Reinforced Concrete, Prestressed Concrete and Steel Design — ESE Civil

Weightage: Design of concrete and steel structures is a heavy block in Civil Prelims Paper II and the Mains. The questions are code-driven: a clause number, a factor or a limiting value decides the answer. Confirm which edition of each code the current ESE notification expects, since BIS revisions are under discussion.

1. Limit state philosophy

Design is checked at two limit states. The limit state of collapse guards against strength failure (flexure, shear, torsion, compression). The limit state of serviceability guards against excessive deflection and cracking.

Safety is built in through partial safety factors. In IS 456:2000 the material factors are 1.5 for concrete and 1.15 for steel. Loads are multiplied by factors, commonly 1.5 for dead plus live load. Characteristic strength is the value below which not more than 5 percent of results fall.

2. The rectangular stress block

At collapse the compressive stress in concrete is idealised as a rectangle of average intensity $0.36f_{ck}$ over depth $x_u$, acting at $0.42x_u$ from the compression edge. The steel yields at design stress $0.87f_y$.

Equilibrium of the section gives:

$0.36f_{ck}b{x}_u=0.87f_y{A}_{st}$

and the moment of resistance of a singly reinforced beam is:

$M_u=0.87f_y{A}_{st}(d-0.42x_u)$

3. Under-reinforced, balanced and over-reinforced

A section is under-reinforced when steel yields before concrete crushes. This is the desired mode because it fails gradually with warning. IS 456 limits the depth of the neutral axis:

The limiting moment of resistance is $M_{u,lim}=0.36f_{ck}b{x}_{u,max}(d-0.42x_{u,max})$. For Fe 415 this is about $0.138f_{ck}b{d}^2$. If the moment exceeds this, use a doubly reinforced section with compression steel, or deepen the beam.

Worked example. A beam 250 mm by 500 mm effective depth uses M20 and Fe 415, with $A_{st}=1000{\text{mm}}^2$. Then $x_u=0.87\times 415\times 1000/(0.36\times 20\times 250)=200.6$ mm, which is below $0.48\times 500=240$ mm, so it is under-reinforced.

4. Shear and bond

Shear is resisted by the concrete, with strength ${\tau }_c$ that depends on $f_{ck}$ and the percentage of tension steel, plus stirrups. Nominal shear stress is ${\tau }_v=V_u/(bd)$. If ${\tau }_v>{\tau }_c$, stirrups carry the excess: $V_{us}=0.87f_y{A}_{sv}d/s_v$. There is also a maximum ${\tau }_{c,max}$, above which the section must be enlarged.

Development length transfers bar force to concrete by bond:

$L_d=\frac{\varphi {\sigma }_s}{4{\tau }_{bd}}$

with ${\sigma }_s=0.87f_y$ at the section considered. Deformed bars and higher grades of concrete shorten it.

5. Slabs and serviceability

A slab spanning in one direction, with $l_y/l_x>2$, is one-way. If the ratio is 2 or less and supports exist on all sides, it is two-way. Deflection control uses span-to-effective-depth ratios, basic values being 7 for a cantilever, 20 for a simply supported span and 26 for a continuous span, modified for steel stress and percentage of reinforcement.

6. Columns

A short column has $L_e/D$ below 12, and its behaviour is governed by crushing. IS 456 gives:

$P_u=0.4f_{ck}{A}_c+0.67f_y{A}_{sc}$

Longitudinal steel lies between 0.8 and 6 percent of the gross area (in practice the upper bound is kept near 4 percent to ease placing). Minimum eccentricity applies, taken as the larger of $L/500+D/30$ and 20 mm. Lateral ties prevent buckling of bars and confine the core.

7. Prestressed concrete

Prestressing applies a compressive force to concrete so that tension under load is reduced or removed. It lets concrete, weak in tension, be used efficiently for long spans.

• Pre-tensioning: steel is tensioned before concreting and released after hardening, with bond transferring force. It suits factory products.
• Post-tensioning: ducts are cast in, steel is tensioned against the hardened concrete and anchored. It suits site work and long spans.

For a concentric tendon the stress at a fibre is $\sigma =P/A\pm My/I$. Eccentricity $e$ adds $\mp Pey/I$. Keep the kern in mind: the tendon line lies within the middle third for a rectangle if tension must be avoided.

Losses of prestress are:

High-strength concrete and steel are used because losses are a smaller share of a large prestress.

8. Steel design (IS 800:2007)

IS 800 is also a limit state code. Partial safety factors on material are 1.10 for yielding and buckling and 1.25 for ultimate strength.

Plastic analysis. At full yield the section becomes a plastic hinge with $M_p=f_y{Z}_p$. The shape factor is $S=Z_p/Z_e$, which is 1.5 for a rectangle and roughly 1.1 to 1.2 for rolled I-sections. A beam fails as a mechanism when enough hinges form, and the collapse load follows from the virtual work equation.

Compression members. Strength depends on the slenderness ratio $KL/r$ and the buckling class. Slenderness limits apply: 180 for members carrying dead and live load, 250 for members in which stress reversal is due to wind.

Connections.

• Bolts: a bolt may fail in shear, bearing or tension. The design strength is the smallest of these. High-strength friction-grip bolts transfer load by friction.
• Welds: effective throat thickness for a fillet weld is $0.7\times$ size. Strength is $f_u/(\sqrt{3}{\gamma }_{mw})$ per unit area of throat. Minimum and maximum weld sizes depend on plate thickness.
• Beams also need checks for lateral-torsional buckling, web buckling and web crippling at supports.

Common traps

• Using the wrong $x_{u,max}/d$ for the steel grade.
• Confusing the 1.5 and 1.15 material factors.
• Counting friction loss in a pre-tensioned member. It occurs only in post-tensioning.
• Using the area of the whole section for the net-area check. Deduct bolt holes.
• Quoting the slab ratio for the wrong span type. 7, 20 and 26 apply to cantilever, simple and continuous.

Memory aids

• "0.36 and 0.42": the stress block and its lever.
• "0.48 for 415": neutral axis limit.
• "Friction and slip belong to post": prestress losses.

Summary

Concrete design in IS 456 rests on a rectangular stress block, a neutral-axis limit that keeps beams under-reinforced, and checks for shear, bond, deflection and columns. Prestressing offsets concrete's tensile weakness, at the cost of time-dependent losses.

Steel design under IS 800 uses plastic capacity, slenderness limits and checks on bolt and weld connections.

Exam protocol

• Quote the factor or clause and then compute.
• Check the neutral axis limit before finding $M_u$.
• Separate pre-tension losses from post-tension losses.
• Confirm code editions on the current notification.