Cálculo Vigas

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Plan1
	1 - Calculo das áreas
	Laje	A1	A2	A3	A4
	1	5.48	4.48	9.49	7.77
	20	5.92	7.7	10.24	7.76
	21	5.67	4.69	9.82	2.71
	22	8.81	7.42	8.81	7.42
	23	4.95	13.05	8.6	7.55
	24	8	4.7	4.65	2.75
	2 - Cálculo dos carregamentos
	Peso da Laje	Espessura t [m]	0.15	Concreto	Aço CA-50
	Gpl [kN/m²] = ϒ [kN/m³] * t [m]	ϒ [kN/m³]	25	Fyd [kN/cm²]
	Gpl [kN/m²]	3.75	Fck [Mpa]	35	43.5
	Fyk [Mpa]
	Cargas na laje	Viga	500
	Revetimento	Gr [kN/m²]	1	b [cm]	15
	Sobrecarga	Gs [kN/m²]	1.5	h [cm]	45
	Alvenaria	Ga [kN/m²]	1.5	Gv = A*ϒ
	Totais	ΣGi [kN/m²]	7.75	Gv [kN/m]	1.6875
	Reação nas vigas [kN/m]
	Ql [kN/m] = A [m²] * ΣGl [kN/m²] / L [m]
	Viga (laje)	V1 (L1)	V1 (L20)	V1 (L21)	V2 (L21 L22)	V2 (L23)	V6 (L24)
	L (m)	5.5	6.4	5.95	5.95	5.2	5.2
	Ql [kN/m]	7.722	7.169	7.385	24.266	7.377	24.740
	Carregamento na viga [kN/m]
	Q [kN/m] = Ql + Gv
	Viga (laje)	V1 (L1)	V1 (L20)	V1 (L21)	V2 (L21 L22)	V2 (L23)	V6 (L24)
	Q [kN/m]	9.409	8.856	9.073	25.953	9.065	26.428
	3 - Momento e cortante
	Viga (V1)	P1	Vão L1	P2 (E)	P2 (D)	Vão L20	P3 (E)	P3 (D)	Vão L21	P4
	V [kN]	26.7	0	28.1	30	0	30.2	29.2	0	28.1
	M [kNm]	22.8	12.9	26.8	31.7	16.3	32.1	29.7	14.7	26.2
	Vd [kN]	37.38	0	39.34	42	0	42.28	40.88	0	39.34
	Md [kNm]	31.92	18.06	37.52	44.38	22.82	44.94	41.58	20.58	36.68
	Viga (V2)	V13	Vão L22	V14 (E)	V14 (D)	Vão L23	P5
	V [kN]	64.5	0	89.9	38.1	0	9
	M [kNm]	0	80.2	75.6	75.6	4.5	0
	Vd [kN]	90.3	0	125.86	53.34	0	12.6
	Md [kNm]	0	112.28	105.84	105.84	6.3	0
	Viga (laje)	V14	Vão L24	V15
	V [kN]	68.7	0	68.7
	M [kNm]	0	89.3	0
	Vd [kN]	96.18	0	96.18
	Md [kNm]	0	125.02	0
	4 - Armadura de Flexão
	ρmin	0.201%	Fcd = Fck / 1,4
	As,min[cm²] = ρmin*b[cm]*h[cm]	Fcd [MPa]	25
	As,min[cm²]	1.357	Fcd [kN/cm²]	2.5
	Área da armadura
	μd = Md [kN.cm] / b [cm] * d² [cm] * fcd [kN/cm²]
	μd = ω * (1 - 0,4*ω/0,68)
	As = b [cm] * d[cm] * Fcd [kN/cm²] * ω / fyd [kN/cm²]
	As,d deve ser maior que As,min, caso contrários As = As,min
	Viga (V1)	P1	Vão L1	P2 (E)	P2 (D)	Vão L20	P3 (E)	P3 (D)	Vão L21	P4
	μd	0.053	0.030	0.063	0.074	0.038	0.075	0.069	0.034	0.061
	ω	0.055	0.031	0.065	0.077	0.039	0.079	0.072	0.035	0.064
	As,d [cm²]	1.896	1.057	2.242	2.672	1.342	2.708	2.496	1.208	2.190
	As [cm²]	1.896	1.357	2.242	2.672	1.357	2.708	2.496	1.357	2.190
	Bitolas
	#	1	1	2	2	1	2	2	1	2
	φ	16	16	16	16	16	16	16	16	16
	As [cm²]	2.011	2.011	4.021	4.021	2.011	4.021	4.021	2.011	4.021
	Viga (V2)	V13	Vão L22	V14 (E)	V14 (D)	Vão L23	P5
	μd	0.000	0.187	0.176	0.176	0.011	0.000
	ω	0.000	0.214	0.200	0.200	0.011	0.000
	As,d [cm²]	0.000	7.383	6.893	6.893	0.364	0.000
	As [cm²]	1.357	7.383	6.893	6.893	1.357	1.357
	Bitolas
	#	2	4	4	4	2	2
	φ	10	16	16	16	10	10
	As [cm²]	1.571	8.042	8.042	8.042	1.571	1.571
	Viga (V6)	V14	Vão L24	V15
	μd	0.000	0.208	0.000
	ω	0.000	0.243	0.000
	As,d [cm²]	0.000	8.384	0.000
	As [cm²]	1.357	8.384	1.357
	Bitolas
	#	2	3	2
	φ	10	20	10
	As [cm²]	1.571	9.425	1.571
	5 - Armadura de cisalhamento
	Asw,min [cm²/m] = 0,06 * fck^(2/3) [Mpa] * b [cm] * s [cm] * sen(α) / fyk [Mpa]
	Asw,min [cm²/m]	1.722
	τc [Mpa] = 0,09 * fck^(2/3) 
	τc [kN/cm²]	0.096
	Resistência do Asw,min
	Asw,min = s*bw*(τwd-τc)/(0,9*fyd)
	τwd [kN/cm²]	0.141
	Vd = τwd*bw*d
	Vd,min [kN]	84.743
	Valores de cortante menores do que Vd,min As = As,min
	Viga (V1)	P1	Vão L1	P2 (E)	P2 (D)	Vão L20	P3 (E)	P3 (D)	Vão L21	P4
	Vd [kN]	37.38	0	39.34	42	0	42.28	40.88	0	39.34
	τwd	0.141	0.141	0.141	0.141	0.141	0.141	0.141	0.141	0.141
	Asw	1.722	1.722	1.722	1.722	1.722	1.722	1.722	1.722	1.722
	φ	5.0	5.0	5.0	5.0	5.0	5.0	5.0	5.0	5.0
	Aest	0.393	0.393	0.393	0.393	0.393	0.393	0.393	0.393	0.393
	e [cm]	22.807	22.807	22.807	22.807	22.807	22.807	22.807	22.807	22.807
	Viga (V2)	V13	Vão L22	V14 (E)	V14 (D)	Vão L23	P5
	Vd [kN]	90.3	0	125.86	53.34	0	12.6
	τwd	0.151	0.141	0.210	0.141	0.141	0.141
	Asw	2.077	1.722	4.347	1.722	1.722	1.722
	φ	5.0	5.0	6.3	5.0	5.0	5.0
	Aest	0.393	0.393	0.623	0.393	0.393	0.393
	e [cm]	18.910	22.807	14.341	22.807	22.807	22.807
	Viga (V6)	V14	Vão L24	V15
	Vd [kN]	96.18	0	96.18
	τwd	0.160	0.141	0.160
	Asw	2.452	1.722	2.452
	φ	5.000	5.000	5.000
	Aest	0.393	0.393	0.393
	e [cm]	16.014	22.807	16.014
Plan2
Plan3