Example On The Analysis and Design of Continuous Slab and Beam Footing Per Bs 8110-1:1997
Example On The Analysis and Design of Continuous Slab and Beam Footing Per Bs 8110-1:1997
Example On The Analysis and Design of Continuous Slab and Beam Footing Per Bs 8110-1:1997
(2016)
1.1 Introduction
This design is just an excerpt from my final year project ‘Structural Analysis and Design of 35,000
Capacity Reinforced Concrete Stadium’. After analysis and design of the superstructure (see figure
1.1), I realized I had a very large magnitude of axial loads and moments at the foundation.
Foundations must be designed to resist geotechnical and structural failure, and at the same time
should be economical. The ultimate bearing capacity of the supporting soil at 2.00m depth was very
good at 380 KN/m2, (gravely sand at Naze, Owerri) so shallow foundation was adopted.
However, adopting a pad footing proved very uneconomical given the large area of excavation
required (columns are spaced at 6.0m), and the depth of concrete needed to handle shear forces was
much. Raft foundation proved to be too expensive for a soil with such good bearing capacity. After
much consideration, I realized that chaining the columns continuously will do the trick, but at the
same time, I could combine the slab with upstand beams running continuously along the axis of the
column. My whole aim was to reduce the great quantity of concrete that would have been required to
control diagonal shear by using shear reinforcements (stirrups) in the beams which proved to be much
cheaper (see Figure 1.1).
For this paper, I selected an axis from the structure in which the intermediate columns had
approximately an ultimate axial load of 3081.075 KN each while the end columns had an axial load of
1680.3 KN (see Figure 1.3).
From the symmetrical arrangement of the loads, it is quite obvious that the centroid will pass through
the middle column, hence, soil pressure can be assumed to be uniform under the whole length of the
footing.
Concrete cover = 50mm; Fy = 460 N/mm2; Fyv = 460 N/mm2; Fcu = 30 N/mm2
Dimension of all columns = (500 × 300 mm); Bearing Capacity = 380 KN/m2
Bending moment on the slab is maximum at the face of the column (in this case at the face of the
upstand beams) (clause 3.11.2.2 BS 8110-1:1997)
Width of the beam = 500mm = 0.5m
. .
Hence, Moment arm (jxx) = = 0.30 m
Assume depth of slab h = 300mm; concrete cover = 50mm and assuming that Y12mm bars will be
used at the slab;
Hence, the effective depth (d) = 300 – 50 − (12/2) = 244mm
× . × .
The design moment Mx-x = = = 21.14 KN.m
. ×
k= = = 0.012; k < 0.156, no compression steel needed (clause 3.4.4.4)
× ×
. ×
Area of tension steel required ASreq =
. . .
= . × × . ×
= 212.17 mm
. . × ×
Minimum area of steel ASmin = = = 390 mm2 (Table 3.25 BS 8110-1:1997)
Provide Y12 @ 200 mm c/c (Asprov = 566 mm2/m)
. . × ×
ASmin = = = 390 mm2 (Table 3.25 BS 8110-1:1997)
Provide Y12 @ 200 mm c/c (Asprov = 566 mm2/m) in longitudinal direction as distribution bars
The concrete resistance shear stress (Vc) = 0.632 × (Table 3.8 BS 8110-1:1997)
×
Vc = 0.632 × ×
×
Vc = 0.632 × 0.6144 × 1.1315 = 0.439 N/mm2
1
2 30 3
For Fcu = 30N/mm , Vc = 0.439 × = 0.4665 N/mm2
25
Critical diagonal shear force at d from face of support = V = q(jxx – d)
V = 467.97 × (0.30 – 0.244) = 28.078 KN/m
. ×
The shear stress v = = = 0.1151 N/mm2 (clause 3.4.5.2 BS 8110-1:1997)
×
0.1151 N/mm2 < 0.4665 N/mm2
Diagonal Shear is ok
Punching shear is also ok (perimeter falls outside the footing dimensions). Hence design is ok.
Uniformly distributed soil reaction on beam = 467.97 KN/m2 × 1.1m = 514.77 KN/m
M = 1960.09 KN.m
. ×
k= = = 0.124 (clause 3.4.4.4 BS 8110-1:1997)
× ×
k < 0.156, no compression steel needed
. ×
ASreq =
. . .
= . × × . ×
= 5252 mm
. . × ×
ASmin = = = 1430mm2 (Table 3.25 BS 8110-1:1997)
. ×
ASreq = = = 4124 mm
. . . . × × . ×
. . × ×
ASmin = = = 1430 mm2 (Table 3.25 BS 8110-1:1997)
Provide 4Y32mm + 3Y25mm BOT (Asprov = 4689mm2) mainly around the mid span supports. (See
detailed drawings)
. ×
ASreq =
. . .
= . × × . ×
= 3387.5 mm
. . × ×
ASmin = = = 990 mm2 (Table 3.25 BS 8110-1:1997)
. ×
ASreq = = = 1888.224 mm
. . . . × × . ×
. . × ×
ASmin = = = 990mm2 (Table 3.25 BS 8110-1:1997)
Shear design
. ×
Hence maximum shear stress v = = = 3.654 N/mm2 (clause 3.4.5.2 BS 8110-1:1997)
×
3.654 N/mm2 < 0.8√30 < 5 N/mm2
. ×
Shear stress v = = = 1.197 N/mm2 (clause 3.4.5.2 BS 8110-1:1997)
×
×
Vc = 0.632 × ×
×
. ×
Shear stress at d from the face of column v = = = 2.474 N/mm2
×
×
Vc = 0.632 × ×
×
Vc = 0.632 × 1.032 × 1 = 0.652 N/mm2
×
v = = = 2.00 N/mm2 (clause 3.4.5.2 BS 8110-1:1997)
×
×
Vc = 0.632 × ×
×
Vc = 0.632 × 1.032 × 1 = 0.652 N/mm2
. ×
Shear stress v = = = 1.893 N/mm2 (clause 3.4.5.2 BS 8110-1:1997)
×
×
Vc = 0.632 × ×
×
Stop shear links at 1.1 m from face of column and provide nominal reinforcement = 3Y10 @ 300mm
Detailing
Typical sections cut through points Band C is shown in Figure 1.5. Kindly download full detailed
drawing from www.structville.blogspot.com