« Exercise 3 Seismic accelerations and loadings »

 

Exercise 4


Figure 5.4.7.4a
Figure 5.4.7.4a

In the storey of exercise 5.4.7-1 calculate the results for the following cases:

(a) replacement of columns C5, C12, C14 with walls of cross-section 2000/300 parallel to the respective sides of the perimeter.

Using the same file (sheet B_547-4a) and modifying the geometric data of the C5, C12, C14 from 500/500 to 2000/300 the results obtained are listed in the following table (k=5 and k=1,5 for the walls):


δ x

δ y

Vx

Vy

Mx,1

Mx,2

My,1

My,2

(mm)

(mm)

(kN)

(kN)

(kNm)

(kNm)

(kNm)

(kNm)

C1

3,365

-0,370

42,8

-4,7

64,3

-64,3

-7,1

7,1

C3

3,365

0,123

103,6

3,8

155,4

-155,4

5,7

-5,7

C4

3,365

0,369

42,8

4,7

64,3

-64,3

7,1

-7,1

C6

3,118

-0,124

96,0

-3,8

144,0

-144,0

-5,7

5,7

C11

2,872

0,123

88,4

3,8

132,6

-132,6

5,7

-5,7

C13

2,625

-0,370

33,4

-4,7

50,1

-50,1

-7,1

7,1

C16

2,625

0,369

33,4

4,7

50,1

-50,1

7,1

-7,1


The displacement of the centre of stiffness CT is δxo=2.84 mm. The maximum primary and secondary displacements are δ xx=3.37 mm (3.37/2.84=119%) and δxy=0.37 mm (0.37/2.84=10%) respectively, whereas the minimum values RE δxx =2.63 mm (2.63/2.84=92%) and δxy=0.12 mm (0.12/2.84=4%) respectively.

rx=8.06 m, ry=9,60 m (E=797/1067), θz=0,00004929, Kθ=64.899.8 MN·m

(b) replacement of the columns C12, C14, with walls of cross-section 2000/300 parallel to the respective sides of the perimeter.


Figure 5.4.7.4b
Figure 5.4.7.4b

The results obtained from modifying the geometric data of the C12, C14, from 500/500 to 2000/300, in the same file (sheet B_547-4b), are listed in the following table (k=5 and k=1,5 for walls):


δ x

δ y

Vx

Vy

Mx,1

Mx,2

My,1

My,2

(mm)

(mm)

(kN)

(kN)

(kNm)

(kNm)

(kNm)

(kNm)

C1

3,620

-0,795

46,1

-10,1

69,1

-69,1

-15,2

15,2

C3

3,620

-0,045

111,4

-1,4

167,1

-167,1

-2,1

2,1

C4

3,620

0,330

46,1

4,2

69,1

-69,1

6,3

-6,3

C6

3,245

-0,420

99,9

-12,9

149,8

-149,8

-19,4

19,4

C11

2,870

-0,045

88,3

-1,4

132,5

-132,5

-2,1

2,1

C13

2,495

-0,795

31,8

-10,1

47,7

-47,7

-15,2

15,2

C16

2,495

0,330

31,8

4,2

47,7

-47,7

6,3

-6,3


The displacement of CT is δxo=2.83 mm. The maximum primary and secondary displacements are δxx=3.62 mm (3.62/2.83=128 %) and δxy=0.33 mm (0.33/2.83=12%) respectively, whereas the minimum values are δxx=2.49 mm (2.49/2.83=88%) and δxy=0.05 mm (0.05/2.80=2%) respectively.

rx=7.69 m, ry=7,69 m (E=858/858), θz=0,00007498, Kθ=41.877.5 MN·m

(c) replacement of the columns C5, C12, with walls of cross-section 2000/300 parallel to the corresponding sides of the perimeter.


Figure 5.4.7.4c
Figure 5.4.7.4c

The results obtained from modifying the geometric data of the C5, C12 from 500/500 to 2000/300, in the same file (sheet B_547-4c), are listed in the following table (k=5 and k=1,5 for walls):


δ x

δ y

Vx

Vy

Mx,1

Mx,2

My,1

My,2

(mm)

(mm)

(kN)

(kN)

(kNm)

(kNm)

(kNm)

(kNm)

C1

4,438

0,407

56,5

5,2

84,7

-84,7

7,8

-7,8

C3

4,438

-0,136

136,6

-4,2

204,9

-204,9

-6,3

6,3

C4

4,438

-0,407

56,5

-5,2

84,7

-84,7

-7,8

7,8

C6

4,709

0,136

144,9

4,2

217,4

-217,4

6,3

-6,3

C11

4,980

-0,136

153,3

-4,2

229,9

-229,9

-6,3

6,3

C13

5,251

0,407

66,9

5,2

100,3

-100,3

7,8

-7,8

C16

5,251

-0,407

66,9

-5,2

100,3

-100,3

-7,8

7,8


The displacement of CT is δxo=4.84 mm. The maximum primary and secondary displacements are δxx=5.25 mm (5.25/4.84=108 %) and δxy=0.41 mm (0.41/4.84=8 %) respectively, whereas the minimum values are δxx=4.44 mm (4.44/4.84=92 %) and δxy=0.14 mm (0.14/4.84=3 %) respectively.

rx=7.43 m, ry=11.58 m (E=560/1205), θz=-0,00005422, Kθ=55.325.8 MN·m

(d) replacement of the column C5 with wall of cross-section 2000/300 in parallel to the respective side of the perimeter.


Figure 5.4.7.4d
Figure 5.4.7.4d

The results obtained from modifying the geometric data of the C5 from 500/500 to 2000/300, in the same file (sheet B_547-4d), are listed in the following table (k=5 and k=1,5 for walls):


δ x

δ y

Vx

Vy

Mx,1

Mx,2

My,1

My,2

(mm)

(mm)

(kN)

(kN)

(kNm)

(kNm)

(kNm)

(kNm)

C1

4,113

0,406

52,4

5,2

78,5

-78,5

7,7

-7,7

C3

4,113

-0,509

126,6

-15,7

189,9

-189,9

-23,5

23,5

C4

4,113

-0,967

52,4

-12,3

78,5

-78,5

-18,5

18,5

C6

4,570

-0,052

140,7

-1,6

211,0

-211,0

-2,4

2,4

C11

5,028

-0,509

154,8

-15,7

232,1

-232,1

-23,5

23,5

C13

5,485

0,406

69,8

5,2

104,8

-104,8

7,7

-7,7

C16

5,485

-0,967

69,8

-12,3

104,8

-104,8

-18,5

18,5


The displacement of CT is δxo=4.80 mm. The maximum primary and secondary displacements are δxx=5.49 mm (5.49/4.80=114%) and δxy=0.41 mm (0.41/4.80=8%) respectively, whereas the minimum values are δxx=4.11 mm (4.11/4.80=86%) and δxy=-ΧΧ mm (0.96/4.78=4%) respectively.

rx=6.74 m, ry=8,81 m (E=604/971), θz=-0,00009149, Kθ=32.303.2 MN·m


Synopsis of results of the six cases

 


« Exercise 3 Seismic accelerations and loadings »