Diseño De Una Columna Por La Norma Española

1 .- MATERIALES fck := 25MPa fyk := 400MPa γc := 1.5 γs := 1.15 b := 30cm fck fcd := γc fyk fyd := γs fcd = 16.667⋅ MPa fyd = 347.826 ⋅ MPa d 1 := 4cm ε y := fyd Es ⋅ 1000Es := 200000MPa ε y = 1.739

Geometria

h := 30cm

Recubrimiento

d 2 := d 1 N'd := NdG

Altura util d := h − d 1 = 26⋅ cm

2 .- SOLICITACIONES

M dG := 101kN⋅ mNdG := 353kN

h  M'd := M dG − NdG⋅  − d 1  2





M'd = 62.17⋅ kN⋅ m N'd 0.85⋅ fcd⋅ b ⋅ h = 0.867

3 .- DIMENSIONAMIENTO

μ' :=

M'd 0.85⋅ fcd⋅ b ⋅ h2

μ' = 0.163

ν' :=

ν' = 0.277

d1 δ1 := = 0.133 h −17 μmin := ⋅ 0.416 − δ2 21

d2 δ2 := = 0.133 h

δ :=

d h

(

)

μmin = −0.229 μmax = −0.367 4 4⋅ξ
2

μmin > μ' μmax < μ'

cuantia minima armadura doble 1 − 8 49 ψ ⋅ξ
2

μmax := δ2 − 0.5

Imponiendo " α "

α := 0.721

ξ :=

7⋅ α − 3
−3

= 1.954 ψ := 1 −2 ⋅ α − δ2 α− 3 7

21

= 0.273

δG :=

2

= −0.453

ω2 := ν' +

μ' − ψ⋅ δ − δG δ − δ2

(

)

= 7.948 × 10 ε s2 :=
−3

(

) = 4.019

ε s1 :=

2 ⋅( α − δ) α− 3 7
2

= −0.996

ω1 := ν' − ψ − ω2 = −3.767 × 10 kN σs1 = −19.925⋅ 2 cm σs2 = 34.783⋅ kN cm fydc := 400MPa
2

ω1 As1 := ⋅ 0.85⋅ fcd⋅ b ⋅ h σs1 ω2 As2 :=⋅ 0.85fcd⋅ b ⋅ h σs2 Asmin := 0.05⋅ N'd fydc 0.5⋅ fcd⋅ b ⋅ h fydc

As1 = 0.241⋅ cm As2 = 0.291⋅ cm

2

ASUMIDO POR CUANTIA MINIMA
2

Cuantia Minima

Asmin = 0.44⋅ cm2ϕ10mm

Cuantia Maxima ϕmax := 10mm ϕmin := 10mm 1 ϕt := ⋅ ϕmax = 2.5⋅ mm Minimo 4

Asmax := ϕ6mm

Asmax = 18.75⋅ cm

2

St := 15⋅ ϕmin = 15⋅ cm 4ϕ10mm CADA15cm

pero no mayor a 30cm

σs1 :=

 ε s1   Es⋅  if ε s1 < εy  1000 
fyd otherwise

σs2 :=

 ε s2   Es⋅  if ε s2 < εy  1000 
fyd otherwise