Examen Ae I III Unidad

 

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3  EÁMEN DE UNIDAD DE ANALISIS ESTRUCTURAL I DESARROLLADO ALUMNO: EST ESTEEBAN K KOR ORA AFI APONTE

CÓDI ÓDIGO: 0200 200913 91304 048 8

PROB. 1 18 Tn

6EI

1.- RIGIDECES Y COEFICIENTES DE DISTRIBUCIÓN

2EI

EI

4m

6m

3m

2.- MOMENTOS DE EMPOTRAMIENTO PERFECTO M23 = M32 =

Pab /L

2

2

2

2

Pa b/L

=

-24 Tn

=

12

Tn

3.- PRIMER CROSS (SIN DESPLAZAMINETO) 0.429 0.57 -24 10.3 1 13 3.7 -6.9 2.9 3.9 -0.7 0.3 0.4 -0.1 0.0 0.0 13.6 --1 13.6

0.727 0.27 12 6.9 -13.7 -5.1 2.0 -1.4 -0.5 0.2 -0.1 -0.1 0.0 0.0 0.0 5.7 -5.7

5.1 1.5 0.2 0.0 6.8

-2.6 -0.3 0.0 0.0 -2.9

k12

= 2EI/4   ≈

k23

= 6EI/9   ≈ 0.67

k34

=

0.5

EI/4   ≈ 0.25

C21 =

k12/(k12+k23)

=

0.429

C23 =

k23/(k12+k23)

=

0.571

C32 =

k23/(k23+k34)

=

0.727

C34 =

k34/(k23+k34)

=

0.273

 

13.6

5.7

γ

δ

12.9

12.9

5.1

13.6

5.1 5.7

γ

δ

ΣM1=0 13.6+6.8-4γ=0 γ=5.1 ΣM2=0 -5.7-2.9-4δ=0 δ=2.2

  6.8

2.9

A NIVEL DE 2-3 H 5.1 H

2.2

= 2.9

4.- MOMENTOS POR DESPLAZAMIENTOS Δ 

Δ 

M12 = 6EIΔ/42 ≈ 375 M21 = 6EIΔ/42 ≈ 375

4m

3m

6m

M23 =

0   ≈

0

M32 =

0   ≈

0

2

M34 = 6EIΔ/4 ≈ 375 M43 = 6EIΔ/42 ≈ 375

 

5.- SEGUNDO CROSS (POR DESPLAZAMINETO) 0.429 0.57 375 0 -161 --2 214 -97 42 56 -10 4 6 -1 0 261

0.727 0.27 0 375 -107 -195 --7 73 28 -20 --8 8 3 -2 -1

1 -261

0 0 -293

375 188 -80 21 2 0 505

0 293

375 188 -37 -4 0 0 522

261

293

γ

δ

62 261

62

62

62 293

θ

ρ

ΣM1=0

261+505-4 θ=0 θ=191.5 ΣM2=0

293+522-4 ρ=0 ρ=203.75

505

522

A NIVEL DE 2-3 H' 192 H' x

203.8

= 395 = 2.9/395 = 0.00733713

M12 = 6.8+(505x0.007)

= 10.489 Tn

M21 = 13.6+(261x0.007)

= 15.475 Tn

M23 = -13.6+(-261x0.007)

= -15.475 Tn

M32 = 5.7+(-293x0.007)

=

M34 = -5.7+(293x0.007) M43 = -2.9+(522x0.007)

= -3.585 Tn =

3.585 Tn 0.959 Tn

 

PROB. 2 3

3

4

2 1

2

5

L

1

L/2

L

Q 1=1 L

L/3

2/3

2/3 2/3

1

2/3

L/3

0 -L L -L/3 L/3 0

L

1 2/3

2/3

Q 1=1 2/3 2/3L

2/3L 2/3L

2/3L

1/3

0 0 0 2/3 1/3 0

2/3L

2/3L

Q 1=1 1/3

2/3 1/3

1/3

0 0 0 0 0 0

1/3

2/3

6

 

Entonces la matriz B quedaría expresada

=

B

0 -L L -L/3 L/3 0

0 0 0 2/3 1/3 0

0 0 0 0 0 0

PROB. 3 3 2

1 E, A, I L

D1=1 , D2=0 , D3=0 1

k11 EA/L 0 0

L k11=EA/L , K21=0 , K31=0 D1=0 , D2=1 , D3=0 k22

k32 1

0 4EI/L 2EI/L

L k12=0 , K22=4EI/L , K32=2EI/L D1=0 , D2=0 , D3=1 k23

k33 1

0 2EI/L 4EI/L

L k13=0 , K23=2EI/L , K33=4EI/L

k

=

EA/L 0 0 0 4EI/L 2E 2 EI/L 0 2EI/L AEI/L

=

E/L

A 0 0

0 4I 2I

0 2I 4I