References:
-
ACI 318
-
ACI 350
-
ACI 360
-
ASCE 7-22
-
Project Design Criteria
Loads:
-
Distributed load of 150psf
-
Concentrated load of 3,000lb, over an area of 10x10”
The concentrated load of 3,000lb is less than the total weight of a typical oil tote
(2200lb for 275-gallon tote).
Soil bearing capacity
For a distributed live load of 150psf and 12” thick concrete slab the pressure on the soil will
be 300psf < the soil bearing capacity of 2,000psf.
For a concentrated load of 3,000lb over 10x10” area, the pressure on soil will be over an
area of 22x22”, resulting in 893psf < 2,000psf.
Slab thickness
For a concentrated load of 3,000lb close to the corner of the 6” thick slab, the tensile stress,
ft, at the top of the slab would be (ACI 360):
𝑓𝑡 =
3𝑃 3 ∗ 3,000
6√4,000
=
= 250𝑝𝑠𝑖 <
= 271𝑝𝑠𝑖 → 𝑂𝐾
2
2
ℎ
6
1.4
Considering a load factor of 1.40.
Considering Westergaard’s expression, for the tensile stress at a distance of 2√𝑎1 𝐿 from the
corner of the slab (ACI 360):
0.6
𝑓𝑡 =
3𝑃
1−
ℎ2
𝑎√2
4
√
[
(
𝐸ℎ3
12(1 − 𝜐 2 )𝑘
)
]
0.6
𝑓𝑡 =
3 ∗ 3,000
10√2
1−
2
6
4
3,600,000 ∗ 63
√
( 12(1 − 0.152 ) ∗ 200)
[
]
𝑓𝑡 = 103𝑝𝑠𝑖 < 271𝑝𝑠𝑖 → 𝑂𝐾
Punching Shear Strength
For a 6” thick slab and a 10x10” loaded area the punching strength would be:
∅𝑉𝑐 = ∅𝑐 4√𝑓𝑐′ 𝑏𝑤 𝑑 = 0.75 ∗ 4 ∗ √4,000 ∗ (4 ∗ 16) ∗ 3 = 36,000𝑙𝑏 > 1.4 ∗ 3,000𝑙𝑏 → 𝑂𝐾
Flexural Capacity
The cracking moment for a 12” strip would be:
12 ∗ 63
(
)
(6.0
∗
4,000)
∗
√
𝑓𝑟 ∗ 𝐼𝑔
12
𝑀𝑐𝑟 =
=
= 27,000𝑙𝑏 − 𝑖𝑛/𝑓𝑡
𝑦𝑡
3
𝑓𝑟 = 6.0 ∗ √𝑓𝑐′ = 6.0 ∗ √4,000 = 379𝑝𝑠𝑖
where:
Finite Element Model
An FE model was developed in SAP2000 (Fig. 2).
Figure 2 – SAP2000 FE Model
The model consists of 6” thick shell elements, supported on linear springs with a stiffness
of 200pci.
The loading consists of 3,000lb distributed over an area of 10x10”. Three typical locations
have been considered:
-
Slab corner
-
Slab edge
-
Slab interior
Soil pressure
The highest soil pressure value is reached at corners (Fig. 3):
5psi = 720psf < 2,000psf
Figure 3 – Soil Pressure
Flexural Strength
The highest tensile stress value is reached at the edge; x-x direction (Fig. 4):
130psi < fr = 379psi → OK
Similarly, the bending moment at the same location is (Fig. 5):
770lb −
in
in
= 9,240lb − < Mcr = 27,000lb − in/ft → OK
in
ft
Figure 4 – Tensile Stress
Figure 5 – Bending Moment
Deflections
The highest deflections occur at the corner (Fig. 6):
v = 0.025" → OK
Figure 6 - Deflections
Steel Reinforcement
Since the slab has been designed to not crack, the reinforcement shall be considered for
temperature and shrinkage only.
The required minimum amount of temperature and shrinkage reinforcement shall be:
0.0018 ∗ 6 ∗ 12 = 0.13in2 /ft
#4 rebar spaced at 12” each way would result in 0.20in2 /ft → OK
Reinforcement Configuration
The reinforcement shall be installed in one layer, with 2” top concrete cover and 3” bottom
concrete cover.
Control joints
1.5” deep saw-cut control joints shall be spaced at 12ft in each direction.
Sub-base
The sub-base shall consist of min 6” thick granular base material. This material shall be
stable, compatible angular or subangular with 100% passing the 1” sieve and not more
than 8% passing the No. 200 sieve size.
A minimum 6mil-thick plastic sheeting shall be placed on top of the granular base material,
directly beneath the concrete slab.