Understanding Cracking in Deep Beams and Thin Webbed Members

In reinforced concrete (R.C.C.) members, cracks are indicators of stresses exceeding the material's capacity in certain areas. The type and location of the first crack formed depend heavily on the geometry of the member and the type of loading.

Why Deep Beams and Thin Webbed Members are Different

Deep beams are structural members where the depth is comparable to the span (typically, the span-to-depth ratio is small, e.g., less than 2 to 4 depending on codes and loading conditions). Thin webbed members, like those found in box girders or some pre-stressed beams, have a relatively slender web area connecting thicker flanges.

Unlike slender beams where flexural bending stresses are dominant, deep beams and thin webbed members experience significant shear stresses, especially in the web region. These shear stresses interact with normal stresses to create principal stresses.

Principal Stresses and Crack Formation

Under shear loading, diagonal tensile stresses are induced in the concrete. The orientation of these principal tensile stresses is typically at an angle (around 45 degrees in a state of pure shear) to the longitudinal axis of the beam.

Concrete is much weaker in tension than in compression. Therefore, when the diagonal tensile stress induced by shear exceeds the tensile strength of the concrete, the concrete will crack along planes perpendicular to the direction of this maximum principal tensile stress. These cracks are known as diagonal tension cracks or shear cracks.

First Crack in Deep Beams

In deep beams and thin webbed R.C.C. members, because of the high shear-to-moment ratio and the significant shear stresses developed, the diagonal tensile stresses can reach the tensile strength of concrete before the flexural tensile stresses do (which would cause flexural cracks). This is why the first crack observed in these members is often a diagonal crack, originating in the web and inclined towards the support.

Comparing Crack Types

• Flexural cracks: Caused by bending moment, appearing perpendicular to the beam axis, typically starting at the tension face in regions of maximum moment.
• Shear cracks (Diagonal tension cracks): Caused by shear forces, appearing as inclined cracks (diagonal) in the web region. They are a result of concrete failing in tension under diagonal principal stress.
• Diagonal cracks due to compression: Less common as an *initial* crack type. Compression failure typically leads to crushing or spalling, not diagonal cracks due to compression itself, although inclined cracks can occur under high compressive stress due to complex stress states or buckling in thin webs.

Given the characteristics of deep beams and thin webbed members where shear effects are predominant, the failure criterion governed by concrete's low tensile strength under diagonal tension is reached first.

Therefore, the first crack formed in deep beams or thin webbed R.C.C members is a diagonal crack due to tension.

Conclusion

Based on the structural behavior of deep beams and thin webbed R.C.C. members, the dominant failure mode initiating cracking is related to shear. Shear forces induce significant diagonal tensile stresses in the concrete web. Since concrete is weak in tension, it cracks when this diagonal tension exceeds its tensile strength. This results in the formation of diagonal cracks. Thus, the first crack formed is a diagonal crack due to tension.

Revision Table: Deep Beam Cracking

Additional Information: Reinforced Concrete Cracking

Understanding crack patterns is crucial in reinforced concrete design and assessment. Different crack types indicate different structural issues:

• Flexural Cracks: Normal and expected under service loads in tension zones of beams and slabs. Controlled by reinforcement spacing.
• Shear Cracks: Can be more critical than flexural cracks, especially if they propagate and widen, indicating potential shear failure, which is often brittle. Shear reinforcement (stirrups) is provided to resist these diagonal tensile stresses after cracking initiates.
• Torsional Cracks: Caused by twisting moments, typically appear as spiral or inclined cracks on the faces of the member.
• Shrinkage Cracks: Occur due to concrete volume change (drying shrinkage), not directly related to load. Often irregular or random patterns.
• Settlement Cracks: Occur due to differential settlement of fresh concrete around reinforcement or other elements before hardening.

In the context of load-induced cracks, flexural and shear (diagonal tension) cracks are the primary types. For deep beams and thin webbed members, shear governs the initiation of the first crack due to the high diagonal tensile stresses.