Principles & Materials of Prestressing

The idea

Plain concrete is strong in compression but weak in tension. Reinforced concrete lets steel carry the tension, but the concrete around the steel still cracks under service load. Prestressing puts a permanent compressive force into the concrete before the external loads act. The external load then only has to cancel this pre-compression before any tension appears, so the concrete stays uncracked and the whole section works.

Three ways to understand it

1. Concrete made elastic. Prestressing turns concrete into an elastic material that can carry tension up to the pre-compression. The section is analysed as a homogeneous elastic beam: $\sigma =\frac{P}{A}\pm \frac{Pey}{I}\pm \frac{My}{I}$.
2. A steel–concrete couple. The prestressing steel in tension and the concrete in compression form an internal couple $C=T=P$ with lever arm $z$ that balances the external moment $M=Pz$. As the load grows, the lever arm (not the force) changes, so the stresses hardly change until cracking — the difference from RCC, where the force grows.
3. Load balancing. The curved tendon exerts an upward force on the concrete that balances part of the external load. A parabolic tendon with sag $e$ gives an equivalent uniform upward load $w_b=8Pe/L^2$ (see the analysis note).

Advantages

• Uncracked section under service load → better durability and stiffness.
• Higher span–depth ratio — lighter, shallower members; economical for long spans and heavy loads.
• High-strength materials are used efficiently (steel is stressed before it is loaded).
• Deflection is small (or even camber under permanent load) and cracks close after overload.
• Better fatigue performance since the stress range in the steel is small.
• Shear is reduced by the inclination of the tendon; watertight for tanks and pressure pipes.
• Precast production is fast and controlled.

Limitations

• Needs high-quality concrete, special steel, jacks, anchorages and skilled workers.
• Losses of prestress must be estimated and allowed.
• Fire resistance is lower for steel that is thinly covered; corrosion of tendons can be sudden and hidden if ducts are poorly grouted.
• Brittle failure if over-reinforced (too much steel).
• Design is more complex — stages, losses, anchorage zones and secondary effects.

Materials

Concrete

Prestressed concrete needs high compressive strength to carry the high pre-compression, to give bond to the tendon and to keep losses due to creep and shrinkage low. Typical minimum grades are M40 for pre-tensioned and M30–M35 for post-tensioned members, often M45–M60 for bridge girders (check the code in use). Requirements:

• high early strength for transfer (usually 70–75 % of the 28-day strength) — achieved with rapid-hardening cement or steam curing;
• low water–cement ratio (about 0.35–0.4), well-graded aggregates and good compaction;
• low shrinkage and creep; a high modulus of elasticity;
• durable, low-permeability concrete with adequate cover.

Prestressing steel

Plain reinforcing bars cannot be used for prestressing: a bar of yield strength 415 N/mm² would lose almost all its prestress to shrinkage and creep of concrete (the strain loss is about 0.0005–0.001; on steel of $E_s=2\times 10^5$ N/mm² this is 100–200 N/mm²). High-tensile steel stressed to 1000–1400 N/mm² keeps most of its prestress after these losses.

Stress–strain behaviour. High-tensile steel has no clear yield plateau; the yield is defined as the 0.2 % proof stress ($\approx 0.85$ of the ultimate). Its modulus of elasticity is about 195–210 kN/mm² for wires and strands (lower for bars). The steel is stressed at jacking to a limit of about 0.8 of its characteristic strength and settles to about 0.7–0.75 after anchoring (check code limits).

Relaxation — the drop in stress in steel held at constant length. It is a function of the initial stress, time and temperature. Ordinary stress-relieved strand relaxes about 5–8 % in 1000 h at 70 % of ultimate, while low-relaxation strand loses only about 2–3 %.

Auxiliary reinforcement

Ordinary mild or high-yield steel is added as non-prestressed reinforcement for shear (stirrups), end blocks (bursting), handling stresses, temperature and shrinkage, and to improve ultimate strength and crack control.