Short Answer:

Shear strength in prestressed concrete beams is determined by considering the concrete’s own ability to resist shear and the contribution of prestressing tendons and shear reinforcement (like stirrups). Prestressing helps by introducing compressive forces that reduce the diagonal tension caused by shear.

The total shear strength is calculated using code-based formulas that include the effects of concrete strength, tendon profile, prestressing force, and additional reinforcement. Proper shear strength ensures the beam does not fail due to diagonal cracking or sudden collapse near supports.

Detailed Explanation:

Shear strength in prestressed concrete beams

In prestressed concrete beams, shear forces arise due to loads acting perpendicular to the beam’s axis, especially near supports. If not properly accounted for, these forces can cause diagonal tension cracks, which are dangerous and can lead to sudden failure. Determining shear strength is a vital part of structural design, ensuring safety and serviceability of the beam.

Unlike in normal reinforced concrete beams, prestressed concrete beams benefit from the compressive forces introduced by prestressing, which help to control shear cracking. The prestressing tendons (especially when profiled or curved) also contribute to the shear resistance by creating vertical components of force that counteract the external shear.

How shear strength is determined

1. Concrete Contribution (Vc):
   The basic shear strength provided by the concrete is influenced by:

• Grade of concrete (higher grade = more strength)
• Depth of the beam
• Prestressing level
• Axial compressive stress from prestressing force

In prestressed beams, the clamping effect due to prestress compresses the concrete and reduces the chances of diagonal tension cracks, thus improving shear strength.

2. Prestressing Tendon Contribution (Vp):
   If the tendons are curved (with vertical component), they help resist shear directly. The upward force from a sloped tendon can counteract part of the external shear force. This component is especially useful near supports where shear is high.
3. Shear Reinforcement Contribution (Vs):
   Stirrups or shear reinforcement are provided to:

• Prevent propagation of diagonal cracks
• Carry excess shear beyond concrete’s capacity

They are calculated based on the spacing, size, and yield strength of the stirrups.

4. Total Shear Strength (Vtotal):
   Vtotal=Vc+Vp+VsV_{total} = V_c + V_p + V_sVtotal​=Vc​+Vp​+Vs​

This total is compared with the applied shear force from loading. If Vtotal≥VappliedV_{total} \geq V_{applied}Vtotal​≥Vapplied​, the beam is considered safe in shear.

5. Design Standards:
   Codes like IS 1343, ACI 318, or Eurocode provide formulas and limits for each component based on experimental and theoretical research. These standards ensure conservative and safe designs.
6. Cracking Considerations:
   Even if shear strength is sufficient, crack control is also important. Spacing and detailing of stirrups must ensure cracks remain within allowable limits.

Conclusion:

Shear strength in prestressed concrete beams is calculated by combining the resistance offered by concrete, prestressing tendons, and stirrups. Prestressing not only strengthens the beam but also improves shear resistance by introducing beneficial compressive forces and upward components through curved profiles. Accurate design based on codes ensures structural safety and durability.