ASDEvaluacin de las cargasSeparacin entre cerchas=8mCarga muertaDiseo a la tensin por ASDDiseo a la tensin por LRFDPeso propio0.4kN/m2Pu=iQi0Losa en concreto t=,12.4kN/m2Pu=Pu=Cielo raso en yeso0.4kN/m2Instalaciones0.4kN/m2Total carga muerta por unidad de rea3.6kN/m2Ancho aferente para carga Pu3.82mPerfil en acero A-36Fy=248MPaFy=248MPaTotal carga muerta por unidad de longitud13.77kN/m=1.67Total carga muerta puntual 110.14kNAg=6335.0mm2Agreq=9.819in2Carga viva0.5kN/m2Ancho aferente para carga Pu3.824mUSE PERFIL W 8X35Total carga viva por unidad de longitud1.912kN/mAg=10.3in2Total carga viva puntual 15.30kNPu=125.4kNMATRIZ DE CORRELACINMiembroD1D2D3D4100127.51.52123433411040056556786789103.750.7511.250.757910110856129127810783411349100050100150Miembro1234567891011xi051003.757.511.253.7557.510yi00000.751.50.750.7501.50xj510153.757.511.251557.51011.25yj0000.751.50.75001.500.75L5553.82426463523.82426463523.82426463523.82426463521.45773797372.91547594742.91547594741.4577379737Long t=39.043486383Peso t=20.1083715744kNPeso/Area0.1675697631kN/m2cos 1110.98058067570.98058067570.98058067570.98058067570.85749292570.85749292570.85749292570.8574929257sin 0000.19611613510.1961161351-0.1961161351-0.1961161351-0.51449575540.5144957554-0.51449575540.5144957554A3.00E-033.00E-033.00E-033.00E-033.00E-033.00E-033.00E-033.00E-033.00E-033.00E-033.00E-03E [kN/m2]2.00E+082.00E+082.00E+082.00E+082.00E+082.00E+082.00E+082.00E+082.00E+082.00E+082.00E+08k1-11-11-11-11-11-11-11-11-11-11-1-11-11-11-11-11-11-11-11-11-11-11120000-120000120000-120000120000-120000156892.908110547-156892.908110547156892.908110547-156892.908110547156892.908110547-156892.908110547156892.908110547-156892.908110547411596.604342021-411596.604342021205798.302171011-205798.302171011205798.302171011-205798.302171011411596.604342021-411596.604342021-120000120000-120000120000-120000120000-156892.908110547156892.908110547-156892.908110547156892.908110547-156892.908110547156892.908110547-156892.908110547156892.908110547-411596.604342021411596.604342021-205798.302171011205798.302171011-205798.302171011205798.302171011-411596.604342021411596.604342021A1000100010000.98058067570.1961161351000.98058067570.1961161351000.9805806757-0.1961161351000.9805806757-0.1961161351000.8574929257-0.5144957554000.85749292570.5144957554000.8574929257-0.5144957554000.85749292570.514495755400001000100010000.98058067570.1961161351000.98058067570.1961161351000.9805806757-0.1961161351000.9805806757-0.1961161351000.8574929257-0.5144957554000.85749292570.5144957554000.8574929257-0.5144957554000.85749292570.5144957554AT1010100.980580675700.980580675700.980580675700.980580675700.857492925700.857492925700.857492925700.857492925700000000.196116135100.19611613510-0.19611613510-0.19611613510-0.514495755400.51449575540-0.514495755400.5144957554001010100.980580675700.980580675700.980580675700.980580675700.857492925700.857492925700.857492925700.857492925700000000.196116135100.19611613510-0.19611613510-0.19611613510-0.514495755400.51449575540-0.514495755400.5144957554ATk120000-120000120000-120000120000-120000153846.153846154-153846.153846154153846.153846154-153846.153846154153846.153846154-153846.153846154153846.153846154-153846.153846154352941.176470588-352941.176470588176470.588235294-176470.588235294176470.588235294-176470.588235294352941.176470588-352941.17647058800000030769.2307692308-30769.230769230830769.2307692308-30769.2307692308-30769.230769230830769.2307692308-30769.230769230830769.2307692308-211764.705882353211764.705882353105882.352941176-105882.352941176-105882.352941176105882.352941176211764.705882353-211764.705882353-120000120000-120000120000-120000120000-153846.153846154153846.153846154-153846.153846154153846.153846154-153846.153846154153846.153846154-153846.153846154153846.153846154-352941.176470588352941.176470588-176470.588235294176470.588235294-176470.588235294176470.588235294-352941.176470588352941.176470588000000-30769.230769230830769.2307692308-30769.230769230830769.230769230830769.2307692308-30769.230769230830769.2307692308-30769.2307692308211764.705882353-211764.705882353-105882.352941176105882.352941176105882.352941176-105882.352941176-211764.705882353211764.7058823530012123434110005656787891091011056121278783434910ATkA1200000-120000001200000-120000011200000-12000003150858.56549091130171.7130981822-150858.565490911-30171.71309818220150858.56549091130171.7130981822-150858.565490911-30171.71309818225150858.565490911-30171.7130981822-150858.56549091130171.71309818227150858.565490911-30171.7130981822-150858.56549091130171.71309818229302644.562016192-181586.737209715-302644.562016192181586.7372097155151322.28100809690793.3686048576-151322.281008096-90793.36860485761151322.281008096-90793.3686048576-151322.28100809690793.36860485767302644.562016192181586.737209715-302644.562016192-181586.737209715300000000020000430171.71309818226034.3426196364-30171.7130981822-6034.3426196364030171.71309818226034.3426196364-30171.7130981822-6034.34261963646-30171.71309818226034.342619636430171.7130981822-6034.34261963648-30171.71309818226034.342619636430171.7130981822-6034.342619636410-181586.737209715108952.042325829181586.737209715-108952.042325829690793.368604857654476.0211629146-90793.3686048576-54476.02116291462-90793.368604857654476.021162914690793.3686048576-54476.02116291468181586.737209715108952.042325829-181586.737209715-108952.0423258294-120000012000001-120000012000003-1200000120000011-150858.565490911-30171.7130981822150858.56549091130171.71309818225-150858.565490911-30171.7130981822150858.56549091130171.71309818227-150858.56549091130171.7130981822150858.565490911-30171.71309818229-150858.56549091130171.7130981822150858.565490911-30171.713098182211-302644.562016192181586.737209715302644.562016192-181586.7372097151-151322.281008096-90793.3686048576151322.28100809690793.36860485767-151322.28100809690793.3686048576151322.281008096-90793.36860485763-302644.562016192-181586.737209715302644.562016192181586.7372097159000020000400000-30171.7130981822-6034.342619636430171.71309818226034.34261963646-30171.7130981822-6034.342619636430171.71309818226034.3426196364830171.7130981822-6034.3426196364-30171.71309818226034.34261963641030171.7130981822-6034.3426196364-30171.71309818226034.34261963640181586.737209715-108952.042325829-181586.737209715108952.0423258292-90793.3686048576-54476.021162914690793.368604857654476.0211629146890793.3686048576-54476.0211629146-90793.368604857654476.02116291464-181586.737209715-108952.042325829181586.737209715108952.04232582910Matrices expandidas12345678910111234567891011123456789101112345678910111234567891011123456789101112345678910111234567891011123456789101112345678910111234567891011120000011200000-1200000111111302644.562016192-181586.737209715-302644.562016192181586.7372097151151322.28100809690793.3686048576-151322.281008096-90793.36860485761110020000222222-181586.737209715108952.042325829181586.737209715-108952.042325829290793.368604857654476.0211629146-90793.3686048576-54476.02116291462223-1200000120000031200000-1200003333333151322.281008096-90793.3686048576-151322.28100809690793.36860485763302644.562016192181586.737209715-302644.562016192-181586.73720971534000040004444444-90793.368604857654476.021162914690793.3686048576-54476.02116291464181586.737209715108952.042325829-181586.737209715-108952.0423258294555150858.56549091130171.71309818225150858.56549091130171.7130981822-150858.565490911-30171.7130981822555-302644.562016192181586.737209715302644.562016192-181586.737209715555566630171.71309818226034.3426196364630171.71309818226034.3426196364-30171.7130981822-6034.3426196364666181586.737209715-108952.042325829-181586.737209715108952.04232582966667777-150858.565490911-30171.7130981822150858.56549091130171.71309818227150858.565490911-30171.7130981822-150858.56549091130171.7130981822777-151322.281008096-90793.3686048576151322.28100809690793.36860485767-151322.28100809690793.3686048576151322.281008096-90793.3686048576778888-30171.7130981822-6034.342619636430171.71309818226034.34261963648-30171.71309818226034.342619636430171.7130981822-6034.3426196364888-90793.3686048576-54476.021162914690793.368604857654476.0211629146890793.3686048576-54476.0211629146-90793.368604857654476.02116291468899999-150858.56549091130171.7130981822150858.565490911-30171.71309818229150858.565490911-30171.7130981822-150858.5654909119999-302644.562016192-181586.737209715302644.562016192181586.7372097159101010101030171.7130981822-6034.3426196364-30171.71309818226034.342619636410-30171.71309818226034.342619636430171.713098182210101010-181586.737209715-108952.042325829181586.737209715108952.042325829101111-120000012000011111111-150858.56549091130171.7130981822150858.5654909111111111111Matriz de rigidez de la estructura K12345678910111693967-90793-1200000-302645181587-151322-907930002-9079316342800181587-108952-90793-544760003-12000006939679079300-15132290793-302645-181587-120000400907931634280090793-54476-181587-10895205-30264518158700604362-121243-150859-301720006181587-10895200-121243121021-30172-60340007-151322-90793-15132290793-150859-301726043620-1508593017208-90793-5447690793-54476-30172-6034012102130172-60340900-302645-18158700-15085930172604362121243-1508591000-181587-1089520030172-6034121243121021301721100-12000000000-15085930172270859Matriz de flexibilidad de la estructura F123456789101110.0000083333-0.00002777780.0000083333-0.00001388890.00000625-0.000031250.0000041667-0.00002083330.00000625-0.00001041670.00000833332-0.00002777780.0003413768-0.00004166670.0002630457-0.00004157920.0003183745-0.00001672990.000304607-0.00002091240.0002284553-0.000055555630.0000083333-0.00004166670.0000166667-0.00002777780.0000083333-0.00004166670.0000083333-0.00004166670.0000125-0.00002083330.00001666674-0.00001388890.0002630457-0.00002777780.0003413768-0.00003464320.0002284553-0.00003882570.000304607-0.00001397640.0003183745-0.000055555650.00000625-0.00004157920.0000083333-0.00003464320.0000092488-0.0000379580.0000060369-0.00003847050.0000059422-0.0000306580.00001041676-0.000031250.0003183745-0.00004166670.0002284553-0.0000379580.0003140784-0.00001361280.0002752117-0.00002142530.0001947197-0.000052083370.0000041667-0.00001672990.0000083333-0.00003882570.0000060369-0.00001361280.0000128787-0.000031250.0000081203-0.00003847050.00001258-0.00002083330.000304607-0.00004166670.000304607-0.00003847050.0002752117-0.000031250.0003219681-0.00002402950.0002752117-0.000062590.00000625-0.00002091240.0000125-0.00001397640.0000059422-0.00002142530.0000081203-0.00002402950.0000134154-0.00001412540.000014583310-0.00001041670.0002284553-0.00002083330.0003183745-0.0000306580.0001947197-0.00003847050.0002752117-0.00001412540.0003140784-0.0000520833110.0000083333-0.00005555560.0000166667-0.00005555560.0000104167-0.00005208330.0000125-0.00006250.0000145833-0.00005208330.000025Vector de cargas Q10203040506-125.4358800344708-125.43588003449010-125.4358800344110Vector de desplazamientos10.00783974252-0.106800729230.01306623754-0.106800729250.01343249066-0.098342953170.010452998-0.109429290.007473489410-0.0983429531110.02090598Clculo de fuerzas internas en los miembrosq=kADmkA1200000-12000001200000-12000001200000-1200000153846.15384615430769.2307692308-153846.153846154-30769.2307692308153846.15384615430769.2307692308-153846.153846154-30769.2307692308153846.153846154-30769.2307692308-153846.15384615430769.2307692308153846.153846154-30769.2307692308-153846.15384615430769.2307692308352941.176470588-211764.705882353-352941.176470588211764.705882353176470.588235294105882.352941176-176470.588235294-105882.352941176176470.588235294-105882.352941176-176470.588235294105882.352941176352941.176470588211764.705882353-352941.176470588-211764.705882353-12000001200000-12000001200000-12000001200000-153846.153846154-30769.2307692308153846.15384615430769.2307692308-153846.153846154-30769.2307692308153846.15384615430769.2307692308-153846.15384615430769.2307692308153846.153846154-30769.2307692308-153846.15384615430769.2307692308153846.153846154-30769.2307692308-352941.176470588211764.705882353352941.176470588-211764.705882353-176470.588235294-105882.352941176176470.588235294105882.352941176-176470.588235294105882.352941176176470.588235294-105882.352941176-352941.176470588-211764.705882353352941.176470588211764.705882353Dm00.00783974250.013066237500.01343249060.010452990.00747348940.01343249060.00783974250.010452990.01306623750-0.1068007292-0.10680072920-0.0983429531-0.1094292-0.0983429531-0.0983429531-0.1068007292-0.1094292-0.10680072920.00783974250.01306623750.020905980.01343249060.010452990.00747348940.020905980.00783974250.010452990.01306623750.0074734894-0.1068007292-0.10680072920-0.0983429531-0.1094292-0.09834295310-0.1068007292-0.1094292-0.1068007292-0.0983429531q=kADm-940.7691002579-627.1794001719-940.7691002579959.4799.5799.5959.4182.852645592-182.852645592-182.852645592182.852645592940.7691002579627.1794001719940.7691002579-959.4-799.5-799.5-959.4-182.852645592182.852645592182.852645592-182.852645592Disee el miembro No. 5 sabiendo que:Fy=248MpaL=3.824m Carga ltima=-799.5kNAsuma Lx=Ly=LzConsidere estas tres alternativas:Perfil principalConectorDistancia entre conectores1. Un ngulo individual2. Dos ngulos en T (separados 3/8")3. Dos ngulos separados y enfrentados con ancho total de seccin 300 mm

1

8

5

3

2

D1

D2

D3

D4

6

4

7

9

10

11

11

Pu

Pu

Pu

LRFDEvaluacin de las cargasSeparacin entre cerchas=8m=154.194350091Carga muertaDiseo a la tensin por LRFDPeso propio0.4kN/m2Pu=iQi1175Losa en concreto t=,12.4kN/m2Pu=Cielo raso en yeso0.4kN/m2Estado lmite de fluencia en la seccin total=156.6418794576Instalaciones0.4kN/m2Total carga muerta por unidad de rea3.6kN/m2Estado lmite de rotura en la seccin neta efectivaAncho aferente para carga Pu3.82mPerfil en acero A-36PERFILES en acero A-36Fy=248MPaFu=400MPaTotal carga muerta por unidad de longitud13.77kN/mt=0.9t=0.75Total carga muerta puntual 110.14kNAgreq=5263.5mm2An=4263Agreq=8.158in2xbarra=18.6436Carga viva0.5kN/m2L=240Ancho aferente para carga Pu3.824mUSE PERFIL W 8X28U=0.92Total carga viva por unidad de longitud1.912kN/mAg=8.24in2=1187kNPn=FuAe=1573Total carga viva puntual 15.30kNAg=5316mm2tf=0.465in=1179kNPu=156.6kNtf=11.81mm2CUMPLEMATRIZ DE CORRELACINMiembroD1D2D3D4100127.51.52123433411040056556786789103.750.7511.250.757910110856129127810783411349100050100150Miembro1234567891011xi051003.757.511.253.7557.510yi00000.751.50.750.7501.50xj510153.757.511.251557.51011.25yj0000.751.50.75001.500.75L5553.82426463523.82426463523.82426463523.82426463521.45773797372.91547594742.91547594741.4577379737Long t=39.043486383Peso t=20.1083715744kNPeso/Area0.1675697631kN/m2cos 1110.98058067570.98058067570.98058067570.98058067570.85749292570.85749292570.85749292570.8574929257sin 0000.19611613510.1961161351-0.1961161351-0.1961161351-0.51449575540.5144957554-0.51449575540.5144957554A3.00E-033.00E-033.00E-033.00E-033.00E-033.00E-033.00E-033.00E-033.00E-033.00E-033.00E-03E [kN/m2]2.00E+082.00E+082.00E+082.00E+082.00E+082.00E+082.00E+082.00E+082.00E+082.00E+082.00E+08k1-11-11-11-11-11-11-11-11-11-11-1-11-11-11-11-11-11-11-11-11-11-11120000-120000120000-120000120000-120000156892.908110547-156892.908110547156892.908110547-156892.908110547156892.908110547-156892.908110547156892.908110547-156892.908110547411596.604342021-411596.604342021205798.302171011-205798.302171011205798.302171011-205798.302171011411596.604342021-411596.604342021-120000120000-120000120000-120000120000-156892.908110547156892.908110547-156892.908110547156892.908110547-156892.908110547156892.908110547-156892.908110547156892.908110547-411596.604342021411596.604342021-205798.302171011205798.302171011-205798.302171011205798.302171011-411596.604342021411596.604342021A1000100010000.98058067570.1961161351000.98058067570.1961161351000.9805806757-0.1961161351000.9805806757-0.1961161351000.8574929257-0.5144957554000.85749292570.5144957554000.8574929257-0.5144957554000.85749292570.514495755400001000100010000.98058067570.1961161351000.98058067570.1961161351000.9805806757-0.1961161351000.9805806757-0.1961161351000.8574929257-0.5144957554000.85749292570.5144957554000.8574929257-0.5144957554000.85749292570.5144957554AT1010100.980580675700.980580675700.980580675700.980580675700.857492925700.857492925700.857492925700.857492925700000000.196116135100.19611613510-0.19611613510-0.19611613510-0.514495755400.51449575540-0.514495755400.5144957554001010100.980580675700.980580675700.980580675700.980580675700.857492925700.857492925700.857492925700.857492925700000000.196116135100.19611613510-0.19611613510-0.19611613510-0.514495755400.51449575540-0.514495755400.5144957554ATk120000-120000120000-120000120000-120000153846.153846154-153846.153846154153846.153846154-153846.153846154153846.153846154-153846.153846154153846.153846154-153846.153846154352941.176470588-352941.176470588176470.588235294-176470.588235294176470.588235294-176470.588235294352941.176470588-352941.17647058800000030769.2307692308-30769.230769230830769.2307692308-30769.2307692308-30769.230769230830769.2307692308-30769.230769230830769.2307692308-211764.705882353211764.705882353105882.352941176-105882.352941176-105882.352941176105882.352941176211764.705882353-211764.705882353-120000120000-120000120000-120000120000-153846.153846154153846.153846154-153846.153846154153846.153846154-153846.153846154153846.153846154-153846.153846154153846.153846154-352941.176470588352941.176470588-176470.588235294176470.588235294-176470.588235294176470.588235294-352941.176470588352941.176470588000000-30769.230769230830769.2307692308-30769.230769230830769.230769230830769.2307692308-30769.230769230830769.2307692308-30769.2307692308211764.705882353-211764.705882353-105882.352941176105882.352941176105882.352941176-105882.352941176-211764.705882353211764.7058823530012123434110005656787891091011056121278783434910ATkA1200000-120000001200000-120000011200000-12000003150858.56549091130171.7130981822-150858.565490911-30171.71309818220150858.56549091130171.7130981822-150858.565490911-30171.71309818225150858.565490911-30171.7130981822-150858.56549091130171.71309818227150858.565490911-30171.7130981822-150858.56549091130171.71309818229302644.562016192-181586.737209715-302644.562016192181586.7372097155151322.28100809690793.3686048576-151322.281008096-90793.36860485761151322.281008096-90793.3686048576-151322.28100809690793.36860485767302644.562016192181586.737209715-302644.562016192-181586.737209715300000000020000430171.71309818226034.3426196364-30171.7130981822-6034.3426196364030171.71309818226034.3426196364-30171.7130981822-6034.34261963646-30171.71309818226034.342619636430171.7130981822-6034.34261963648-30171.71309818226034.342619636430171.7130981822-6034.342619636410-181586.737209715108952.042325829181586.737209715-108952.042325829690793.368604857654476.0211629146-90793.3686048576-54476.02116291462-90793.368604857654476.021162914690793.3686048576-54476.02116291468181586.737209715108952.042325829-181586.737209715-108952.0423258294-120000012000001-120000012000003-1200000120000011-150858.565490911-30171.7130981822150858.56549091130171.71309818225-150858.565490911-30171.7130981822150858.56549091130171.71309818227-150858.56549091130171.7130981822150858.565490911-30171.71309818229-150858.56549091130171.7130981822150858.565490911-30171.713098182211-302644.562016192181586.737209715302644.562016192-181586.7372097151-151322.281008096-90793.3686048576151322.28100809690793.36860485767-151322.28100809690793.3686048576151322.281008096-90793.36860485763-302644.562016192-181586.737209715302644.562016192181586.7372097159000020000400000-30171.7130981822-6034.342619636430171.71309818226034.34261963646-30171.7130981822-6034.342619636430171.71309818226034.3426196364830171.7130981822-6034.3426196364-30171.71309818226034.34261963641030171.7130981822-6034.3426196364-30171.71309818226034.34261963640181586.737209715-108952.042325829-181586.737209715108952.0423258292-90793.3686048576-54476.021162914690793.368604857654476.0211629146890793.3686048576-54476.0211629146-90793.368604857654476.02116291464-181586.737209715-108952.042325829181586.737209715108952.04232582910Matrices expandidas12345678910111234567891011123456789101112345678910111234567891011123456789101112345678910111234567891011123456789101112345678910111234567891011120000011200000-1200000111111302644.562016192-181586.737209715-302644.562016192181586.7372097151151322.28100809690793.3686048576-151322.281008096-90793.36860485761110020000222222-181586.737209715108952.042325829181586.737209715-108952.042325829290793.368604857654476.0211629146-90793.3686048576-54476.02116291462223-1200000120000031200000-1200003333333151322.281008096-90793.3686048576-151322.28100809690793.36860485763302644.562016192181586.737209715-302644.562016192-181586.73720971534000040004444444-90793.368604857654476.021162914690793.3686048576-54476.02116291464181586.737209715108952.042325829-181586.737209715-108952.0423258294555150858.56549091130171.71309818225150858.56549091130171.7130981822-150858.565490911-30171.7130981822555-302644.562016192181586.737209715302644.562016192-181586.737209715555566630171.71309818226034.3426196364630171.71309818226034.3426196364-30171.7130981822-6034.3426196364666181586.737209715-108952.042325829-181586.737209715108952.04232582966667777-150858.565490911-30171.7130981822150858.56549091130171.71309818227150858.565490911-30171.7130981822-150858.56549091130171.7130981822777-151322.281008096-90793.3686048576151322.28100809690793.36860485767-151322.28100809690793.3686048576151322.281008096-90793.3686048576778888-30171.7130981822-6034.342619636430171.71309818226034.34261963648-30171.71309818226034.342619636430171.7130981822-6034.3426196364888-90793.3686048576-54476.021162914690793.368604857654476.0211629146890793.3686048576-54476.0211629146-90793.368604857654476.02116291468899999-150858.56549091130171.7130981822150858.565490911-30171.71309818229150858.565490911-30171.7130981822-150858.5654909119999-302644.562016192-181586.737209715302644.562016192181586.7372097159101010101030171.7130981822-6034.3426196364-30171.71309818226034.342619636410-30171.71309818226034.342619636430171.713098182210101010-181586.737209715-108952.042325829181586.737209715108952.042325829101111-120000012000011111111-150858.56549091130171.7130981822150858.5654909111111111111Matriz de rigidez de la estructura K12345678910111693967-90793-1200000-302645181587-151322-907930002-9079316342800181587-108952-90793-544760003-12000006939679079300-15132290793-302645-181587-120000400907931634280090793-54476-181587-10895205-30264518158700604362-121243-150859-301720006181587-10895200-121243121021-30172-60340007-151322-90793-15132290793-150859-301726043620-1508593017208-90793-5447690793-54476-30172-6034012102130172-60340900-302645-18158700-15085930172604362121243-1508591000-181587-1089520030172-6034121243121021301721100-12000000000-15085930172270859Matriz de flexibilidad de la estructura F123456789101110.0000083333-0.00002777780.0000083333-0.00001388890.00000625-0.000031250.0000041667-0.00002083330.00000625-0.00001041670.00000833332-0.00002777780.0003413768-0.00004166670.0002630457-0.00004157920.0003183745-0.00001672990.000304607-0.00002091240.0002284553-0.000055555630.0000083333-0.00004166670.0000166667-0.00002777780.0000083333-0.00004166670.0000083333-0.00004166670.0000125-0.00002083330.00001666674-0.00001388890.0002630457-0.00002777780.0003413768-0.00003464320.0002284553-0.00003882570.000304607-0.00001397640.0003183745-0.000055555650.00000625-0.00004157920.0000083333-0.00003464320.0000092488-0.0000379580.0000060369-0.00003847050.0000059422-0.0000306580.00001041676-0.000031250.0003183745-0.00004166670.0002284553-0.0000379580.0003140784-0.00001361280.0002752117-0.00002142530.0001947197-0.000052083370.0000041667-0.00001672990.0000083333-0.00003882570.0000060369-0.00001361280.0000128787-0.000031250.0000081203-0.00003847050.00001258-0.00002083330.000304607-0.00004166670.000304607-0.00003847050.0002752117-0.000031250.0003219681-0.00002402950.0002752117-0.000062590.00000625-0.00002091240.0000125-0.00001397640.0000059422-0.00002142530.0000081203-0.00002402950.0000134154-0.00001412540.000014583310-0.00001041670.0002284553-0.00002083330.0003183745-0.0000306580.0001947197-0.00003847050.0002752117-0.00001412540.0003140784-0.0000520833110.0000083333-0.00005555560.0000166667-0.00005555560.0000104167-0.00005208330.0000125-0.00006250.0000145833-0.00005208330.000025Vector de cargas Q10203040506-156.6418794576708-156.64187945769010-156.6418794576110Vector de desplazamientos10.00979011752-0.133370666730.01631686244-0.133370666750.01677423226-0.12280876170.013053498-0.136653049890.009332747710-0.122808761110.0261069799Clculo de fuerzas internas en los miembrosq=kADmkA1200000-12000001200000-12000001200000-1200000153846.15384615430769.2307692308-153846.153846154-30769.2307692308153846.15384615430769.2307692308-153846.153846154-30769.2307692308153846.153846154-30769.2307692308-153846.15384615430769.2307692308153846.153846154-30769.2307692308-153846.15384615430769.2307692308352941.176470588-211764.705882353-352941.176470588211764.705882353176470.588235294105882.352941176-176470.588235294-105882.352941176176470.588235294-105882.352941176-176470.588235294105882.352941176352941.176470588211764.705882353-352941.176470588-211764.705882353-12000001200000-12000001200000-12000001200000-153846.153846154-30769.2307692308153846.15384615430769.2307692308-153846.153846154-30769.2307692308153846.15384615430769.2307692308-153846.15384615430769.2307692308153846.153846154-30769.2307692308-153846.15384615430769.2307692308153846.153846154-30769.2307692308-352941.176470588211764.705882353352941.176470588-211764.705882353-176470.588235294-105882.352941176176470.588235294105882.352941176-176470.588235294105882.352941176176470.588235294-105882.352941176-352941.176470588-211764.705882353352941.176470588211764.705882353Dm00.00979011750.016316862400.01677423220.013053490.00933274770.01677423220.00979011750.013053490.01631686240-0.1333706667-0.13337066670-0.122808761-0.1366530498-0.122808761-0.122808761-0.1333706667-0.1366530498-0.13337066670.00979011750.01631686240.02610697990.01677423220.013053490.00933274770.02610697990.00979011750.013053490.01631686240.0093327477-0.1333706667-0.13337066670-0.122808761-0.1366530498-0.1228087610-0.1333706667-0.1366530498-0.1333706667-0.122808761q=kADm-1174.8140959318-783.2093972879-1174.81409593181198.08998.4998.41198.08228.3428159588-228.3428159588-228.3428159588228.34281595881174.8140959318783.20939728791174.8140959318-1198.08-998.4-998.4-1198.08-228.3428159588228.3428159588228.3428159588-228.3428159588-269.2Disee el miembro No. 5 sabiendo que:Fy=248MpaL=3.824m Carga ltima=-998.4kNAsuma Lx=Ly=LzConsidere estas tres alternativas:Perfil principalConectorDistancia entre conectores1. Un ngulo individual2. Dos ngulos en T (separados 3/8")3. Dos ngulos separados y enfrentados con ancho total de seccin 300 mm

1

8

5

3

2

D1

D2

D3

D4

6

4

7

9

10

11

11

Pu

Pu

Pu

EmpalmeEvaluacin de las cargasSeparacin entre cerchas=8m=154.194350091Carga muertaDiseo a la tensin por LRFDPeso propio0.4kN/m2Pu=iQi783Losa en concreto t=,12.4kN/m2Pu=Cielo raso en yeso0.4kN/m2Estado lmite de fluencia en la seccin total=156.6418794576Instalaciones0.4kN/m2Total carga muerta por unidad de rea3.6kN/m2Estado lmite de rotura en la seccin netaAncho aferente para carga Pu3.82mPlatinas en acero A-36Fy=248MPabf=166Fu=400MPaTotal carga muerta por unidad de longitud13.77kN/mt=0.9bp=190190.9t=0.75Total carga muerta puntual 110.14kNAgreq=3509.0mm2tp req=9.234An=2770Agreq=5.439in2tp =9.525Carga viva0.5kN/m2Pn=FuAn=1108kNAncho aferente para carga Pu3.824mUSE 2 PLATINAS 3/8"x 190Total carga viva por unidad de longitud1.912kN/mAg=3620mm2=808kN=831kNTotal carga viva puntual 15.30kNCUMPLECUMPLEPu=156.6kNMATRIZ DE CORRELACINMiembroD1D2D3D4100127.51.52123433411040056556786789103.750.7511.250.757910110856129127810783411349100050100150Miembro1234567891011xi051003.757.511.253.7557.510yi00000.751.50.750.7501.50xj510153.757.511.251557.51011.25yj0000.751.50.75001.500.75L5553.82426463523.82426463523.82426463523.82426463521.45773797372.91547594742.91547594741.4577379737Long t=39.043486383Peso t=20.1083715744kNPeso/Area0.1675697631kN/m2cos 1110.98058067570.98058067570.98058067570.98058067570.85749292570.85749292570.85749292570.8574929257sin 0000.19611613510.1961161351-0.1961161351-0.1961161351-0.51449575540.5144957554-0.51449575540.5144957554A3.00E-033.00E-033.00E-033.00E-033.00E-033.00E-033.00E-033.00E-033.00E-033.00E-033.00E-03E [kN/m2]2.00E+082.00E+082.00E+082.00E+082.00E+082.00E+082.00E+082.00E+082.00E+082.00E+082.00E+08k1-11-11-11-11-11-11-11-11-11-11-1-11-11-11-11-11-11-11-11-11-11-11120000-120000120000-120000120000-120000156892.908110547-156892.908110547156892.908110547-156892.908110547156892.908110547-156892.908110547156892.908110547-156892.908110547411596.604342021-411596.604342021205798.302171011-205798.302171011205798.302171011-205798.302171011411596.604342021-411596.604342021-120000120000-120000120000-120000120000-156892.908110547156892.908110547-156892.908110547156892.908110547-156892.908110547156892.908110547-156892.908110547156892.908110547-411596.604342021411596.604342021-205798.302171011205798.302171011-205798.302171011205798.302171011-411596.604342021411596.604342021A1000100010000.98058067570.1961161351000.98058067570.1961161351000.9805806757-0.1961161351000.9805806757-0.1961161351000.8574929257-0.5144957554000.85749292570.5144957554000.8574929257-0.5144957554000.85749292570.514495755400001000100010000.98058067570.1961161351000.98058067570.1961161351000.9805806757-0.1961161351000.9805806757-0.1961161351000.8574929257-0.5144957554000.85749292570.5144957554000.8574929257-0.5144957554000.85749292570.5144957554AT1010100.980580675700.980580675700.980580675700.980580675700.857492925700.857492925700.857492925700.857492925700000000.196116135100.19611613510-0.19611613510-0.19611613510-0.514495755400.51449575540-0.514495755400.5144957554001010100.980580675700.980580675700.980580675700.980580675700.857492925700.857492925700.857492925700.857492925700000000.196116135100.19611613510-0.19611613510-0.19611613510-0.514495755400.51449575540-0.514495755400.5144957554ATk120000-120000120000-120000120000-120000153846.153846154-153846.153846154153846.153846154-153846.153846154153846.153846154-153846.153846154153846.153846154-153846.153846154352941.176470588-352941.176470588176470.588235294-176470.588235294176470.588235294-176470.588235294352941.176470588-352941.17647058800000030769.2307692308-30769.230769230830769.2307692308-30769.2307692308-30769.230769230830769.2307692308-30769.230769230830769.2307692308-211764.705882353211764.705882353105882.352941176-105882.352941176-105882.352941176105882.352941176211764.705882353-211764.705882353-120000120000-120000120000-120000120000-153846.153846154153846.153846154-153846.153846154153846.153846154-153846.153846154153846.153846154-153846.153846154153846.153846154-352941.176470588352941.176470588-176470.588235294176470.588235294-176470.588235294176470.588235294-352941.176470588352941.176470588000000-30769.230769230830769.2307692308-30769.230769230830769.230769230830769.2307692308-30769.230769230830769.2307692308-30769.2307692308211764.705882353-211764.705882353-105882.352941176105882.352941176105882.352941176-105882.352941176-211764.705882353211764.7058823530012123434110005656787891091011056121278783434910ATkA1200000-120000001200000-120000011200000-12000003150858.56549091130171.7130981822-150858.565490911-30171.71309818220150858.56549091130171.7130981822-150858.565490911-30171.71309818225150858.565490911-30171.7130981822-150858.56549091130171.71309818227150858.565490911-30171.7130981822-150858.56549091130171.71309818229302644.562016192-181586.737209715-302644.562016192181586.7372097155151322.28100809690793.3686048576-151322.281008096-90793.36860485761151322.281008096-90793.3686048576-151322.28100809690793.36860485767302644.562016192181586.737209715-302644.562016192-181586.737209715300000000020000430171.71309818226034.3426196364-30171.7130981822-6034.3426196364030171.71309818226034.3426196364-30171.7130981822-6034.34261963646-30171.71309818226034.342619636430171.7130981822-6034.34261963648-30171.71309818226034.342619636430171.7130981822-6034.342619636410-181586.737209715108952.042325829181586.737209715-108952.042325829690793.368604857654476.0211629146-90793.3686048576-54476.02116291462-90793.368604857654476.021162914690793.3686048576-54476.02116291468181586.737209715108952.042325829-181586.737209715-108952.0423258294-120000012000001-120000012000003-1200000120000011-150858.565490911-30171.7130981822150858.56549091130171.71309818225-150858.565490911-30171.7130981822150858.56549091130171.71309818227-150858.56549091130171.7130981822150858.565490911-30171.71309818229-150858.56549091130171.7130981822150858.565490911-30171.713098182211-302644.562016192181586.737209715302644.562016192-181586.7372097151-151322.281008096-90793.3686048576151322.28100809690793.36860485767-151322.28100809690793.3686048576151322.281008096-90793.36860485763-302644.562016192-181586.737209715302644.562016192181586.7372097159000020000400000-30171.7130981822-6034.342619636430171.71309818226034.34261963646-30171.7130981822-6034.342619636430171.71309818226034.3426196364830171.7130981822-6034.3426196364-30171.71309818226034.34261963641030171.7130981822-6034.3426196364-30171.71309818226034.34261963640181586.737209715-108952.042325829-181586.737209715108952.0423258292-90793.3686048576-54476.021162914690793.368604857654476.0211629146890793.3686048576-54476.0211629146-90793.368604857654476.02116291464-181586.737209715-108952.042325829181586.737209715108952.04232582910Matrices expandidas12345678910111234567891011123456789101112345678910111234567891011123456789101112345678910111234567891011123456789101112345678910111234567891011120000011200000-1200000111111302644.562016192-181586.737209715-302644.562016192181586.7372097151151322.28100809690793.3686048576-151322.281008096-90793.36860485761110020000222222-181586.737209715108952.042325829181586.737209715-108952.042325829290793.368604857654476.0211629146-90793.3686048576-54476.02116291462223-1200000120000031200000-1200003333333151322.281008096-90793.3686048576-151322.28100809690793.36860485763302644.562016192181586.737209715-302644.562016192-181586.73720971534000040004444444-90793.368604857654476.021162914690793.3686048576-54476.02116291464181586.737209715108952.042325829-181586.737209715-108952.0423258294555150858.56549091130171.71309818225150858.56549091130171.7130981822-150858.565490911-30171.7130981822555-302644.562016192181586.737209715302644.562016192-181586.737209715555566630171.71309818226034.3426196364630171.71309818226034.3426196364-30171.7130981822-6034.3426196364666181586.737209715-108952.042325829-181586.737209715108952.04232582966667777-150858.565490911-30171.7130981822150858.56549091130171.71309818227150858.565490911-30171.7130981822-150858.56549091130171.7130981822777-151322.281008096-90793.3686048576151322.28100809690793.36860485767-151322.28100809690793.3686048576151322.281008096-90793.3686048576778888-30171.7130981822-6034.342619636430171.71309818226034.34261963648-30171.71309818226034.342619636430171.7130981822-6034.3426196364888-90793.3686048576-54476.021162914690793.368604857654476.0211629146890793.3686048576-54476.0211629146-90793.368604857654476.02116291468899999-150858.56549091130171.7130981822150858.565490911-30171.71309818229150858.565490911-30171.7130981822-150858.5654909119999-302644.562016192-181586.737209715302644.562016192181586.7372097159101010101030171.7130981822-6034.3426196364-30171.71309818226034.342619636410-30171.71309818226034.342619636430171.713098182210101010-181586.737209715-108952.042325829181586.737209715108952.042325829101111-120000012000011111111-150858.56549091130171.7130981822150858.5654909111111111111Matriz de rigidez de la estructura K12345678910111693967-90793-1200000-302645181587-151322-907930002-9079316342800181587-108952-90793-544760003-12000006939679079300-15132290793-302645-181587-120000400907931634280090793-54476-181587-10895205-30264518158700604362-121243-150859-301720006181587-10895200-121243121021-30172-60340007-151322-90793-15132290793-150859-301726043620-1508593017208-90793-5447690793-54476-30172-6034012102130172-60340900-302645-18158700-15085930172604362121243-1508591000-181587-1089520030172-6034121243121021301721100-12000000000-15085930172270859Matriz de flexibilidad de la estructura F123456789101110.0000083333-0.00002777780.0000083333-0.00001388890.00000625-0.000031250.0000041667-0.00002083330.00000625-0.00001041670.00000833332-0.00002777780.0003413768-0.00004166670.0002630457-0.00004157920.0003183745-0.00001672990.000304607-0.00002091240.0002284553-0.000055555630.0000083333-0.00004166670.0000166667-0.00002777780.0000083333-0.00004166670.0000083333-0.00004166670.0000125-0.00002083330.00001666674-0.00001388890.0002630457-0.00002777780.0003413768-0.00003464320.0002284553-0.00003882570.000304607-0.00001397640.0003183745-0.000055555650.00000625-0.00004157920.0000083333-0.00003464320.0000092488-0.0000379580.0000060369-0.00003847050.0000059422-0.0000306580.00001041676-0.000031250.0003183745-0.00004166670.0002284553-0.0000379580.0003140784-0.00001361280.0002752117-0.00002142530.0001947197-0.000052083370.0000041667-0.00001672990.0000083333-0.00003882570.0000060369-0.00001361280.0000128787-0.000031250.0000081203-0.00003847050.00001258-0.00002083330.000304607-0.00004166670.000304607-0.00003847050.0002752117-0.000031250.0003219681-0.00002402950.0002752117-0.000062590.00000625-0.00002091240.0000125-0.00001397640.0000059422-0.00002142530.0000081203-0.00002402950.0000134154-0.00001412540.000014583310-0.00001041670.0002284553-0.00002083330.0003183745-0.0000306580.0001947197-0.00003847050.0002752117-0.00001412540.0003140784-0.0000520833110.0000083333-0.00005555560.0000166667-0.00005555560.0000104167-0.00005208330.0000125-0.00006250.0000145833-0.00005208330.000025Vector de cargas Q10203040506-156.6418794576708-156.64187945769010-156.6418794576110Vector de desplazamientos10.00979011752-0.133370666730.01631686244-0.133370666750.01677423226-0.12280876170.013053498-0.136653049890.009332747710-0.122808761110.0261069799Clculo de fuerzas internas en los miembrosq=kADmkA1200000-12000001200000-12000001200000-1200000153846.15384615430769.2307692308-153846.153846154-30769.2307692308153846.15384615430769.2307692308-153846.153846154-30769.2307692308153846.153846154-30769.2307692308-153846.15384615430769.2307692308153846.153846154-30769.2307692308-153846.15384615430769.2307692308352941.176470588-211764.705882353-352941.176470588211764.705882353176470.588235294105882.352941176-176470.588235294-105882.352941176176470.588235294-105882.352941176-176470.588235294105882.352941176352941.176470588211764.705882353-352941.176470588-211764.705882353-12000001200000-12000001200000-12000001200000-153846.153846154-30769.2307692308153846.15384615430769.2307692308-153846.153846154-30769.2307692308153846.15384615430769.2307692308-153846.15384615430769.2307692308153846.153846154-30769.2307692308-153846.15384615430769.2307692308153846.153846154-30769.2307692308-352941.176470588211764.705882353352941.176470588-211764.705882353-176470.588235294-105882.352941176176470.588235294105882.352941176-176470.588235294105882.352941176176470.588235294-105882.352941176-352941.176470588-211764.705882353352941.176470588211764.705882353Dm00.00979011750.016316862400.01677423220.013053490.00933274770.01677423220.00979011750.013053490.01631686240-0.1333706667-0.13337066670-0.122808761-0.1366530498-0.122808761-0.122808761-0.1333706667-0.1366530498-0.13337066670.00979011750.01631686240.02610697990.01677423220.013053490.00933274770.02610697990.00979011750.013053490.01631686240.0093327477-0.1333706667-0.13337066670-0.122808761-0.1366530498-0.1228087610-0.1333706667-0.1366530498-0.1333706667-0.122808761q=kADm-1174.8140959318-783.2093972879-1174.81409593181198.08998.4998.41198.08228.3428159588-228.3428159588-228.3428159588228.34281595881174.8140959318783.20939728791174.8140959318-1198.08-998.4-998.4-1198.08-228.3428159588228.3428159588228.3428159588-228.3428159588Disee el miembro No. 5 sabiendo que:Fy=248MpaL=3.824m Carga ltima=-998.4kNAsuma Lx=Ly=LzConsidere estas tres alternativas:Perfil principalConectorDistancia entre conectores1. Un ngulo individual2. Dos ngulos en T (separados 3/8")3. Dos ngulos separados y enfrentados con ancho total de seccin 300 mm

1

8

5

3

2

D1

D2

D3

D4

6

4

7

9

10

11

11

Pu

Pu

Pu

Union atornillada tipo aplastaEvaluacin de las cargasSeparacin entre cerchas=8m=154.194350091Carga muertaDiseo a la tensin por LRFDPeso propio0.4kN/m2Pu=iQi783Losa en concreto t=,12.4kN/m2Pu=Cielo raso en yeso0.4kN/m2Estado lmite de fluencia en la seccin total=156.6418794576Instalaciones0.4kN/m2Total carga muerta por unidad de rea3.6kN/m2Estado lmite de rotura en la seccin netaEstado lmite de rotura por cortante en los tornillosEstado lmite de aplastamiento de los agujeros de los tornillosEstado lmite de desgarramiento en bloqueAncho aferente para carga Pu3.82mPlatinas en acero A-36Fy=248MPabf=166Fu=400MPaTotal carga muerta por unidad de longitud13.77kN/mFu=400MPat=0.9bp=190190.9t=0.75=0.75Total carga muerta puntual 110.14kNAgreq=3509.0mm2tp req=9.234An=2770Tornillos:A325-XCon la NSR-10Con la NSR-10Tornillos:A325-XCon la NSR-10Rn = 0.60FuAnv + UbsFuAnt 0.6FyAgv + UbsFuAntAgreq=5.439in2tp =9.525Dimetro:19.1mmrea tornillo:287mm2Area req:2285mm2Dimetro:19.1mmAgt=952.5mm2Carga viva0.5kN/m2Pn=FuAn=1108kNTipo de cortante:SimpleResist al corte Fnv:457MPaTabla F 2,10,3-2Dimetro tornillo:19.1mmResistencia por tornillo:22.5kipsTabla7-5 AISCAnt=527.7mm2Ancho aferente para carga Pu3.824mUSE 2 PLATINAS 3/8"x 190 x 370Resistencia por tornillo:22.5kipsTabla7-1 AISC=0.75rea tornillo:287mm2Espesor crtico:9.525mm=0.75Agv=5715Total carga viva por unidad de longitud1.912kN/mAg=3620mm2=808kN=831kNResistencia por tornillo:100.12kNPn=FnvAv=130.9kNNmero de torn req:8Resistencia por tornillo int:62.00kips/inRn = 1.2LctFu 2.4dtFu179.7kN