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