Hoja1EJEMPLO DE ESCALERAt=0.15mtEJEMPLO DE ESCALERAt=0.15mt0.3p=0.3mt0.3p=0.3mtcp=0.17mtcp=0.17mtfc=210kg/cm2fc=210kg/cm2fy=4200kg/cm2fy=4200kg/cm20.150.152.80.20.12.80.20.12.71.22.71.2tg =0.17 / 0.3tg =0.17 / 0.3tg =0.5666666667tg =0.5666666667 =29.5388 =29.53880.170.17t1 =t / cos t =0.15t1 =t / cos t =0.150.3t1 =0.1724094267mtcos =0.87002203320.3t1 =0.1724094267mtcos =0.8700220332h = t1 + cp/2h = t1 + cp/2h =0.2574094267mth =0.2574094267mtLAS CARGAS EN LA RAMPA SON:LAS CARGAS EN LA RAMPA SON:C.M. =pe=2.4t/mt3C.M. =pe=2.4t/mt3a.esc. =1.2mta.esc. =1.2mth =0.2574094267mth =0.2574094267mtACAB. =0.1t/mt2ACAB. =0.1t/mt2S/C =0.5t/mt2S/C =0.5t/mt2P.P. =pe*a.esc.*hP.P. =pe*a.esc.*hP.P. =0.741339149t/mtP.P. =0.741339149t/mtP.A. =ACAB.*a. esc.P.A. =ACAB.*a. esc.P.A. =0.12t/mtP.A. =0.12t/mtCM =0.861339149t/mtCM =0.861339149t/mtC.V. =C.V. =C.V. =S/C*a. esc.C.V. =S/C*a. esc.C.V. =0.6t/mtC.V. =0.6t/mtWU.=1.5CM+1.8CVWU.=1.5CM+1.8CVWU.=2.3720087235t/mtWU.=2.3720087235t/mtLAS CARGAS EN EL DESCANSO SON:anch. desca. =1.2mtLAS CARGAS EN EL DESCANSO SON:anch. desca. =1.2mtp.e. =2.4t/mt3p.e. =2.4t/mt3ACAB. =0.1t/mt2ACAB. =0.1t/mt2P.P. =(0.2+0.1)/2*a. desc.*p.e.S/C =0.5t/mt2P.P. =(0.2+0.1)/2*a. desc.*p.e.S/C =0.5t/mt2P.P. =0.432t/mtP.P. =0.432t/mtP.A. =ACAB.*anch. desc.P.A. =ACAB.*anch. desc.P.A. =0.12t/mtP.A. =0.12t/mtCM =0.552t/mtCM =0.552t/mtC.V. =C.V. =C.V. =S/C*anch. desc.C.V. =S/C*anch. desc.C.V. =0.6t/mtC.V. =0.6t/mtWU. =1.5CM+1.8CVWU. =1.5CM+1.8CVWU. =1.908t/mtWU. =1.908t/mtsin sobre cargasin sobre carga2.3720087235t/mtCM =0.8282.3720087235t/mtCM =0.8280.828t/mt0.828t/mt2.71.22.71.2ABCABCRA=2.98tnRB=4.42tnRA=2.98tnRB=4.42tn0.60.61.861.86MB(+) max.=0.6t-mtMB(+) max.=0.6t-mtMA(+)=1.86t-mtMA(+)=1.86t-mtCONSIDERANDO SOBRE CARGA TAMBIEN EN EL DESCANSOCONSIDERANDO SOBRE CARGA TAMBIEN EN EL DESCANSO2.3720087235t/mt2.3720087235t/mt1.908t/mt1.908t/mt2.71.22.71.2ABCABCRA=2.7tnRB=6.01tnRA=2.7tnRB=6.01tn1.381.381.481.48MB(-)max. =1.38t-mtMB(-)max. =1.38t-mtALTURA UTIL PARA EL MEYOR MOMENTO :ALTURA UTIL PARA EL MEYOR MOMENTO :M max.=1.86t-mtM max.=1.86t-mtM max.h=0.2574094267mtM max.h=0.2574094267mtd =h*a. esc.a. esc.=1.2mtd =h*a. esc.a. esc.=1.2mtd=2.4538817199d=2.4538817199como :h =0.15mtcomo :h =0.15mtd = h -0.03d = h -0.03d =0.12mtd =0.12mtAs min =0.0018*12*100=2.16cm2As min =0.0018*12*100=2.16cm2calculando As(+)M =1.86tn-mtAs =4.28cm2por metrocalculando As(+)M =1.86tn-mtAs =4.28cm2por metrocalculando As(-)M=1.38tn-mtAs =3.14cm2por metrocalculando As(-)M=1.38tn-mtAs =3.14cm2por metroARMADURA TRANSVERSAL EN EL DESCANSOARMADURA TRANSVERSAL EN EL DESCANSOM (-) = RB*b*(b+m) / 2RB=6.01tnM (-) = RB*b*(b+m) / 2RB=6.01tnb=1.2mtb=1.2mtm=0.1mtm=0.1mtM (-) =4.6878d=12As (-)=11.4M (-) =4.6878d=12As (-)=11.4tg =1.4=0.5185185185tg =1.4=0.51851851852.72.7f1*t*cos =RB1-3*(b+m)=11.5907142857*-2.25=-26.0791071429f1*t*cos =RB1-3*(b+m)=11.5907142857*-2.25=-26.0791071429tgbtgbf2*t*cos =RB1+3*(b+m)=11.5907142857*4.25=49.2605357143f2*t*cos =RB1+3*(b+m)=11.5907142857*4.25=49.2605357143tgbtgbf3*t*cos = -RB1+3*(b+m)=-11.5907142857*4.25=-49.2605357143f3*t*cos = -RB1+3*(b+m)=-11.5907142857*4.25=-49.2605357143tgbtgbf4*t*cos = -RB1-3*(b+m)=-11.5907142857*-2.25=26.0791071429f4*t*cos = -RB1-3*(b+m)=-11.5907142857*-2.25=26.0791071429tgbtgbf1*t*cosf1*t*cosa1a1bba2a2f2*t*cosf2*t*cos =b*(f1/f1+f2) =b*(f1/f1+f2) =1.35mt =1.35mtcalculando las fuerzas tenemoscalculando las fuerzas tenemosF1 =1/2 *f1*1*cos*=-17.6033973214tnF1 =1/2 *f1*1*cos*=-17.6033973214tnF2 =1/2 *f2*1*cos*=33.2508616071tnF2 =1/2 *f2*1*cos*=33.2508616071tnF3=-33.2508616071tnF3=-33.2508616071tnF4=17.6033973214tnF4=17.6033973214tncalculando momentos tenemoscalculando momentos tenemosM = F2 a2 - F1 a1M = F2 a2 - F1 a1M = F4 a4 - F3 a3M = F4 a4 - F3 a3donde :donde :a1 =0.75=a3a1 =0.75=a3a2 =-0.05=a4a2 =-0.05=a4M =11.5400049107tn-mtM =11.5400049107tn-mt-26.0791071429tn-26.0791071429tn49.2605357143tn49.2605357143tn-49.2605357143tn-49.2605357143tn26.0791071429tn26.0791071429tnchequeando si el concreto toma este momento:chequeando si el concreto toma este momento:f =Mu*c28.9827534924por lo tanto el esfuerzo no lo toma el concretopor lo tanto el esfuerzo no lo toma el concretocon un :M =11.5400049107tn-mtcon un :M =11.5400049107tn-mtd =1.2-0.05=1.15mtd =1.2-0.05=1.15mtAs =2.65cm2As =2.65cm2Flexo traccion para la rampa superiorFlexo traccion para la rampa superiorM =F(b+m)M =F(b+m)22F =RB*b=6.01*1.2=7212F =RB*b=6.01*1.2=7212sen 1.40.4375sen 1.40.43753.23.2F =16484.5714285714kgF =16484.5714285714kgM =16485 (1.2+0.1)=10715.25kg-mtM =16485 (1.2+0.1)=10715.25kg-mt22M =10715.25kg-mtM =10715.25kg-mtFlexo traccion para la rampa inferiorFlexo traccion para la rampa inferiorF =RA*b=2.98*1.2=3576F =RA*b=2.98*1.2=3576sen 1.40.4375sen 1.40.43753.23.2F =8173.7142857143kgF =8173.7142857143kgM =F(b+m)=8173.7*(1.2+0.1)M =F(b+m)=8173.7*(1.2+0.1)2222M =5312.9142857143kg-mtM =5312.9142857143kg-mt1)Para flexo compresion1)Para flexo compresionusar :M =10715.25kg-mtusar :M =10715.25kg-mtf =(+/-)6M+Ff =(+/-)6M+Ft*b^2t*bt*b^2t*bf =38.9226785714