豎向荷載作用下框架結構內力計算過程案例綜述目錄TOC\o"1-3"\h\u20173豎向荷載作用下框架結構內力計算過程案例綜述 1124041.1橫向框架計算簡圖 1319611.1.1框架梁荷載計算 258351.1.2柱集中荷載計算 446151.2彎矩分配系數計算 8127451.3恒載桿端彎矩計算 961631.4恒載下彎矩分配計算 9262961.5恒載跨中彎矩計算 12163001.6恒載柱端剪力計算 12188971.7恒載梁端內力計算 133381.8活載桿端彎矩計算 17230931.9活載下彎矩分配計算 1835341.10活載跨中彎矩計算 20171281.11活載柱端剪力計算 20214621.12活載梁端內力計算 211.1橫向框架計算簡圖板傳至梁上的三角形或梯形荷載等效為均布荷載，荷載的傳遞示意圖如圖所示。圖1.1荷載傳遞示意圖按彈性理論設計計算梁的支座彎矩時，可按支座彎矩等效的原則，按下式將三角形荷載和梯形荷載等效為均布荷載pe：三角形荷載作用：梯形荷載作用：其中：g，q—分別為板面的均布恒荷載以及均布活荷載；l01，l02—分別為短跨、長跨的計算跨度。AB跨左板梯形荷載轉換系數：α1=0.5×4.5/7.5=0.3AB跨右板梯形荷載轉換系數：α1=0.5×4.5/7.5=0.3BC跨左板梯形荷載轉換系數：α1=0.5×3/4.5=0.33BC跨左板梯形荷載轉換系數：α1=0.5×3/4.5=0.33CD跨左板梯形荷載轉換系數：α1=0.5×4.5/7.5=0.3CD跨板梯形荷載轉換系數：α1=0.5×4.5/7.5=0.3由第三章計算可知：表1.1荷載統計類型恒載活載墻體自重梁自重屋面樓面屋面辦公室走廊標準層女兒墻AB跨BC跨CD跨荷載(kN/m2)4.2243.550.522.54.561.713.6252.2153.6251.1.1框架梁荷載計算AB跨梁荷載計算首先判斷AB跨板是否為雙向板：l02/l01=7.5/4.5=1.67<3，為雙向板（1）屋面板傳遞給梁的荷載：恒載：4.224×5/8×4.5/2+4.224×5/8×4.5/2=11.88kN/m活載：0.5×5/8×4.5/2+0.5×5/8×4.5/2=1.41kN/m（2）樓面板傳遞給梁的荷載：恒載：3.55×5/8×4.5/2+3.55×5/8×4.5/2=9.98kN/m活載：2×5/8×4.5/2+2×5/8×4.5/2=5.63kN/mAB跨梁自重標準值：3.625kN/m；AB跨墻體自重標準值：4.56kN/m故AB跨梁均布荷載為：（3）屋面梁：恒載=AB跨梁自重+屋面板傳遞的荷載=3.625+11.88=15.51kN/m活載=屋面板傳遞的荷載=1.41kN/m（4）樓面梁：恒載=AB跨梁自重+樓面板傳遞的荷載+AB跨墻體自重=3.625+9.98+4.56=18.17kN/m活載=樓面板傳遞的荷載=5.63kN/mBC跨梁荷載計算首先判斷BC跨板是否為雙向板：l02/l01=4.5/3=1.50<3，為雙向板（1）屋面板傳遞給梁的荷載：板為雙向板，根據彈塑性分析可取折減系數取5/8恒載：4.224×5/8×3/2+4.224×5/8×3/2=7.92kN/m活載：0.5×5/8×3/2+0.5×5/8×3/2=0.94kN/m（2）樓面板傳遞給梁的荷載：恒載：3.55×5/8×3/2+3.55×5/8×3/2=1.66kN/m活載：2.5×5/8×3/2+2.5×5/8×3/2=4.69kN/mBC跨梁自重標準值：2.215kN/m；（3）屋面梁：恒載=BC跨梁自重+屋面板傳遞的荷載=2.215+7.92=10.14kN/m活載=屋面板傳遞的荷載=0.94kN/m（4）樓面梁：恒載=BC跨梁自重+樓面板傳遞的荷載=2.215+1.66+0=8.88kN/m活載=樓面板傳遞的荷載=4.69kN/mCD跨梁荷載計算首先判斷CD跨板是否為雙向板：l02/l01=7.5/4.5=1.67<3，為雙向板（1）屋面板傳遞給梁的荷載：恒載：4.224×5/8×4.5/2+4.224×5/8×4.5/2=11.88kN/m活載：0.5×5/8×4.5/2+0.5×5/8×4.5/2=1.41kN/m（2）樓面板傳遞給梁的荷載：恒載：3.55×5/8×4.5/2+3.55×5/8×4.5/2=9.98kN/m活載：2×5/8×4.5/2+2×5/8×4.5/2=5.63kN/mCD跨梁自重標準值：3.625kN/m；CD跨墻體自重標準值：4.56kN/m故CD跨梁均布荷載為：（3）屋面梁：恒載=CD跨梁自重+屋面板傳遞的荷載=3.625+11.88=15.51kN/m活載=屋面板傳遞的荷載=1.41kN/m（4）樓面梁：恒載=CD跨梁自重+樓面板傳遞的荷載+CD跨墻體自重=3.625+9.98+4.56=18.17kN/m活載=樓面板傳遞的荷載=5.63kN/m1.1.2柱集中荷載計算在計算出每一跨的均布荷載之后，還需要對每一個柱的集中荷載進行計算。A柱集中荷載計算：（1）頂層柱：恒載=女兒墻自重+縱梁自重+AB梁自重+AB跨板傳遞的梯形荷載+AB跨板傳遞的三角形荷載+次梁自重=1.71×2.25+1.71×2.25+3.625×2.25+3.625×2.25+3.625×7.2/2+11.88×7.2/2+4.224×(1-2×0.3^2+0.3^3)×4.5/2×2.25+4.224×(1-2×0.3^2+0.3^3)×4.5/2×2.25+2.92×7.2/4+2.92×7.2/4=121.56kN梁柱偏心彎矩：M=0×121.56=0kN·m活載=AB跨板傳遞的梯形荷載+AB跨板傳遞的三角形荷載=1.41×7.2/2+0.5×(1-2×0.3^2+0.3^3)×4.5/2×2.25+0.5×(1-2×0.3^2+0.3^3)×4.5/2×2.25=9.36kN梁柱偏心彎矩：M=0×9.36=0kN·m（2）標準層柱：恒載=墻體自重+縱梁自重+AB梁自重+AB跨墻體自重+AB跨板傳遞的梯形荷載+AB跨板傳遞的三角形荷載+次梁自重=4.56×2.25+4.56×2.25+3.625×2.25+3.625×2.25+3.625×7.2/2+9.98×7.2/2+3.55×(1-2×0.3^2+0.3^3)×4.5/2×2.25+3.55×(1-2×0.3^2+0.3^3)×4.5/2×2.25+2.92×7.2/4+2.92×7.2/4=143.18kN梁柱偏心彎矩：M=0×143.18=0kN·m活載=AB跨板傳遞的梯形荷載+AB跨板傳遞的三角形荷載=5.63×7.2/2+2×(1-2×0.3^2+0.3^3)×4.5/2×2.25+2×(1-2×0.3^2+0.3^3)×4.5/2×2.25=37.42kN梁柱偏心彎矩：M=0×37.42=0kN·mB柱集中荷載計算：（1）頂層柱：恒載=縱梁自重+AB梁自重+BC梁自重+AB跨板傳遞的梯形荷載+AB跨板傳遞的三角形荷載+BC跨板傳遞的梯形荷載+BC跨板傳遞的三角形荷載+次梁自重=3.625×2.25+3.625×2.25+3.625×7.2/2+2.215×2.4/2+0+0+11.88×7.2/2+4.224×(1-2×0.3^2+0.3^3)×4.5/2×2.25+4.224×(1-2×0.3^2+0.3^3)×4.5/2×2.25+4.224×(1-2×0.33^2+0.33^3)×3/2×2.25+4.224×(1-2×0.33^2+0.33^3)×3/2×2.25+7.92×2.4/2+2.92×0/4+2.92×7.2/4+2.92×0/4+2.92×7.2/4=154.36kN梁柱偏心彎矩：M=0×154.36=0kN·m活載=AB跨板傳遞的梯形荷載+AB跨板傳遞的三角形荷載+BC跨板傳遞的梯形荷載+BC跨板傳遞的三角形荷載=1.41×7.2/2+0.5×(1-2×0.3^2+0.3^3)×4.5/2×2.25+0.5×(1-2×0.3^2+0.3^3)×4.5/2×2.25+0.5×(1-2×0.33^2+0.33^3)×3/2×2.25+0.5×(1-2×0.33^2+0.33^3)×3/2×2.25+0.94×2.4/2=13.25kN梁柱偏心彎矩：M=0×13.25=0kN·m（2）標準層柱：恒載=縱梁自重+AB梁自重+BC梁自重+AB跨墻體自重+墻體自重+AB跨板傳遞的梯形荷載+AB跨板傳遞的三角形荷載+BC跨板傳遞的梯形荷載+BC跨板傳遞的三角形荷載+次梁自重=3.625×2.25+3.625×2.25+3.625×7.2/2+2.215×2.4/2+4.56×2.25+4.56×2.25+9.98×7.2/2+3.55×(1-2×0.3^2+0.3^3)×4.5/2×2.25+3.55×(1-2×0.3^2+0.3^3)×4.5/2×2.25+3.55×(1-2×0.33^2+0.33^3)×3/2×2.25+3.55×(1-2×0.33^2+0.33^3)×3/2×2.25+1.66×2.4/2+2.92×0/4+2.92×7.2/4+2.92×0/4+2.92×7.2/4=173.44kN梁柱偏心彎矩：M=0×173.44=0kN·m活載=AB跨板傳遞的梯形荷載+AB跨板傳遞的三角形荷載+BC跨板傳遞的梯形荷載+BC跨板傳遞的三角形荷載=5.63×7.2/2+2×(1-2×0.3^2+0.3^3)×4.5/2×2.25+2×(1-2×0.3^2+0.3^3)×4.5/2×2.25+2.5×(1-2×0.33^2+0.33^3)×3/2×2.25+2.5×(1-2×0.33^2+0.33^3)×3/2×2.25+4.69×2.4/2=51.85kN梁柱偏心彎矩：M=0×51.85=0kN·mC柱集中荷載計算：（1）頂層柱：恒載=縱梁自重+CD梁自重+BC梁自重+CD跨板傳遞的梯形荷載+BC跨板傳遞的梯形荷載+CD跨板傳遞的三角形荷載++BC跨板傳遞的三角形荷載+次梁自重=3.625×2.25+3.625×2.25+3.625×7.2/2+2.215×2.4/2+0+0+11.88×7.2/2+4.224×(1-2×0.33^2+0.33^3)×3/2×2.25+4.224×(1-2×0.33^2+0.33^3)×3/2×2.25+4.224×(1-2×0.3^2+0.3^3)×4.5/2×2.25+4.224×(1-2×0.3^2+0.3^3)×4.5/2×2.25+7.92×2.4/2+2.92×7.2/4+2.92×0/4+2.92×7.2/4+2.92×0/4=154.36kN梁柱偏心彎矩：M=0×154.36=0kN·m活載=CD跨板傳遞的梯形荷載+BC跨板傳遞的梯形荷載+CD跨板傳遞的三角形荷載+BC跨板傳遞的三角形荷載=1.41×7.2/2+0.5×(1-2×0.33^2+0.33^3)×3/2×2.25+0.5×(1-2×0.33^2+0.33^3)×3/2×2.25+0.5×(1-2×0.3^2+0.3^3)×4.5/2×2.25+0.5×(1-2×0.3^2+0.3^3)×4.5/2×2.25+0.94×2.4/2=13.25kN梁柱偏心彎矩：M=0×13.25=0kN·m（2）標準層柱：恒載=縱梁自重+CD梁自重+BC梁自重+CD跨墻體自重+墻體自重+CD跨板傳遞的梯形荷載+CD跨板傳遞的三角形荷載+BC跨板傳遞的梯形荷載+BC跨板傳遞的三角形荷載+次梁自重=3.625×2.25+3.625×2.25+3.625×7.2/2+2.215×2.4/2+4.56×7.2/2+4.56×2.25+4.56×2.25+9.98×7.2/2+3.55×(1-2×0.33^2+0.33^3)×3/2×2.25+3.55×(1-2×0.33^2+0.33^3)×3/2×2.25+3.55×(1-2×0.3^2+0.3^3)×4.5/2×2.25+3.55×(1-2×0.3^2+0.3^3)×4.5/2×2.25+1.66×2.4/2+2.92×7.2/4+2.92×0/4+2.92×7.2/4+2.92×0/4=173.44kN梁柱偏心彎矩：M=0×173.44=0kN·m活載=CD跨板傳遞的梯形荷載+BC跨板傳遞的梯形荷載+CD跨板傳遞的三角形荷載+BC跨板傳遞的三角形荷載=5.63×7.2/2+2.5×(1-2×0.33^2+0.33^3)×3/2×2.25+2.5×(1-2×0.33^2+0.33^3)×3/2×2.25+2×(1-2×0.3^2+0.3^3)×4.5/2×2.25+2×(1-2×0.3^2+0.3^3)×4.5/2×2.25+4.69×2.4/2=51.85kN梁柱偏心彎矩：M=0×51.85=0kN·mD柱集中荷載計算：（1）頂層柱：恒載=女兒墻自重+縱梁自重+CD梁自重+CD跨板傳遞的梯形荷載+CD跨板傳遞的三角形荷載+次梁自重=1.71×2.25+1.71×2.25+3.625×2.25+3.625×2.25+3.625×7.2/2+11.88×7.2/2+4.224×(1-2×0.3^2+0.3^3)×4.5/2×2.25+4.224×(1-2×0.3^2+0.3^3)×4.5/2×2.25+2.92×7.2/4+2.92×7.2/4=121.56kN梁柱偏心彎矩：M=0×121.56=0kN·m活載=AB跨板傳遞的梯形荷載+AB跨板傳遞的三角形荷載=1.41×7.2/2+0.5×(1-2×0.3^2+0.3^3)×4.5/2×2.25+0.5×(1-2×0.3^2+0.3^3)×4.5/2×2.25=9.36kN梁柱偏心彎矩：M=0×9.36=0kN·m（2）標準層柱：恒載=墻體自重+縱梁自重+CD梁自重+CD跨墻體自重+CD跨板傳遞的梯形荷載+CD跨板傳遞的三角形荷載+次梁自重=4.56×2.25+4.56×2.25+3.625×2.25+3.625×2.25+3.625×7.2/2+9.98×7.2/2+3.55×(1-2×0.3^2+0.3^3)×4.5/2×2.25+3.55×(1-2×0.3^2+0.3^3)×4.5/2×2.25+2.92×7.2/4+2.92×7.2/4=143.18kN梁柱偏心彎矩：M=0×143.18=0kN·m活載=CD跨板傳遞的梯形荷載+CD跨板傳遞的三角形荷載=5.63×7.2/2+2×(1-2×0.3^2+0.3^3)×4.5/2×2.25+2×(1-2×0.3^2+0.3^3)×4.5/2×2.25=37.42kN梁柱偏心彎矩：M=0×37.42=0kN·m1.2彎矩分配系數計算根據梁、柱的線剛度計算各個節點桿件的彎矩分配系數，各節點分配系數按下式進行計算：圖1.2彎矩分配系數計算簡圖其余彎矩分配系數計算下表所示：表1.2彎矩分配系數計算樓層節點線剛度ib×10^10(N·mm)∑ib分配系數μi左梁右梁上柱下柱左梁右梁上柱下柱6A柱03.75021.3730.1200.12500.875B柱3.753.33021.3733.450.1120.100.788C柱3.333.75021.3733.450.10.11200.788D柱3.750021.3730.120.125000.8755A柱03.7521.3721.3751.4900.0660.4670.467B柱3.753.3321.3721.3759.820.0630.0560.4410.441C柱3.333.7521.3721.3759.820.0560.0630.4410.441D柱3.75021.3721.3751.490.06600.4670.4674A柱03.7521.3721.3751.4900.0660.4670.467B柱3.753.3321.3721.3759.820.0630.0560.4410.441C柱3.333.7521.3721.3759.820.0560.0630.4410.441D柱3.75021.3721.3751.490.06600.4670.4673A柱03.7521.3721.3751.4900.0660.4670.467B柱3.753.3321.3721.3759.820.0630.0560.4410.441C柱3.333.7521.3721.3759.820.0560.0630.4410.441D柱3.75021.3721.3751.490.06600.4670.4672A柱03.7521.3721.3751.4900.0660.4670.467B柱3.753.3321.3721.3759.820.0630.0560.4410.441C柱3.333.7521.3721.3759.820.0560.0630.4410.441D柱3.75021.3721.3751.490.06600.4670.4671A柱03.7521.3715.6645.7800.0820.5760.342B柱3.753.3321.3715.6649.110.0760.0680.5370.319C柱3.333.7521.3715.6649.110.0680.0760.5370.319D柱3.75021.3715.6645.780.08200.5760.3421.3恒載桿端彎矩計算梁固端彎矩計算如下式所示：（以順時針為正）表1.3恒載作用梁固端彎矩計算樓層均布荷載q（kN/m）跨度l（m）AB跨BC跨CD跨AB跨BC跨CD跨AB跨BC跨CD跨Mb左Mb右Mb左Mb右Mb左Mb右615.5110.1415.517.22.47.2-6767-4.874.87-6767518.178.8818.177.22.47.2-78.4978.49-4.264.26-78.4978.49418.178.8818.177.22.47.2-78.4978.49-4.264.26-78.4978.49318.178.8818.177.22.47.2-78.4978.49-4.264.26-78.4978.49218.178.8818.177.22.47.2-78.4978.49-4.264.26-78.4978.49118.178.8818.177.22.47.2-78.4978.49-4.264.26-78.4978.491.4恒載下彎矩分配計算彎矩二次分配計算要點分為四步：第一步：將各節點的不平衡彎矩進行第一次分配；第二步：將分配后的彎矩向遠端傳送，傳遞系數均為0.5；第三步：第一次分配彎矩傳遞后的彎矩，再進行第二次彎矩分配，分配結果不再傳遞；第四步：將各桿端的所有桿端彎矩疊加即為各桿端的最后彎矩。其余層彎矩二次分配具體過程及結果如下：上柱下柱右梁左梁上柱下柱右梁左梁上柱下柱右梁左梁上柱下柱0.0000.8750.1250.11200.7880.1000.10000.7880.1120.12500.8750.00-67.0067.000.00-4.874.870.00-67.0067.000.000.0058.638.38-1.960.00-48.96-1.211.210.0048.961.96-8.380.00-58.630.0018.33-3.484.190.00-11.373.11-3.110.0011.37-4.193.480.00-18.330.00-12.99-1.861.020.007.150.91-0.910.00-7.15-1.021.860.0012.990.0063.96-63.9665.250.00-58.18-7.077.070.0058.18-65.2563.960.00-63.960.4670.4670.0660.0630.4410.4410.0560.0560.4410.4410.0630.0660.4670.4670.00-78.4978.490.00-4.264.260.00-78.4978.490.0031.6531.655.18-4.68-32.74-32.74-4.164.1632.7432.744.68-5.18-31.65-31.6529.3118.33-2.342.59-24.48-11.372.08-2.0824.4811.37-2.592.34-29.31-18.33-21.16-21.16-2.992.2815.9515.952.03-2.03-15.95-15.95-2.282.9921.1621.1644.8133.83-78.6478.68-41.26-33.15-4.314.3141.2633.15-78.6878.64-44.81-33.830.4670.4670.0660.0630.4410.4410.0560.0560.4410.4410.0630.0660.4670.4670.00-78.4978.490.00-4.264.260.00-78.4978.490.0031.6531.655.18-4.68-32.74-32.74-4.164.1632.7432.744.68-5.18-31.65-31.6518.3318.33-2.342.59-11.37-11.372.08-2.0811.3711.37-2.592.34-18.33-18.33-11.03-11.03-2.261.7712.3812.381.57-1.57-12.38-12.38-1.772.2611.0311.0338.9638.96-77.9178.17-31.73-31.73-4.774.7731.7331.73-78.1777.91-38.96-38.960.4670.4670.0660.0630.4410.4410.0560.0560.4410.4410.0630.0660.4670.4670.00-78.4978.490.00-4.264.260.00-78.4978.490.0031.6531.655.18-4.68-32.74-32.74-4.164.1632.7432.744.68-5.18-31.65-31.6518.3318.33-2.342.59-11.37-11.372.08-2.0811.3711.37-2.592.34-18.33-18.33-11.03-11.03-2.261.7712.3812.381.57-1.57-12.38-12.38-1.772.2611.0311.0338.9638.96-77.9178.17-31.73-31.73-4.774.7731.7331.73-78.1777.91-38.96-38.960.4670.4670.0660.0630.4410.4410.0560.0560.4410.4410.0630.0660.4670.4670.00-78.4978.490.00-4.264.260.00-78.4978.490.0031.6531.655.18-4.68-32.74-32.74-4.164.1632.7432.744.68-5.18-31.65-31.6518.3322.61-2.342.59-11.37-19.932.08-2.0811.3719.93-2.592.34-18.33-22.61-18.02-18.02-2.551.9913.9513.951.77-1.77-13.95-13.95-1.992.5518.0218.0231.9641.24-78.2078.40-35.15-38.72-4.574.5735.1538.72-78.4078.20-31.96-41.240.5760.3420.0820.0760.5370.3190.0680.0680.5370.3190.0760.0820.5760.3420.00-78.4978.490.00-4.264.260.00-78.4978.490.0045.2121.841.44-5.64-39.86-23.68-5.055.0539.8623.685.64-1.44-45.21-21.8418.330.00-2.823.22-11.370.002.52-2.5211.370.00-3.222.82-18.330.00-8.93-5.30-1.270.815.713.390.72-0.72-5.71-3.39-0.811.278.935.3054.6121.54-71.1571.87-50.52-20.29-1.061.0650.5220.29-71.8771.15-54.61-21.5410.77-10.1410.14-10.771.5恒載跨中彎矩計算在實際分布荷載的作用下，框架梁跨中彎矩按下面的式子計算：表1.4跨中彎矩計算樓層均布荷載q（kN/m）跨度l（m）AB跨BC跨CD跨AB跨BC跨CD跨AB跨BC跨CD跨615.5110.1415.517.22.47.235.90.2335.9518.178.8818.177.22.47.239.082.0839.08418.178.8818.177.22.47.239.71.6339.7318.178.8818.177.22.47.239.71.6339.7218.178.8818.177.22.47.239.451.8339.45118.178.8818.177.22.47.241.230.3341.231.6恒載柱端剪力計算圖1.3受力分析圖因此柱端剪力可按下式進行計算：表1.5柱端剪力計算樓層類別柱高柱端彎矩柱端剪力上下上下6A3.0063.9644.8131.2631.26B3.00-58.18-41.2633.1533.15C3.0058.1841.2633.1533.15D3.00-63.96-44.8131.2631.265A3.0033.8338.9624.2624.26B3.00-33.15-31.7323.2923.29C3.0033.1531.7323.2923.29D3.00-33.83-38.9624.2624.264A3.0038.9638.9625.9725.97B3.00-31.73-31.7324.4824.48C3.0031.7331.7324.4824.48D3.00-38.96-38.9625.9725.973A3.0038.9631.9625.3125.31B3.00-31.73-35.1523.9623.96C3.0031.7335.1523.9623.96D3.00-38.96-31.9625.3125.312A3.0041.2454.6131.9531.95B3.00-38.72-50.5229.7529.75C3.0038.7250.5229.7529.75D3.00-41.24-54.6131.9531.951A5.0521.5410.771.401.40B5.05-20.29-10.141.031.03C5.0520.2910.141.031.03D5.05-21.54-10.771.401.401.7恒載梁端內力計算計算梁端剪力梁平衡受力及柱軸力圖如下：圖1.4梁平衡受力圖由梁的平衡條件，梁端剪力按下列公式求得：表1.6梁端剪力計算樓層均布荷載q（kN/m）跨度l（m）AB跨BC跨CD跨AB跨BC跨CD跨AB跨BC跨CD跨Vb左Vb右Vb左Vb右Vb左Vb右615.5110.1415.517.202.407.2055.6651.0112.1712.1751.0155.66518.178.8818.177.202.407.2065.4165.4210.6610.6665.4265.41418.178.8818.177.202.407.2065.3865.4510.6610.6665.4565.38318.178.8818.177.202.407.2065.3865.4510.6610.6665.4565.38218.178.8818.177.202.407.2065.3865.4410.6610.6665.4465.38118.178.8818.177.202.407.2065.3165.5110.6610.6665.5165.31柱軸力按下列公式計算：表1.7豎向恒載作用下A柱軸力計算樓層柱高柱荷載（kN/m）集中荷載P柱自重GVb左Vb右Nc（kN）6上部3.0015.26121.560.000.0055.66182.22下部45.790.000.00228.015上部3.0015.26143.180.000.0065.41431.60下部45.790.000.00482.394上部3.0015.26143.180.000.0065.38690.95下部45.790.000.00731.743上部3.0015.26143.180.000.0065.38945.30下部45.790.000.00991.092上部3.0015.26143.180.000.0065.381199.65下部45.790.000.001245.441上部5.0515.26143.180.000.0065.311453.93下部77.080.000.001531.01表1.8豎向恒載作用下B柱軸力計算樓層柱高柱荷載（kN/m）集中荷載P柱自重GVb左Vb右Nc（kN）6上部3.0015.26154.360.0051.0112.17222.54下部45.790.000.00268.335上部3.0015.26173.440.0065.4210.66517.85下部45.790.000.00563.644上部3.0015.26173.440.0065.4510.66813.19下部45.790.000.00858.983上部3.0015.26173.440.0065.4510.661108.53下部45.790.000.001154.322上部3.0015.26173.440.0065.4410.661403.86下部45.790.000.001449.651上部5.0515.26173.440.0065.5110.661699.26下部77.080.000.001771.34表1.9豎向恒載作用下C柱軸力計算樓層柱高柱荷載（kN/m）集中荷載P柱自重GVb左Vb右Nc（kN）6上部3.0015.26154.360.0012.1751.01222.54下部45.790.000.00268.335上部3.0015.26173.440.0010.6665.42517.85下部45.790.000.00563.644上部3.0015.26173.440.0010.6665.45813.19下部45.790.000.00858.983上部3.0015.26173.440.0010.6665.451108.53下部45.790.000.001154.322上部3.0015.26173.440.0010.6665.441403.86下部45.790.000.001449.651上部5.0515.26173.440.0010.6665.511699.26下部77.080.000.001771.34表1.10豎向恒載作用下D柱軸力計算樓層柱高柱荷載（kN/m）集中荷載P柱自重GVb左Vb右Nc（kN）6上部3.0015.26121.560.0055.660.00182.22下部45.790.000.00228.015上部3.0015.26143.180.0065.410.00431.60下部45.790.000.00482.394上部3.0015.26143.180.0065.380.00690.95下部45.790.000.00731.743上部3.0015.26143.180.0065.380.00945.30下部45.790.000.00991.092上部3.0015.26143.180.0065.380.001199.65下部45.790.000.001245.441上部5.0515.26143.180.0065.310.001453.93下部77.080.000.001531.01內力圖繪制：a)彎矩圖b)剪力圖c)軸力圖圖1.5內力圖1.8活載桿端彎矩計算活載的計算與恒載完全一致，梁固端彎矩計算如下式所示：（以順時針為正）表1.11活載作用梁固端彎矩計算樓層均布荷載q（kN/m）跨度l（m）AB跨BC跨CD跨AB跨BC跨CD跨AB跨BC跨CD跨Mb左Mb右Mb左Mb右Mb左Mb右61.410.941.417.22.47.2-1.091.09-0.450.45-1.091.0955.634.695.637.22.47.2-24.3224.32-2.252.25-24.3224.3245.634.695.637.22.47.2-24.3224.32-2.252.25-24.3224.3235.634.695.637.22.47.2-24.3224.32-2.252.25-24.3224.3225.634.695.637.22.47.2-24.3224.32-2.252.25-24.3224.3215.634.695.637.22.47.2-24.3224.32-2.252.25-24.3224.321.9活載下彎矩分配計算活載彎矩二次分配計算與恒載完全一致，同樣分為四步：第一步：將各節點的不平衡彎矩進行第一次分配；第二步：將分配后的彎矩向遠端傳送，傳遞系數均為0.5；第三步：第一次分配彎矩傳遞后的彎矩，再進行第二次彎矩分配，分配結果不再傳遞；第四步：將各桿端的所有桿端彎矩疊加即為各桿端的最后彎矩上柱下柱右梁左梁上柱下柱右梁左梁上柱下柱右梁左梁上柱下柱0.0000.8750.1250.11200.7880.1000.10000.7880.1120.12500.8750.00-1.091.090.00-0.450.450.00-1.091.090.000.005.330.76-0.630.00-4.44-0.560.560.004.440.63-0.760.00-5.330.005.68-0.320.380.00-4.870.28-0.280.004.87-0.380.320.00-5.680.00-4.69-0.670.470.003.310.42-0.420.00-3.31-0.470.670.004.690.001.31-1.311.310.00-1.00-0.310.310.001.00-1.311.310.00-1.310.4670.4670.0660.0630.4410.4410.0560.0560.4410.4410.0630.0660.4670.4670.00-24.3224.320.00-2.252.250.00-24.3224.320.0011.3611.361.61-1.39-9.73-9.73-1.241.249.739.731.39-1.61-11.36-11.362.665.68-0.700.80-2.22-4.870.62-0.622.224.87-0.800.70-2.66-5.68-3.57-3.57-0.500.362.502.500.32-0.32-2.50-2.50-0.360.503.573.5710.4513.46-23.9124.09-9.46-12.10-2.552.559.4612.10-24.0923.91-10.45-13.460.4670.4670.0660.0630.4410.4410.0560.0560.4410.4410.0630.0660.4670.4670.00-24.3224.320.00-2.252.250.00-24.3224.320.0011.3611.361.61-1.39-9.73-9.73-1.241.249.739.731.39-1.61-11.36-11.365.685.68-0.700.80-4.87-4.870.62-0.624.874.87-0.800.70-5.68-5.68-4.98-4.98-0.700.523.673.670.47-0.47-3.67-3.67-0.520.704.984.9812.0612.06-24.1124.26-10.93-10.93-2.402.4010.9310.93-24.2624.11-12.06-12.060.4670.4670.0660.0630.4410.4410.0560.0560.4410.4410.0630.0660.4670.4670.00-24.3224.320.00-2.252.250.00-24.3224.320.0011.3611.361.61-1.39-9.73-9.73-1.241.249.739.731.39-1.61-11.36-11.365.685.68-0.700.80-4.87-4.870.62-0.624.874.87-0.800.70-5.68-5.68-4.98-4.98-0.700.523.673.670.47-0.47-3.67-3.67-0.520.704.984.9812.0612.06-24.1124.26-10.93-10.93-2.402.4010.9310.93-24.2624.11-12.06-12.060.4670.4670.0660.0630.4410.4410.0560.0560.4410.4410.0630.0660.4670.4670.00-24.3224.320.00-2.252.250.00-24.3224.320.0011.3611.361.61-1.39-9.73-9.73-1.241.249.739.731.39-1.61-11.36-11.365.687.00-0.700.80-4.87-5.930.62-0.624.875.93-0.800.70-5.68-7.00-5.60-5.60-0.790.594.134.130.52-0.52-4.13-4.13-0.590.795.605.6011.4412.76-24.2024.32-10.47-11.53-2.342.3410.4711.53-24.3224.20-11.44-12.760.5760.3420.0820.0760.5370.3190.0680.0680.5370.3190.0760.0820.5760.3420.00-24.3224.320.00-2.252.250.00-24.3224.320.0014.018.321.99-1.68-11.85-7.04-1.501.5011.857.041.68-1.99-14.01-8.325.680.00-0.841.00-4.870.000.75-0.754.870.00-1.000.84-5.680.00-2.79-1.66-0.400.241.670.990.21-0.21-1.67-0.99-0.240.402.791.6611.901.66-23.5623.88-15.04-1.05-2.792.7915.041.05-23.8823.56-11.90-1.663.33-3.023.02-3.33PAGEPAGE181.10活載跨中彎矩計算在實際分布荷載的作用下，框架梁跨中彎矩按下面的式子計算：表1.12跨中彎矩計算樓層均布荷載q（kN/m）跨度l（m）AB跨BC跨CD跨AB跨BC跨CD跨AB跨BC跨CD跨61.410.941.417.22.47.22.820.372.8255.634.695.637.22.47.212.480.8312.4845.634.695.637.22.47.212.30.9712.335.634.695.637.22.47.212.30.9712.325.634.695.637.22.47.212.221.0312.2215.634.695.637.22.47.212.760.5912.761.11活載柱端剪力計算圖1.6受力分析圖因此柱端剪力可按下式進行計算：表1.13柱端剪力計算樓層類別柱高柱端彎矩柱端剪力上下上下6A3.001.3110.455.595.59B3.00-1.00-9.465.155.15C3.001.009.465.155.15D3.00-1.31-10.455.595.595A3.0013.4612.068.518.51B3.00-12.10-10.937.687.68C3.0012.1010.937.687.68D3.00-13.46-12.068.518.514A3.0012.0612.068.048.04B3.00-10.93-10.937.297.29C3.0010.9310.937.297.29D3.00-12.06-12.068.048.043A3.0012.0611.447.837.83B3.00-10.93-10.477.137.13C3.0010.9310.477.137.13D3.00-12.06-11.447.837.832A3.0012.7611.909.899.89