The floor system, which is a flat slab shown, supports a service live load of 70 psf and a service dead load of 50 psf. The dead load does not include the slab weight. There is no beam between columns.
- Based on the deflection limitation, choose an appropriate slab thickness (h0)
h0= which give the thickness of the slab that is ~ 4.115
- Check one-way shear and two way shear and modify “h0” if needed.
One-way shear calculations in slab bands are done similar to shear in two-way slabs, except the column strip is substituted by the band strip. Transverse reinforcement is not considered
Therefore, for two-way shear is given by Vc = 1+ that gives 48800.3 kN
One way shear is done by Vc = that is 1466.6 kN
Where
Pu =
hmin= which give 2.46
hmax = which sums to 3.69
Where
ln is the largest clear distance in the direction of the panel
sn is the shortest distance in the direction in the panel
β=
Therefore, the h to be used hmin ≤h ≤hmax
- Find the bending moments for column strip and middle strip by using direct design method.
| Column strip moments (KN.m) | Interior negative moment | Positive moment | Exterior negative moment |
| 1.25 | 1.25 | 1.25 | |
| = 0 | 187.5 | 160 | 75 |
| 225 | 225 | 225 |
| Middle strip moments | FRAME 1-2 | FRAME 2-3 |
| MS-M1 | 110.15 -97.72 | -105.47 90.87 |
| MS-M2 | 116.15 -97.72 | -105.47 90.87 |
| MS-Mtot | 232.29 -195.44 | -210.94 181.74 |
- Design the longitudinal bars based on moment found in section “c”
- Model the slab in SAP2000 and compare the result of section “b”, “c” and “d” with the modeling results.
(f) Use your SAP model and redesign the slab for h1 = h0 + 1″ and h2 = h0 + 2″ .
(g) Compare the volume of rebars and concrete for three models (h0, h1 and h2) and discuss which one is the most economical design.
| Slab type | Slab thickness | RFT/m3 (net RC vol.
kgm-3) |
| Model h0 | 4.11 | 11.2 |
| Model h1 | 5.11 | 14 |
| Model h2 | 6.11 | 23 |
Normally, design and quantities will be influenced by several variables such as loads, spans, boundary conditions, used materials, rebar detailing. This load transfer generates primarily bending moments and shear stresses in the slab. Usually, some empirical values are used as optimum rebar percentage to evaluate the economy of certain design. The connection between the considered bending element and adjacent elements have a major effect on bending moment distribution along this element. As per the codes, maximum bending moments the model for h0 is the most economical compared to the other models as they take a higher volume per psi.
Use normal weight concrete with f′ c = 4000 psi and fy = 60,000 psi. The dead load does not include the slab weight. Columns dimensions are 20″ X 20″.
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