DESIGN OF CONCRETE SECTION AS PER BS 8110: 1997

MATERIAL SAFETY FACTORS

The material safety factors have been assumed for concrete and steel as given below

For Concrete \( \gamma_m = 1.5 \)

For Steel \( \gamma_m = 1.15 \)

Shear strength without reinforcement \( \gamma_m = 1.25 \)

Bond Strength \( \gamma_m = 1.40 \)

Others \( \gamma_m = 1.50 \)

STRESS-STRAIN CURVE OF CONCRETE

The stress-strain relationship of concrete shall be parabolic and can be represented by following curve.

curve

Fig. Stress-Strain Relation for Concrete

STRESS-STRAIN CURVE OF STEEL

Stress-strain curve is linear as given below. The relation is shown as given below.

curve

Fig.Stress-Strain Relation for Steel.

STRESS AND STRAIN DIAGRAM OF THE SECTION

The relation is given as follows.

curve

Fig. Stress-Strain diagram of the section.

Constant \( K'=0.156 \) where redistribution does not exceed 10% (this implies a limitation of the neutral axis depth to \(\frac{d}{2}\)); Otherwise \(K'=0.402(\beta-0.4)-0.18(\beta-0.4)^2 \) where redistribution exceeds 10%

If \(K>K'\), the section is doubly reinforced, otherwise singly reinforced. Where the ratio

\(\beta=\frac{moment at the section after distribution}{moment at the section after redistribution} \)

1. Design of singly reinforced section

If \(K'>K\), the section is singly reinforced section and designed as follows

\( K=\frac{M}{f_{cu}bd^2} \)

Calulation of moment arm, \(z\)

\( z=(0.5+\sqrt{0.25-\frac{K}{0.9}})d \)

but \(Z\) should not be greater than \(0.95d\)

Depth of neutral axis

\(x=\frac{z-d}{0.45} \)

Area of reinforcement is now given by

\(A_{st}=\frac{M}{f_{cu}K'bd^2} \)

2. Design of Doubly reinforced section

If \(K>K'\), the section is doubly reinforced section and designed as follows

Calulation of moment arm, \(z\)

\( z=(0.5+\sqrt{0.25-\frac{K'}{0.9}})d \)

but \(Z\) should not be greater than \(0.776887d\)

Depth of neutral axis

\(x=\frac{z-d}{0.45} \)

Now, area of reinforcement is given by,

\(A'_s=\frac{(K-K')f_{cu}bd^2}{0.87f_y(d-d')} \)

Total area of tension reinforcement is given by;

\( A_s=\frac{K'f_{cu}bd^2}{0.87f_yZ}+A'_s \)

Compression reinforcement is given by

\(A_{sc}=\frac{M-K'f_{cu}bd^2}{(f_{sc}-0.446f_{cu})(d-d')} \)

If \(\frac{d’}{x} \) exceeds 0.37 (for \(f_y=500N/mm^2\)), the compression stress will be less than \(f_{sc} = 0.87f_y\) and obtained from stress-strain curve of reinforcement

SHEAR REINFORCEMENT

Design shear stress of section is given by.

\(v=\frac{V}{bd} \)

In no case, \( v \leq v_{max} \) where \(v_{max}= min. of (0.8\sqrt{f_{cu}}, 5 N/mm^2 \) )

Shear strength shall be calculated by;

\(v_c=\frac{0.79(k_1)^{1/3}(k_2)^{1/4}(k_3)^{1/3}}{\gamma_m} \)

Where,

\( k_1=\frac{100A_s}{bd} \)

Which should not be less than 1.

\( k_2=\frac{400}{d} \leq 0.67 \)

For Plain concrete and \( k_2 > 1 \) for reinforced concrete.

\( k_3=\frac{f_{cu}}{25} \)

and

\( k_3 \geq 1\)

\( f_{cu}\) should not be greater than 40 N/mm2

\( v_c\) is given in Table 3.8 of BS8110.1.

Form and area of shear reinforcement in beam

1. If \(v<0.5v_c \), No shear reinforcement required.

2. If \( v_c+0.4 \leq v \leq 0.8 \sqrt(f_{cu}) or 5N/mm^2 \), then Minimum links for whole length shall be provided.

\( A_{gv}\geq \frac{0.4b_vS_v}{0.87f_{yv}} \)

3. \(v>(v_c+0.4)\) and \(v\leq 0.8\sqrt(f_{cu})\) or 5 N/mm2.

\( A_{gv} \geq \frac{b_vS_v(v-v_c)}{0.87f_{yv}}\)

In case of shear reinforcement in slab \(0.5v_c\) shall be replaced by \(v_c\). Generally, it is not recommended to provide shear reinforcement. Thickness shall be increased if \(v>v_c\).

MINIMUM AND MAXIMUM REINFORCEMENT

As per Table 3.25- Minimum percentage of reinforcement as follows;

Section subjected to pure tension

1. Tension reinforcement

\(p_{min} =0.80 \)% for \(f_y=250 N/mm^2 \)

\(p_{min} =0.45 \)% for \(f_y=500 N/mm^2 \)

2. Compression reinforcement (Rectangular column)

\(p_{min} =0.40 \)% for \(f_y=250 N/mm^2 \)

\(p_{min} =0.40 \)% for \(f_y=500 N/mm^2 \)

3. Rectangular beam

\(p_{min} =0.20 \)% for \(f_y=250 N/mm^2 \)

\(p_{min} =0.20 \)% for \(f_y=500 N/mm^2 \)

In case of Fe415, interpolation shall be carried out.

In slab, minimum reinforcement = \(0.13\)%

Maximum reinforcement = \(4\)% in flexure and 6% in vertically cast columns

The design of One-way slab is similar to Beam design.