Método de La Pendiente
2
Método de la Pendiente – Deflexión: Marcos EI= Constante. ø B , ø C ,ø E ,ø F ,ø H ;Δ B =Δ E =Δ 1 ;Δ C = Δ F = Δ H =Δ 2 → 7GL. M BA + M BC + M BE =0 M CB + M CF =0 M ED + M EB + M EF =0 M FC + M FE + M FH =0 M HF + M HG =0 Columna empotrada R= Δ 1 4 M AB = 2 EI 4 (2 ø A + ø B - 3R) ± M AB → M AB = 0.5 Columna empotrada R= Δ 2 − Δ 1 3 M AB = 2 EI 3 (2 ø B + ø C - 3R) ± M BC → Viga R=0 M BE = 2 EI 5 (2 ø B + ø E - 3R) −62.5 → M BE =0.80 Viga R=0 M CF = 2 EI 5 (2 ø C + ø F - 3R) −31.25 → Columna empotrada R= Δ 1 4 M DE = 2 EI 4 (2 ø D + ø E - 3R) ± M DE → M DE = 0.5 Columna empotrada R= Δ 2 − Δ 1 3 M EF = 2 EI 3 (2 ø E + ø F - 3R) ± M EF → Viga R=0 M FH = 2 EI 5 (2 ø F + ø H - 3R) −41.67 → M FH =0.80 Columna empotrada R= Δ 2 7 M GH = 2 EI 7 (2 ø G + ø H - 3R) ± M AB → M GH = ø Δ
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Transcript of Método de La Pendiente
Método de la Pendiente – Deflexión: Marcos
EI= Constante.
øB , øC , ø E , øF , øH ; ΔB=ΔE=Δ1; ΔC=ΔF=ΔH=Δ2 → 7GL.
MBA+MBC+MBE=0
MCB+MCF=0
MED+MEB+MEF=0
MFC+MFE+MFH =0
MHF+MHG=0
(MCB+M BC)LBC
+
(M EF+MFE)LEF
+
Columna empotrada R=Δ14
M AB=2EI4
(2ø A+øB- 3R)± M AB → M AB= 0.5
øB - 0.375Δ1
Columna empotrada R=Δ2−Δ13
M AB=2EI3
(2øB+øC - 3R)± MBC →
MBC= 1.33øB+0.66øc-0.66Δ2+ 0.66Δ1
Viga R=0 MBE=2EI5
(2øB+ø E- 3R)−62.5 → MBE=0.80
øB+0.40ø E – 62.5
Viga R=0 MCF=2EI5
(2øC+ø F- 3R)−31.25 → MCF=0.80
øC+0.40ø F – 31.25
Columna empotrada R=Δ14
MDE=2EI4
(2øD+ø E- 3R)± MDE → MDE= 0.5
ø E- 0.375Δ1
Columna empotrada R=Δ2−Δ13
MEF=2EI3
(2ø E+ø F- 3R)± MEF →
MEF= 1.33ø E+0.66ø F-0.66Δ2+ 0.66Δ1
Viga R=0 MFH =2EI5
(2ø F+øH- 3R)−41.67 → MFH =0.80ø F+0.40
øH – 41.67
Columna empotrada R=Δ27
MGH=2EI7
(2øG+øH- 3R)± M AB → MGH=
0.286øH- 0.123Δ2
(M HG+MGH)LHG
=0
(MBA+MAB)LAB
+
(M ED+MD E)LED
+
(MG H+MH G)LGH
=0
M AB MBA MBC MCB MBE MEB MCF MFC MDE MED
øB=
21.88639
øC=
8.08079
ø E=
-25.65519
ø F=
15.39190
øH=
-35.29190
Δ1=
-14.91401
Δ2=
-4.82706
3.133
øB0.667
øC0.400
ø E0.292 Δ1
-0.667
Δ2-62.50 =0
0.667
øB2.133
øC0.400
ø F0.667
Δ1-0.667
Δ2-31.25 =0
0.400
øB3.133
ø E0.667
ø F0.292 Δ1
-0.667
Δ262.50 =0
0.400
øC0.667
ø E2.933
ø F0.400
øH0.667
Δ1-0.667
Δ2-10.42 =0
0.400
ø F1.372
øH-0.123
Δ241.67 =0
0.667
øB0.667
øC0.667
ø E0.667
ø F0.123
øH0.888
Δ1-0.923
Δ2=0
0.375
øB0.375
ø E0.123
øH-0.375
Δ1-0.035
Δ2=0
