Ejemplos SUMATORIA DE FUERZAS

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F(x) 2x^2

Luz = 2 m

b=35cm

h=50 cm

E = 22440000 kN/m2

EI = 22440000*0.35*0.5^3/12 = 163625/2

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A = 2 x^3 /3 = 2*2^3/3 = (2)*(8)/3 = 16/3

Centroide = (2*2^4/4) / (16/3) = 24/16 = 1.5 = 3/2

SUMATORIA DE MOMENTO EN EN PUNTO 1 = 0

R2*2 – 16/3 * (3/2) = 0

R2 =  4 kN

SUMATORIA DE FUERZAS EN Y = 0

R1 -  16/3  + 4 = 0

R1 = 4/3 = 1.333 kN

TRAMO

q = -2x^2

V = -2x^3/3+4/3

M = -2x^4/12+4x/3

EIθ = -2x^5/60+4x^2/6 + EIθ1 

EIy = -2x^6/360+4x^3/18 + EIθ1 x

PARA x = 0

V1 = 4/3 = 1.333 kN

M1 = 0 kN*m

EIθ1 = EIθ1 kN*m^2*rad

EIy1 = 0 kN*m^3

PARA x= 2m

V2 = -2(2)^3/3+4/3 = -4 kN

M2 = -2(2)^4/12+4(2)/3 = 0 kN*m

EIθ2 = -2(2)^5/60+4(2)^2/6 + EIθ1 = 8/5 + EIθ1 = 8/9 = 0.889

0 = -2(2)^6/360+4(2)^3/18 + EIθ1(2) => EIθ1 = -32/45 = -0.7111

CONCAVIDAD DE LA FUNCION CORTANTE

V = -2x^3/3+4/3

V´ = -2x^2

V”= -4x

0 < x < 2

V” = NEGATIVO (cóncavo hacia abajo)

V = 0 = -2x^3/3+4/3 ; x=1.26m

Mmax = M(1.26) = -2(1.26)^4/12+4(1.26)/3 = 1.26 kN*m

EIθ = -2x^5/60+4x^2/6 - 32/45 = 0 => x= 1.007 m

EIymax = EIY(1.007)  = -2(1.007)^6/360+4(1.007)^3/18 - 32(1.007)/45 = -0.495  

Y max = (-0.495)/( 163625/2) = -6.049*10^-6 m

Ymax(viga) = 6.049*10^-6 m

Y max(norma) = L/100 = 2/100 = 0.02m

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