Date: Fri, 29 Mar 2024 08:06:30 -0400 (EDT)
Message-ID: <429551432.4171.1711713990373@csi2-roc-conf1>
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A simple model of a tall cruciform building with vertical walls and flat=
slabs exhibits very different buckling behavior depending on whether or not rigid diaphragms are used for the floors. The study which follows in=
vestigates such systems, and the conclusions drawn are described as follows=
:
- With rigid diaphragms, torsional buckling of the whole structure is one=
of the fundamental buckling mode.
- Without rigid diaphragms, torsional buckling occurs at a higher bucklin=
g factor.
- Making the slab stiffer in plane, but without using a diaphragm constraint, does not substantially change t=
his behavior.
- The presence of the diaphragm constraint allows significant horizontal =
compressive stresses to develop in the walls. These are due to Poisson=E2=
=80=99s effect under gravity load, and are sustained by the infinitely stif=
f horizontal diaphragm.
- Without the diaphragm, even with a very stiff slab, the Poisson stresse=
s are less pronounced.
- The horizontal compressive stresses in the walls cause out-of-plane ins=
tability, tending to cause torsional buckling.
- With the diaphragm constraint, the corresponding tension in the slab is=
implicitly developed but no slab stresses are computed. Therefore, there i=
s no tension stiffening included in the P-delta formulation.
- With the stiff or flexible diaphragm, the tension in the slab that resi=
sts the horizontal Poisson stresses is included in the P-Delta effect. This tension stiffening counteracts =
the softening due to the compressive stresses in the wall.
- Vertical compressive stresses do not have a counteracting tensile stres=
s in the slab, and will tend to cause torsional and other types of buckling=
.
- To prove this analysis, setting Poison=E2=80=99s ratio to zero causes t=
he model with diaphragm constraints and the model with a stiff slab to be e=
ssentially identical, with a high torsional buckling factor.
- All conclusions above are for the particular model of this study. Wheth=
er or not they apply to any other model or real structure is a decision to =
be made by the engineer.
- Whether or not these horizontal stresses can be sustained in a real str=
ucture is a modeling decision for the engineer. However, the effect on stru=
ctural behavior is very significant and merits careful consideration.
- All walls and floors are 12=E2=80=99 x 12=E2=80=99 x 8=E2=80=9D concret=
e thin-shell objects.
- Buckling under self-weight load
- Center =E2=80=93 No modification (flexible diaphragms)
- Left =E2=80=93 Slab stiffness modifiers of 1000 for F11, F22, F12 (stif=
f diaphragms)
- Right =E2=80=93 Diaphragm constraints (rigid diaphragms)
Figure 1 - SAP2000 model with three variat=
ions on diaphragm design
Figure 2 - Vertical stresses under self-we=
ight
Figure 3 - Horizontal stresses under self-=
weight
Figure 4 - Slab stresses at Story 2 (top) =
and Story 8 (bottom)
Figure 5 - Buckling modes 1, 2, 3
Figure 6 - Buckling modes 4, 5, 8
Figure 7 - Buckling modes 6, 7, 9
Figure 8 - Buckling modes 10, 11, 12
Figure 9 - Buckling modes 13, 14, 15
Figure 10 - Buckling modes 16, 17, 18
Figure 11 - Buckling modes 19, 20, 21
Figure 12 - Buckling modes 22, 23, 24
Figure 13 - Buckling deformation of Storie=
s 2 and 8
=
Figure 14 - Buckling Factors
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