4x4 CON 5 BARRAS418617390-265.535400-265.50173976641739-265.570800-265.50K017394186-265.53478173900-47.2-265.5-265.5-265.5132.75173934780047.2q0347817390p prim-47.2017393478047.203540-265.5007080-265.5000354-265.5000708-265.5047.20.0003036186-0.00006238070.0000647270.0006119299Q =0K-1-0.00006238070.0001613223-0.00006238070.0000731217-47.20.000064727-0.00006238070.00030361860.000611929900.00061192990.00007312170.00061192990.01012691970.01127568083.99159101773.9915910177D =07.98318203547.9831820354-0.011275680839.2168179646-7.9831820354019.608408982366.8084089823q compl-19.6084089823q final-66.8084089823-39.21681796467.98318203540000-3.9915910177-3.9915910177-7.9831820354-7.9831820354

3x3 CON 3 BARRAS33564.296-2564.295-2564.295-2564.29503419.06-4K-2564.29513676.243419.06-2564.306838.124-2564.2953419.0613676.24q03419.066838.12-92.9306838.123419.06-60.93-2564.2956838.120p prim-13.676-2564.33419.06013.676

40.00035778080.00005366710.0000536671Q =74.606K-10.00005366710.0000860442-0.000011448588.930.0000536671-0.00001144850.0000860442

0.0102076291-2.1993645565-6.1993645565D =0.005615970821.776592211125.77659221110.00701245667.1533567507-25.776643249362.37869008411.4486900841q compl12.2273099159q final-1.4486900841-6.97408226136.7019177387

3x3 CON 2 BARRAS2215.5-2215.52215.52215.5-2215.51477-44.992K =-2215.55857.2522222.5642215.5-2215.5295453.8542215.52222.5642520.688-2215.52215.5-2215.59.431q =2215.5-2215.52215.5q prim =9.431-0.0002386036-0.00025521950.00043474950354.481890.56-85.178K-1 =-0.0002552195-0.00001642120.00023879830354.481299.7674.5880.00043474950.0002387983-0.00019595120-141.792-638.06435.9780141.792638.06421.302-0.570.57R =-121.277Q =121.277-63.40963.409-0.0035212256D =0.01300496920.0167834731-11.8245948532-56.8165948532M12.964594853266.8185948532M-0.578.861Cq comp. =0.57q final=10.001C36.3401642899-48.8378357101M26.4244884074101.0124884074M-12.552930539523.4250694605C12.552930539533.8549305395C

2x2 CON 2 BARRASK =48.941195.443-28.28195.795522.198195.4437844.64728.28195.7951044.3970.0226902996-0.000565310420-69.224-276.937K-1 =-0.00056531040.0001415597q prim20q =69.224276.937-1.12802584.7512.20601846.25Q =14.1427.2230-1107.75-12.70512.76901107.75D =0.328068485159.120213408330.8402134083M-0.009793135254.006247982282.2862479822M-19.99813132060.0018686794Cq comp19.9981313206q final39.9981313206C-25.3128062962-26.4408062962M-18.0805759259-5.8745759259M10.848345555518.0713455555C-10.84834555551.9206544445C

NOSE AUN319.7871598.9350639.5742771.4860-75.031K =1598.93510421.244401.868639.5743624.442054.5640401.8681133.97-319.787-1598.934015.1171598.935q =319.7871598.9340q prim =4.8830.0140720678-0.00218899730.000775759501607.989401.868-67.459K-1 =-0.00218899730.0004377995-0.00015515190803.98401.86867.4590.0007757595-0.00015515190.00093684190-568.51-189.427100568.51189.42710-15.11715.117R =23.695Q =-23.6957.071-7.0710.2591103437D =-0.04236765060.008779070948.2988883539-26.7321116461M12.161146527866.7251465278M-15.1170423677-0.0000423677Cq comp. =15.1170423677q final=20.0000423677C-64.5986885326-132.0576885326M-30.534716102836.9242838972M22.423440006132.4234400061C-22.4234400061-12.4234400061C

MATRIZ ENSAM.METODO DE ENSAMBLAJEDATOSEI CUANDO LA SECCION DEL ELEMENTO ES RECTANGULAREI CUANDO LA SECCION DEL ELEMENTO ES TRIANGULARf'c =280Kg/cm2EI =7843.69OKEI =2631.99SECCIONjala para calculosOJO NO BORRARSIRECTANGULARSINONOTRIANGULARNOSIb =0.3mh =0.5m

88.2414871735f

SOLUCION DE PROBLEMA PRIMARIOASENTAMIENTOJIROL =4m8.875 =0.03m88.24188.241L =7.07m =0.002rad4.438

44.12144.121bbCARGA DISTRIBUIDA RECTANGULAR1.8831.883

L =4mCARGA PUNTUAL q =10t-m13.333333333313.33333333330L =4m2.92968751.7578125P =5m2020a =1.5mCARGA DISTRIBUIDA TRIANGULARb =2.5m3.417968751.58203125

L =4mMOMETNOW =20t-m10.66716.000L =4m0.2340.984375M =3ma =1.5m1228b =2.5m1.0551.055

VARIACION DE TEMPERATURA

=1.00E-05C-1T =1000C156.87156.87d =0.5m

g

Ke ELEMENTOMATRIZ DE RIGIDEZ DE LOS ELEMENTOSDATOSEI CUANDO LA SECCION DEL ELEMENTO ES RECTANGULAREI CUANDO LA SECCION DEL ELEMENTO ES TRIANGULARf'c =280Kg/cm2EI =1350.00EA =227404.20EI =568.51EA =113702.10SECCIONOJO NO BORRARnoRECTANGULARSINOSITRIANGULARNOSIb =0.3mh =0.3mA).L =4568.510284.2551350675284.255568.5106751350B).L =428425.524000568.510284.2550284.255568.510C).L =4106.596213.191253.125213.191568.510D).10458.25126412549962749.541833L =422969.36011484.680-22969.36011484.680253.125506.25-253.125506.2511484.6805976.140-11484.6802988.070506.251350-506.25675-22969.360-11484.68022969.360-11484.680-253.125-506.25253.125-506.2511484.6802988.070-11484.6805976.140506.25675-506.2513505019.9602509.980-5019.9602509.9802509.9808366.600-2509.9804183.300-5019.960-2509.9805019.960-2509.9802509.9804183.300-2509.9808366.600

RESOL.PARA 3 GLMATRIZ DE 13x1300000101000110002.5000A transp. =000-1-2-1000-2-1001.87510000000000000002.50-10-1.8751-202916.66666666674375-2916.6666666667437500000000020A =0-1043758750-43754375000000000q emp. =13.33000-2916.6666666667-43752916.6666666667-43750000000002000043754375-43758750000000000-13.3310000001230.468752460.9375-1230.468752460.93750000001-20Ke =00002460.93756562.5-2460.93753281.250000000-100000-1230.46875-2460.93751230.46875-2460.937500000000000002460.93753281.25-2460.93756562.5000000000 000000001000000000000000001200000000000000018000000000000000000F =000000000000000K = Atransp.(Ke)-2916.6666666667-43752916.6666666667-43751230.468752460.9375-1230.468752460.937510001200000-4375-43754375-8750-4921.875-11484.3754921.875-8203.1250-2400-1800000000000000000K = Atransp.(Ke)(A)6347.1354166667-2946.8750ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!K =-2946.87536678.1250K -1 =ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!000ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!Atransp.(qemp.)D = (K-1)Q22.5-51.455ERROR:#NUM!0D =ERROR:#NUM!ERROR:#NUM!Q = F - Atransp.(qemp.)-22.5d =ADq compl. = Ke(d)q final = q comp. q empQ =51.455ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!0ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!d =ERROR:#NUM!q comp. =ERROR:#NUM!q final =ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!ERROR:#NUM!

MATRIZ DE 14x14-111-10-100000-100011114001A transp. =10101100000011014-110-110-10-100000010014000-4010193.7874564.8903193.787564.892300000000000062.464A =0102564.29440079066838.1184021081-2564.29440079063419.0592010541000000000000q emp. =92.929000-1282.1472003953-2564.29440079061282.1472003953-2564.2944007906000000000000-14.464002564.29440079063419.0592010541-2564.29440079066838.118402108100000000000060.929-10000001282.14720039532564.2944007906-1282.14720039532564.29440079060000000000-10Ke =00002564.29440079066838.1184021081-2564.29440079063419.05920105410000000013.6760000000-1282.1472003953-2564.29440079061282.1472003953-2564.294400790600000000000000002564.29440079063419.0592010541-2564.29440079066838.118402108100000000-13.676111 000000001282.14720039532564.2944007906-1282.14720039532564.294400790600000110000000002564.29440079066838.1184021081-2564.29440079063419.05920105410000010000000000-1282.1472003953-2564.29440079061282.1472003953-2564.29440079060000111000000002564.29440079063419.0592010541-2564.29440079066838.1184021081000000000000000001000000F =00000000000000120000000000000000000180000000000000000002000K = Atransp.(Ke)1088.35980039531999.4041007906-1475.93420039531999.40210079060000-1282.1472003953-2564.29440079061282.1472003953-2564.294400790610001200-1088.3598003953-1999.40410079061475.9342003953-1999.40210079063846.44160118589402.4128028987-3846.44160118585983.3536018446000010001200-193.78742854.1689010541-193.787-3983.9515010541-2564.2944007906-6838.11840210812564.2944007906-3419.0592010541000010000K = Atransp.(Ke)(A)ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!K =ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!K -1 =ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!Atransp.(qemp.)D = (K-1)Q-8163.393ERROR:#VALUE!-88.929D =ERROR:#VALUE!ERROR:#VALUE!Q = F - Atransp.(qemp.)8d =ADq compl. = Ke(d)q final = q comp. q empQ =-163.393ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!88.929ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!d =ERROR:#VALUE!q comp. =ERROR:#VALUE!q final =ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!ERROR:#VALUE!

Hoja116.087-0.01111660186.672-0.0101801603q empo29.1240.009243718929.850.0046218594-2.630107.080-4.470-107.0360.03554590310d-0.0111166018-104.340.02036032070-0.0309240436104.340-1-0.5000000-11000-111000AT1010.50000100.5001-1-100-0.01111660180000000100-100000000.011116601800.011116601800-110652.1118-1304.2238-652.1118-1304.22380000000000000-0.500-1304.22383477.931304.22381738.9650000000000000010-652.11181304.2238652.1118-1304.2238000000000000000.50-1304.22381738.9651304.22383477.9300000000000000000000652.1118-1304.2238-652.1118-1304.2238000000000000Ke0000-1304.22383477.931304.22381738.9650000000000000000-652.11181304.2238652.1118-1304.22380000000000010000-1304.22381738.9651304.22383477.93000000000A-110000000001545.7667-2318.62-1545.7667-2318.620000010000000000-2318.624637.242318.622318.620000000.5-100000000-1545.76672318.621545.76672318.620000000000000000-2318.622318.622318.624637.240000000000000000000010000000-110000000000000012000001-10000000000000001500001-100000000000000002000000000000000000000001800-123.763-123.763-123.76315737.6172-6414.8227-3864.386760.13660.13660.136k-6414.82274651.700375772.88335Q=-ATXqem-107.036-107.036-107.036-3864.3867772.883355023.6967123.763123.763123.763-60.136-60.136-60.1360.00018898210.00024266090.0001080383107.036107.036107.036k.10.00024266090.00053220120.00010478460.00010803830.00010478460.00026604220.02036032070.02036032070.0203603207D0.00924371890.00924371890.00924371890.03554590310.03554590310.0355459031ERROR:#VALUE!-6.0279370437-6.0390536455ERROR:#VALUE!-0.8142184424-0.8243986027ERROR:#VALUE!-6.0279411158-6.0186973969ERROR:#VALUE!24.925975873124.9305977326ERROR:#VALUE!-46.3598127876-46.3598127876ERROR:#VALUE!61.81308134761.813081347ERROR:#VALUE!-46.3598127876-46.3598127876ERROR:#VALUE!123.626162694123.6617085971ERROR:#VALUE!-16.590162694-16.6012792958ERROR:#VALUE!48.48976261148.5101229317ERROR:#VALUE!16.59016269416.5592386504ERROR:#VALUE!1.28191589841.2819158984ERROR:#VALUE!00ERROR:#VALUE!-13.3399221523-13.3510387541ERROR:#VALUE!16.674902690416.6860192922ERROR:#VALUE!22.233203587222.244320189ERROR:#VALUE!00

Hoja2000000-110A11100-11-100000-11-1111-1-10At0011-101000-10-1111001000101000000000001000022969.36011484.680-22969.36011484.68000000000000000011484.6805976.140-11484.6802988.070000000000000000Ke-22969.360-11484.68022969.360-11484.680000000000000-1-1011484.6802988.070-11484.6805976.14000000000000010000005019.9602509.980-5019.9602509.98000000000-1-1000002509.9808366.600-2509.9804183.300000000001100000-5019.960-2509.9805019.960-2509.9800000000011000002509.9804183.300-2509.9808366.60000000000110000000007843.6883921.844-7843.6883921.8440000000000003921.8441350.000-3921.844675.000000000000000-7843.688-3921.8447843.688-3921.84400000-92.436459129115.061-77.3754591291000000003921.844675.000-3921.8441350.00000000-40.4338155923294.366253.932184407700000000000010000000.002974256592.436459129115.061107.49745912910000000000000150000-0.0021001623-46.7092475064-276.438-323.147247506400000000000000180000.0133647275121.44410551739.21160.65410551700000000000000020000.0112645652140.8312475064370.56511.3912475064-0.0051952355-121.444105517-39.21-160.654105517093.7081917724371.26464.96819177240-136.8682172432-78.43-215.2982172432K80272.19511112.2312514950.840.0000201355-0.0000136963-0.00003104320-57.9287801673449.7391.771219832711112.2312540199.6675-10528.5K-1-0.00001369630.0000401130.00004372260.0133647275136.868217243278.43215.298217243214950.84-10528.514342.74-0.00003104320.00004372260.0001341762-0.008169492-63.4431872588-135.96-199.40318725880.013364727513.3647275152013.3647275152-0.0133647275-20.04709127270-20.0470912727Q-545.099-545.099-545.099-0.0133647275-24.05650952730-24.0565095273-418.227-418.227-418.227-0.0133647275-26.72945503030-26.729455030394.12294.12294.122D-0.008169492-0.008169492-0.008169492-0.0051952355-0.0051952355-0.00519523550.01126456520.01126456520.0112645652

Hoja3-189.53qemp-189.537843.6315.165-15.165-10-1010-1001-6.6701-1101111-1-6.6710-1000A-10266.34-1883.04-266.34-1883.0401-1883.04-4437.71883.042218.85-1-1-266.34-1883.04266.34-1883.0401-1883.042218.851883.04-4437.7101470.68-2941.36-1470.6801-2941.36-7843.633921.815-11-1470.68-2941.361470.6801011-1Q157.695157.695-226.53-226.53

analis r0b3thENSAMBLAJE: ROMERO MEJIA ROBERTHcalculo de Ke elementos CALCULO DE MATRICES: PARA 3 GL Y DOS BARRAS 2 RESORTES: DATOSEI CUANDO LA SECCION DEL ELEMENTO ES RECTANGULARSECCION DE LA VIGA O PORTICO:f'c =210Kg/cm2EI =1350.00EA =437639.5826.064* F ( FUERZA QUE HAY EN DONDE SE ELIGIO LA CORDENDA EN GL* CALCULO DE: Q= {F}-Atransp*{qemp}SECCION0.5E=15,000fc=217370.65119284212.36noRECTANGULARI= 1/12(b*h^3)=0.00416666675.456EI=9057.1104663684-9.64F =40Atransp*{qenp}=-12.36b =0.4m{qemp} =13.14800.32h =0.5m9.320-11.8520.411.852-8.24A).0Q=52.36L =40-0.3211.852

0001350.000675.000-100675.0001350.0000000-1000000000-10A transp=000-10-1000-1A =000000000-10000-1000-1000129.6324-129.6324000000B).0003241080-324540000000L =40-10-129.6-324129.6-324000000324540-3241080000000337.50000Ke =0000129.6324-129.63240001350.000675.00000003241080-324540000675.0001350.0000000-129.6-324129.6-324000000324540-32410800000000000100000000000002000C).L =4-324-1080324-540000000253.125506.250K=Atran*Ke -324-540324-1080-324-1080324-5400-2000506.2501350.0000000129.6324-129.632400* CALCULO DE: K= Atransp*Ke*A

D).108054000.0010070948-0.0001623377-0.0004058442L =5k =5404160-324[k]^-1 =-0.00016233770.00032467530.00081168830-324129.6-0.00040584420.00081168830.0097452702129.600324.000-129.600324.000324.0001080.000-324.000540.000-129.600-324.000129.600-324.000324.000540.000-324.0001080.000* CALCULO DE: D= [k]^-1*{Q}0.0479733646D =0.00101623380.0939912017

* CALCULO DE: d= {A}*{D}* CALCULO DE: qe= {Ke}*{d}CALCULO DE MATRICES: PARA 2 GL Y DOS BARRAS 3 RESORTES: 0-15.8726298701-0.0479733646-52.362.5015.87262987011.875-0.0010162338-27.00314935062.5* F ( FUERZA QUE HAY EN DONDE SE ELIGIO LA CORDENDA EN GL* CALCULO DE: Q= {F}-Atransp*{qemp}d=0qe=11.852-1.875-0.001016233829.3556168831{qemp} =20-0.0939912017-11.85213.33F =0Atransp*{qenp}=22.5029.9043831169200-51.45500-13.33-0.0010162338-2.03246753250Q=-22.5051.4550* CALCULO DE Q FINAL : qf = {qemp}*{qe}26.064-15.872629870110.191370129912.36-52.36-4000A transp=001010001105.45615.872629870121.328629870100000-1-2-1000-2-1-9.64-27.0031493506-36.643149350610qf =13.148+11.852=250-1b-1b-2Resortes 9.3229.355616883138.67561688311-22916.66666666674375-2916.66666666674375000000011.852-11.8520A=0-143758750-437543750000000-8.2429.904383116921.664383116900-2916.6666666667-43752916.6666666667-437500000000000043754375-4375875000000000-2.0324675325-2.03246753251000001230.468752460.9375-1230.468752460.93750001-2Ke =00002460.93756562.5-2460.93753281.250000-10000-1230.46875-2460.93751230.46875-2460.937500000002460.93753281.25-2460.93756562.5000000000001000000000000001200000000000001800K=Atran*Ke -2916.6666666667-43752916.6666666667-43751230.468752460.9375-1230.468752460.9375100012000-4375-43754375-8750-4921.875-11484.3754921.875-8203.1250-2400-1800* CALCULO DE: K= Atransp*Ke*A

k =6347.1354166667-2946.875[k]^-1 =0.00016365620.0000131488-2946.87536678.1250.00001314880.0000283206

* CALCULO DE: D= [k]^-1*{Q}D =-0.00300569120.0011613899

* CALCULO DE: d= {A}*{D}* CALCULO DE: qe= {Ke}*{d}

03.685518588408.0688182755-0.0030056912-3.6855185884-0.00116138992.9877374895d=-0.005328471qe=-9.4146249953-0.0011613899-20.734655285309.41462499530-16.9238446958-0.0030056912-3.0056912141-0.005328471-6.3941652023-0.0011613899-2.0905018091

* CALCULO DE Q FINAL : qf = {qemp}*{qe}

2.53.68551858846.1855185884V1.8758.06881827559.9438182755M2.5-3.6855185884-1.1855185884V-1.8752.98773748951.1127374895M20-9.414624995310.5853750047Vqf =13.33+-20.7346552853=-7.4046552853M209.414624995329.4146249953V-13.33-16.9238446958-30.2538446958M0-3.0056912141-3.0056912141V0-6.3941652023-6.3941652023M0-2.0905018091-2.0905018091V

* CALCULO DE D.F.C Y D.M.F+D.F.C--D.M.F+