A wall is a long, thin column. It carries vertical load (N), bends in its own plane under wind or earthquake (the shear-wall action), and can bend out of plane too. The design first decides whether it is short or slender, then checks the whole section in plane, the most stressed end strips, the in-plane shear and the code limits on steel. Every number below comes from the free STATIX RC wall calculator with the inputs in step 1.
1. The problem
Input
Value
Design code
SANS 10100-1
Length lw, in plane
3000 mm
Thickness h
200 mm
Storey height clear
3000 mm
Bracing
Braced
β le = β × storey
0.75
Actions whole wall
One ULS case (factored)
Axial N compression +
1500 kN
In-plane Min
1200 kNm
In-plane shear V
400 kN
Transverse Mout
5 kNm/m
Concrete fcu
30 MPa
Steel fy
450 MPa
Vertical dia / spacing
12 mm
Vertical bar spacing mm
200 mm
Vertical layers
Two (each face)
Horizontal dia / spacing, each face
10 mm
Horizontal bar spacing mm
200 mm
Cover outer bars
30 mm
2. Is it a wall? Short or slender?
A member counts as a wall when its length is more than four times its thickness. The effective height over the thickness decides whether it is short (no extra moment) or slender (an extra moment from its deflection is added), and there is an upper limit.
Wall definition: length > 4 x thickness:
[4.8.1.1, p.83]
lw = 3000 mm > 4h = 800 mm: a wall.
3,000.0 ≥ 800.0 mm OK
Short or slender:
[4.8.1.5 / 4.8.1.6, p.83]
le/h = 2250/200 = 11.25 <= 15 (braced): SHORT - no additional moment.
11.3 ≤ 15.0 le/h OK
Slenderness limit:
[4.8.5.2, p.86]
braced, rho_v 0.565 % not exceeding 1 % -> 40 (rho = 1 % exactly is not covered by the text; 40 used).
11.3 ≤ 40.0 le/h OK
3. The whole wall in plane: N + M
In its own plane the wall is a deep beam-column. The vertical bars along the length are each strained in proportion to their distance from the neutral axis (strain compatibility), and the section must carry the axial load and the in-plane moment together.
Short braced axially loaded wall (cross-check):
[4.8.4.1, p.85]
N <= 0,40 fcu Ac + 0,67 Asc fy per metre (Ac net) = 0,40 x 30 x 198869 + 0,67 x 1131 x 450 = 2727.4 kN/m vs worst nw 1401.5 kN/m. Information only (clause is for short braced walls without significant moments; this wall is moment-loaded); the strip row governs.
1,402 ≤ 2,727 kN/m OK
In-plane N + Min, whole wall section:
[4.8.4.3 -> 4.3.3.1, p.85 / p.22]
[ULS] strain compatibility over 16 bar rows (2 x Y12 each, first/last at 46 mm from the ends): at N = 1500 kN, x = 873.2 mm, Mu = 3169 kNm vs Min = 1200 kNm; axial 1500 kN vs the section compression 9230.4 kN capacity; util = max of the two = 0.379.
1,200 ≤ 3,169 kNm OK
4. The end strips
The ends of the wall take the largest compression and tension from in-plane bending. An end strip is checked as a column for that axial force plus any out-of-plane moment; on the tension side the vertical steel alone must carry the pull.
End strip: nw + transverse moment:
[4.8.4.4, 4.8.3.2.2, p.84-85]
[ULS] cracked transformed section, 4.8.4.4 a) p.85 / 3.4.3.1 c) p.11 (elastic, no tension in the concrete; steel in tension and compression, all 16 bar rows; modular ratio n = Es/Ec = 200/28 = 7.143 (Es 3.4.2.3 p.11; Ec short-term table 1, 3.4.2.1.1 p.10)): neutral axis x = 2147.2 mm from the compressed end, concrete edge stress 6.741 MPa, end-row steel 47.1 MPa (compression +), tension-end row -18.1 MPa. nw = concrete 1348.2 + steel 53.3 kN/m at the end; force per metre = peak intensity at the wall end (strip length -> 0, conservative): nw = 1401.5 kN/m. Mmin = nw x max(0,05h, 15) = 1401.5 x 15 mm = 21.023, Mout = 5 -> Mi = 21.023 kNm/m. Section 1000 x 200, Asc 1131 mm2/m at c0 = 46 (shared McapAtN): Mu = 84.839 kNm/m >= Md = 21.023.
21 ≤ 85 kNm/m OK
End strip in tension (vertical steel alone):
[4.8.4.4 a) -> 4.3.3.1 c), p.85 / p.22]
[ULS] cracked transformed section, 4.8.4.4 a) p.85 / 3.4.3.1 c) p.11 (elastic, no tension in the concrete; steel in tension and compression, all 16 bar rows; modular ratio n = Es/Ec = 200/28 = 7.143 (Es 3.4.2.3 p.11; Ec short-term table 1, 3.4.2.1.1 p.10)): neutral axis x = 2147.2 mm from the compressed end, concrete edge stress 6.741 MPa, end-row steel 47.1 MPa (compression +), tension-end row -18.1 MPa: tension-end bar stress fs = 18.1 MPa vs 0,87 fy = 391.5 MPa, i.e. 20.5 kN/m <= 0,87 fy Asv = 442.8 kN/m (the outermost tension row, no strip averaging); with Mout 5 kNm/m: Mu at the tension = 34.923 kNm/m.
20 ≤ 443 kN/m OK
5. In-plane shear
The horizontal force along the wall is resisted by the concrete and the horizontal bars, checked like the shear in a deep beam, with an upper limit on the shear stress.
In-plane shear stress <= vmax:
[4.3.4.1.1, p.26 (beam method)]
[ULS] SANS 10100-1 has no RC-wall in-plane shear clause; beam method 4.3.4 used. v = V/(0,8 lw h) = 400e3/(0,8 x 3000 x 200) = 0.833 MPa <= lesser of 0,75 sqrt(fcu) and 4,75 = 4.108 MPa.
0.83 ≤ 4.11 MPa OK
In-plane shear: vc + horizontal steel:
[4.3.4.1 eq.(2), 4.3.4.1.2/.3, p.27-28 (beam method)]
[ULS] SANS 10100-1 has no RC-wall in-plane shear clause; beam method 4.3.4 used. vc (eq.2, b = h, d = 0,8 lw = 2400 mm, 100As/bd = 100 rho_v (lw/2)/(0,8 lw) = 0.353) = 0.257 MPa. v > vc: Ash/sh >= h(v - vc)/(0,87 fyv) = 200 x (0.833 - 0.257)/(0,87 x 450) = 0.294 mm2/mm; provided 2 x Y10 @ 200 = 0.785 mm2/mm -> capacity vc + 0,87 fyv Ash/(sh h) = 1.795 MPa. Axial-compression enhancement of vc not used.
0.83 ≤ 1.79 MPa OK
6. Steel limits and spacing
Walls need minimum vertical and horizontal steel (for robustness and cracking), a maximum (so the concrete can be placed), horizontal bars big enough, links when the vertical steel is heavy, and bars close enough to control cracks.
Vertical steel >= 0,4 % of gross:
[4.11.4.2.3, p.94]
2 layer(s) Y12 @ 200: 1131 mm2/m / (1000 x 200) = 0.565 % (util = required/provided).
0.56 ≥ 0.40 % OK
Vertical steel <= 4 % including laps:
[4.11.5.3, p.96]
0.565 % x lap factor 2 (default: all bars lapped at one level) = 1.131 %.
1.13 ≤ 4.00 % OK
Horizontal steel minimum:
[4.11.4.3.2, p.94]
2 layer(s) Y10 @ 200: 785.4 mm2/m / (1000 x 200) = 0.393 % >= 0.25 % (high-yield steel, fy 450). The clause applies where the vertical steel resists compression - applied always.
0.39 ≥ 0.25 % OK
Horizontal bar diameter:
[4.11.4.3.2, p.94]
phi_h = 10 >= max(6, phi_v/4 = 3) = 6 mm.
10.00 ≥ 6.00 mm OK
Links through the thickness:
[4.11.4.5.2, p.94]
rho_v = 0.565 % <= 2 %: no links required.
0.56 ≤ 2.00 % OK
Vertical bar spacing (each layer):
[4.8.7 -> 4.11.8.2.2 slab rule, p.86 / p.107-108]
clear spacing 188 mm <= lesser of 3d = 462 and 750 mm; no further check (4.11.8.2.2.1: grade 450, h <= 200). 4.11.8.2 has no wall rule; the slab rule is applied to each layer (d = 154 mm, rho = 0.367 % of 1000 d).
188.00 ≤ 462.00 mm OK
Horizontal bar spacing (each layer):
[4.8.7 -> 4.11.8.2.2 slab rule, p.86 / p.107-108]
clear spacing 190 mm <= lesser of 3d = 495 and 750 mm; no further check (4.11.8.2.2.1: rho 0.238 % < 0,3 %). 4.11.8.2 has no wall rule; the slab rule is applied to each layer (d = 165 mm, rho = 0.238 % of 1000 d).
190.00 ≤ 495.00 mm OK
Crack control: two layers:
[4.8.7, p.86]
two layers, each to the 4.11.8.2 spacing rows: deemed to satisfy.
2.00 ≤ 2.00 layers OK
7. Cover and fire
The cover protects the steel (durability) and keeps it cool in a fire; both depend on inputs the designer gives.
Nominal cover >= bar diameter and >= maximum aggregate:
[4.11.2.4, 4.11.2.5, p.92]
cover 30 mm to the outer bars (dia 10) >= max(bar dia 10, aggregate 20 (default 20)) = 20 mm.
30 ≥ 20 mm OK
Durability cover:
[4.11.2.2, 4.11.2.10, p.92 -> SABS 0100-2; cover table SANS 2001-CC1:2007 cl.4.4.3.1 table 3, p.23]
NOT CHECKED - give the exposure ('moderate' | 'severe' | 'verySevere' | 'extreme'); the code sets no default exposure.
NOT-CHECKED
Fire resistance:
[7.5, 7.6, tables 48 / 50, p.170-172]
NOT CHECKED - give fireRating (h) from the building regulations (SANS 10400-T); 0 when no rating is required.
NOT-CHECKED
With load cases (G, Q, W) instead of one ULS set, each combination is checked and the worst governs; the calc sheet lists each one.
Run this example yourselfOpen the free STATIX RC wall calculator and press Load the example (3 m wall, N 1 500 kN, M 1 200 kNm) under "How it is calculated". Change any value and every step updates, with a calc sheet. Open the RC wall calculator
A worked example for learning, not a design. Check every value against the current code and your own project, and have the design checked and signed by a registered professional engineer.
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