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76
Valério da Silva Almeida & João Batista de Paiva
Note that taking into account the soil’s rigidity throughout its depth represents a
significant alteration in the displacement values of the soil-raft-building system, since
the relative differences between cases b and c are about 50% (see Fig. 7). This
influence proves more relevant than the consideration of the position of the
indeformable layer, since the relative difference of displacements between cases a
and b is in the order of 20%.
Figure 8 shows the diagrams of bending moments of M
x
along the raft’s BB
2
cut. The variations of these bending moments for the different cases also proved
similar to those presented by the fields of displacement. For these moments, the
average differences between cases b and c and between a and b are, respectively,
52% and 13%.
Figure 9 shows the values of the stresses ( σ
33
) that are mobilized in the area of
contact between soil and raft in the AA cut. The contact stresses also show similar
results in the various cases, the most significant variation occurring between cases b
and c, with a mean value of 33%.
From table 4 it can be noted that, when the soil’s deformability is taken into
account, the columns’ normal values are more closely distributed around the average,
i.e., there is a more uniform redistribution of forces because the mobilisation of the
soil-raft-building system occurs jointly.
Carga permanente
Ação de vento
3 m
r = 10.L
2 m
Radier
h = η L R
36 m
t R
Ω 1
Ω 2
L R
= 20 m
Radier
M t
F x2
F x1 A x 1
x 2
3 m 14 m
5 m 10 m
5 m
Ω 3
Base indeslocável
Edifício de múltiplos andares
Caso a
Caso b
Caso c
Caso d
Limite da superfície discretizada
do semi-espaço
E Ω= E Ω = E Ω= 100 MPa E 3E Ω = 3/2 E Ω = E = 90
1
2 Ω 3/2 E = 3 E = E = 90
1
Ω= E
2 3
Ω = E Ω= 100 MPa
1 2 3
3
Ω 1 Ω 2 Ω 3
η=50 η =1 η =1 (η = η = 3/8η) η =1 (η = η = 3/8η)
Ω
Ω
Ω2
3
Ω2
3
a)
b)
Cadernos de Engenharia de Estruturas, São Carlos, v.9, n. 38, p. 63-82, 2007