Cercha Con Diseño a Compresión
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DESCRIPTION
Diseño de elementos metálicos a compresión, ejemplo particular con una cercha.
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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