上為正。SQk括號內數值表示屋面作用雪荷載時對應的內力。2、豎向荷載作用下（SGk、SQk）彎矩M取調幅0.8。3、上表γRE取值：M取0.75，V取0.85。表6-5橫向框架A柱彎矩和軸力組合層

次截

面內

力恒荷載

SGk活荷載地震

SEkγRE[1.2(SGk+0.5SQk)

+1.3SEk]1.35SGk

+SQk1.2SGk

+1.4SQk|Mmax|

NNmin

MNmax

MSQk→←4柱頂M30.371.6112.7842.3217.4046.6144.3046.6117.4046.61N86.4931.547.1999.0481.02148.30147.94148.3081.02148.30柱底M71.272.251.9167.0263.2998.4688.6798.4663.2998.46N171.4931.547.19171.54161.52263.05249.94263.05161.52263.053柱頂M79.141.8522101.6651.90112.69103.16112.6951.90112.69N282.6863.0148.66352.22251.01444.63427.43444.63251.01444.63柱底M69.962.259.2577.8658.6296.7087.1096.7058.6296.70N367.6863.0148.66433.82332.61559.38529.43559.38332.61559.382柱頂M81.191.8522103.6357.87111.46101.62111.4657.87111.46N477.9694.6148.66554.86453.65739.86706.01739.86453.65739.86柱底M90.722.2523.36112.4763.88124.72112.01124.7263.88124.72N592.9694.6148.66661.26564.05891.11844.01891.11564.05891.111柱頂M68.991.8521.7191.7842.3098.9990.9898.9942.3098.99N696.01126.1470.57802.11651.321061.751011.811061.75651.321061.75柱底M34.52.9242.8579.09-10.0449.5041.4949.50-10.0449.50N793.51126.1470.57891.71748.921197.381128.811197.38748.921197.38

注：1、2、3(底)層柱軸壓比>0.15,γRE取0.8；3(頂)；4、層柱軸壓比<0.15，γRE取0.75。考慮地震荷載時取雪荷載為屋面活荷載表6-6橫向框架A柱彎矩設計值的調整（調整方法見例）層次4（未調）321截面柱頂柱底柱頂柱頂柱頂柱底柱頂柱底γRE（∑Mc＝ηc∑Mb）46.6198.46123.96106.37127.00137.19108.8956.92γREN148.30263.05444.63559.38739.86891.111061.751197.38表6-7橫向框架A柱剪力組合（kN）層

次恒載

SGk活載

SQk地震

SEkγRE[1.2(SGk+

0.5SQk)+1.3SEk]1.35SGk

+SQk1.2SGk

+1.4SQkγRE[ηc(Mcb

+Mct)/Hn]→←413.217.564.3222.1012.5621.3926.4433.20314.387.569.0728.548.5026.9727.8348.20214.287.5613.3433.173.6826.8427.7260.47116.567.5617.5840.171.3229.9230.4672.21注：V：繞柱順時針方向為正，γRE[ηc(Mcb+Mct)/Hn]：相應于本層柱凈高上、下兩端的剪力設計值。表6.8橫向框架B柱彎矩和軸力組合層

次截

面內

力恒荷載

SGk活荷載地震

SEkγRE[1.2(SGk+0.5SQk)

+1.3SEk]1.35SGk

+SQk1.2SGk

+1.4SQk|Mmax|

NNmin

MNmax

MSQk→←4柱頂M-9.77-7.6530.2517.26-41.73-20.84-22.4317.26-41.73-20.84N99.7532.0221.42128.9779.40166.68164.53128.9779.40166.68柱底M36.071.0356.1887.70-21.8549.7244.7387.70-21.8549.72N184.7532.0221.42201.47151.90281.43266.53201.47151.90281.433柱頂M71.41-1.9277.18149.82-10.7291.8882.20149.82-10.7291.88N304.5364.0553.41378.64267.55471.17451.11378.64267.55471.17柱底M51.181.03104.42162.06-51.1371.5267.66162.06-51.1371.52N389.5364.0553.41460.24349.15589.92557.11460.24349.15589.922柱頂M61.521.92120.12190.67-59.1894.3786.91190.67-59.1894.37N510.2196.0778.51617.57454.26784.85746.75617.57454.26784.85柱底M77.751.03146.81227.82-77.55101.9994.74227.82-77.55101.99N591.2196.0778.51699.17531.86899.60848.