Shear and Torsion in PSC

Shear in prestressed concrete is treated like RCC but with the important benefit that the axial precompression delays diagonal cracking, raising the concrete contribution V_c. The design follows V_u = V_c + V_s, with shear reinforcement supplying the excess.

Two cracking modes are distinguished: web-shear cracking in high-shear low-moment regions near supports, and flexure-shear cracking where flexural cracks develop into inclined cracks. IS 1343 gives expressions for each, and the lower governs.

The end (anchorage) zone is a special concern in post-tensioning: the concentrated tendon force spreads out and creates transverse bursting tension that must be resisted by end-zone reinforcement, a topic examiners often pair with the shear discussion.

(IS 456 approach extended to PSC)

Relation 1 —

(IS 456 approach extended to PSC)

Write this relation with symbols exactly as in Prestressed Concrete — N. Krishna Raju before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Relation 2 —

Write this relation with symbols exactly as in Prestressed Concrete — N. Krishna Raju before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Relation 3 —

Write this relation with symbols exactly as in Prestressed Concrete — N. Krishna Raju before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Precompression from prestress increases the principal tensile stress required to cause diagonal cracking, so a prestressed web resists more shear before cracking than an equivalent reinforced-concrete web. This is why V_c is higher in PSC.

Web-shear cracking governs near supports where shear is high and moment low; the concrete carries shear until the principal tension reaches the tensile strength. Flexure-shear cracking governs in regions of combined high shear and moment, initiating from a flexural crack.

Once cracked, additional shear is carried by stirrups (and sometimes inclined or vertical prestress) through the truss analogy, giving V_s. The total design shear capacity is V_c + V_s, and a maximum limit prevents web crushing.

Under combined shear and torsion, the torsional shear stress adds to the flexural shear on one face; the design combines them into an equivalent shear or equivalent moment, and closed stirrups plus longitudinal steel resist the torsion. The end block requires bursting reinforcement to contain the anchorage-zone tension.

State assumptions explicitly before using any relation for shear and torsion in psc — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.

Wrong assumptions invalidate the entire solution even when the formula is correct. In Prestressed Concrete viva and GATE descriptive questions, listing valid assumptions often earns separate marks.

1. Read the question and list given data with SI units (common in Prestressed Concrete papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to shear and torsion in psc.
4. Use equation 1: .
5. Use equation 2: .
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.

Shear and Torsion in PSC appears in long-span bridges and parking floors. In Indian civil curricula this topic is tested because it connects theory to PSC beams and loss calculations.

GATE and semester exams often combine shear and torsion in psc with earlier units — revise prerequisites before attempting mixed problems.

Industry interview panels sometimes ask: "Where did you use shear and torsion in psc?" — answer with a lab, mini-project, or plant visit example if possible.

• Using the RCC value of V_c and ignoring the enhancement from precompression.
• Checking only flexure-shear and missing web-shear near supports (or vice versa).
• Neglecting end-zone bursting reinforcement in post-tensioned members.
• Treating torsion and shear separately instead of combining them.

Before attempting shear and torsion in psc problems, confirm you can:

1. Prestress improves shear capacity via axial compression
2. Vertical prestress or stirrups provide V_s after cracking
3. End zone bursting stresses need bearing reinforcement

Revise the solved examples in Prestressed Concrete — N. Krishna Raju and one previous-year GATE or university paper for this unit.