# Torsion Design Based on Thin-Walled Tube Analogy

RazorSharpAustin
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## 10 Questions

Thin-walled tube

### In the thin-walled tube analogy, where is the torsional resistance primarily assumed to be provided from in a cracked reinforced concrete beam?

Outer skin of the cross-section around the stirrups

### When a beam subjected to torsion has cracked, where is the torsional resistance primarily provided in the thin-walled tube analogy?

On the surface around closed stirrups

### What is the approximate threshold for torques that do not cause a structurally significant reduction in either flexural or shear strength?

One-quarter of the cracking torque

(0.75 Acp / Pcp)

### When does cracking occur according to the thin-walled tube analogy?

When the principal tensile stress reaches 0.75 cf * lambda 33.0

(T/2Aot)

### What part of a reinforced concrete beam is neglected in the thin-walled tube analogy for torsion?

"Core" concrete cross-section

"Hollow section"

### Which part of the reinforced concrete beam provides most of the torsional resistance after cracking according to thin-walled tube analogy?

Outer skin of cross section near stirrups

## Study Notes

### Design for Torsion

• The design for torsion is based on the thin-walled tube, space truss analogy.
• In this analogy, the core concrete cross section in a solid beam is neglected.
• A reinforced concrete beam's torsional resistance is provided primarily by closed stirrups and longitudinal bars near the surface after cracking.
• The thin-walled tube analogy assumes the resistance is provided by the outer skin of the cross section, roughly centered on the closed stirrups.

### Idealization of Sections

• Both hollow and solid sections are idealized as thin-walled tubes before and after cracking.

### Torque Limits

• Torques that do not exceed approximately one-quarter of the cracking torque (Tcr) can be ignored.
• Such torques do not cause a structurally significant reduction in flexural or shear strength.

### Cracking Torsion (Tcr)

• Cracking torsion under pure torsion (Tcr) is derived by replacing the actual section with an equivalent thin-walled tube.
• The tube has a wall thickness (t) of (0.75 Acp / Pcp) prior to cracking.
• The area enclosed by the wall centerline (Ao) is equal to (2/3) Acp.

### Cracking Criteria

• Cracking is assumed to occur when the principal tensile stress reaches −c f λ 33.0.
• In a non-prestressed beam loaded with torsion alone, the principal tensile stress is equal to the torsional shear stress (τ = T/(2Aot)).

Learn about the design approach for torsion in beams, which is based on the thin-walled tube space truss analogy. Explore how reinforced concrete beams resist torsion, with a focus on the role of stirrups and longitudinal bars. Understand the concept of torsional resistance in the context of the outer skin of the cross section in the design.

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