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Designing Members for Torsion
AISC Education
Overview
This webinar focuses on designing steel members for torsion, aiming to demystify the concept for structural engineers. It covers the fundamentals of torsion in thin-walled open cross-sections, including shear flow and the shear center. The presentation contrasts pure torsion with warping torsion and explains their effects on structural behavior. It then delves into the design criteria and analysis methods outlined in the AISC Steel Construction Manual and Design Guide 9, emphasizing stress checks for normal and shear stresses. Finally, a practical example of a steel lintel supporting a wall and facade is used to illustrate the application of these principles and available tools for calculating torsional demands and stresses.
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Chapters
- Torsion in structural design is often avoided due to its complexity, but understanding it is crucial for safe and efficient engineering.
- This webinar aims to make torsion design more accessible by relating it to fundamental mechanics principles.
- The content is based on presentations developed with colleagues and draws from key AISC resources like Design Guide 9.
- The goal is to equip designers with the tools and knowledge to confidently address torsion when encountered.
Many engineers find torsion challenging, leading to potential oversights in design. This chapter sets the stage for understanding why torsion is important and how this presentation will help overcome common fears associated with it.
The speaker mentions that previous presentations on torsion were surprisingly well-attended, indicating a widespread need for this topic.
- Torsion is defined as the twisting of an object due to an applied torque, resulting in shear stresses within the cross-section.
- The fundamental equation for pure torsion in a solid round shaft is derived by relating applied torque (T), length (L), shear modulus (G), and the torsion constant (J) to the angle of twist (θ): θ = TL/GJ.
- This equation is analogous to beam bending, with both involving relationships between applied loads, material properties, and deformations.
- Thin-walled open sections (like I-beams and channels) behave differently under torsion compared to solid round bars, introducing complexities like shear flow and warping.
Understanding the basic mechanics of torsion, including its governing equations and how it relates to familiar concepts like beam bending, is essential before tackling more complex thin-walled sections.
The speaker uses the analogy of twisting two fists together to illustrate the shear stresses generated in a cross-section during torsion.
- Thin-walled open sections, unlike solid bars, require consideration of shear flow, which is the distribution of shear stress around the cross-section.
- The shear center is a critical point in a cross-section; if a load is applied through this point, it will not induce twisting.
- For open sections, the shear center often does not coincide with the geometric centroid, making load application critical.
- The torsion constant (J) for thin-walled sections is calculated differently than for solid sections and is often referred to as the torsional rigidity.
These concepts are fundamental to analyzing how open cross-sections respond to torsional loads, as their behavior deviates significantly from simpler solid shapes.
The speaker uses arrows on diagrams of I-beams, channels, and Z-shapes to visually represent the direction and flow of shear stresses.
- Pure torsion (or St. Venant torsion) involves in-plane shear stresses and assumes plane sections remain plane.
- Warping torsion occurs when cross-sections distort out-of-plane during twisting, leading to additional normal and shear stresses.
- All thin-walled sections have a tendency to warp; the significance depends on whether this warping is restrained.
- Warping can be related to beam bending, where the flanges of an I-section act like small beams bending out-of-plane.
Distinguishing between pure torsion and warping torsion is crucial because warping introduces additional stresses that must be accounted for in design, especially when cross-sectional distortion is restrained.
The speaker uses an analogy of an I-section's flanges acting as small beams that bend out-of-plane when the overall section twists, illustrating the concept of warping.
- While Design Guide 9 suggests avoiding torsion if possible due to the inherent torsional weakness of open sections, certain situations necessitate its consideration.
- Examples in buildings include ledger beams supporting joists with eccentric reactions and facade support systems creating torsional moments.
- In bridges, horizontally curved members and skewed supports under certain loads can induce significant torsion.
- Ignoring torsion in these scenarios can lead to structural failures, highlighting the importance of proper analysis.
Recognizing when torsion is unavoidable is the first step toward applying the correct design procedures and preventing potential failures.
The speaker shows images of structural failures, including the Bailey Building collapse and the Marcy Bridge incident, suggesting that torsional effects were contributing factors.
- AISC specifications address torsion primarily through stress checks, treating it as an analysis problem.
- For closed sections (HSS), torsion is included in interaction equations, but its effect is somewhat mitigated due to their inherent torsional stiffness.
- For open sections, design involves calculating cumulative normal and shear stresses due to axial load, bending (strong and weak axis), and warping.
- Design Guide 9 provides detailed methods and tools, including tables and plots, to calculate these stresses and their derivatives, simplifying the analysis.
This chapter bridges the theoretical concepts to practical design application by outlining the codified requirements and the analytical approach prescribed by AISC.
The speaker references Article H3.2 in the AISC specification for how torsion is incorporated into interaction equations for HSS sections.
- Calculating torsional stresses involves combining stresses from direct torsion (shear) and warping (shear and normal).
- Warping stresses are related to the third derivative of the angle of twist, while direct torsion involves the first derivative.
- Design Guide 9's appendices provide torsional properties (like warping constant) and plots of twist angle derivatives for various loading and boundary conditions.
- Simplified formulas for I-shapes are available in DG9, equating flange behavior to that of a rectangular beam in bending, offering a more accessible approximation.
Understanding how to calculate the various stress components and utilizing the provided design aids are essential for performing accurate torsional analysis.
The speaker explains that Appendix B of Design Guide 9 contains plots showing the variation of the angle of twist and its derivatives along the length of a member for different scenarios.
- A 15-foot steel lintel supporting a CMU wall and a facade is analyzed for torsional effects.
- The analysis involves defining loads (dead load is considered for simplicity), structural system, boundary conditions, and material properties.
- The process includes calculating demands from direct shear, bending, torsion, and axial loads.
- The core of the analysis is determining the angle of twist and its derivatives to calculate cumulative stresses using DG9 equations.
This practical example demonstrates the step-by-step application of the principles and tools discussed throughout the webinar to a real-world design problem.
The example focuses on a steel lintel supporting a CMU wall and a facade, where the facade load is applied eccentrically, inducing torsion in the lintel.
Key takeaways
- Torsion is a critical design consideration for thin-walled open steel sections that should not be ignored when loads are applied eccentrically or when specific geometric conditions exist.
- Understanding the difference between pure (St. Venant) torsion and warping torsion is key, as warping introduces additional stresses that can be significant if restrained.
- The shear center is a vital concept; loads applied through it do not induce torsion, but its location must be determined for open sections.
- AISC Design Guide 9 is an indispensable resource for engineers needing to analyze and design for torsion, providing properties, methods, and calculation aids.
- The design process for torsion primarily involves calculating cumulative stresses (normal and shear) from all load effects (axial, bending, shear, and torsion) and comparing them to code limits.
- While complex, the analysis of torsion can be simplified by using the tools and methodologies provided in AISC publications and by relating the behavior to fundamental mechanics principles.
- Properly defining boundary conditions and understanding how they affect twist and warping is crucial for accurate torsional analysis.
Key terms
TorsionTorqueShear FlowShear CenterTorsion Constant (J)WarpingPure Torsion (St. Venant Torsion)Warping TorsionTorsional StiffnessDesign Guide 9
Test your understanding
- What is the fundamental difference between pure torsion and warping torsion, and why is this distinction important in structural design?
- How does the concept of the shear center influence the design of members subjected to torsional loads, particularly for open cross-sections?
- Describe the primary steps involved in analyzing a steel member for torsion according to AISC guidelines, referencing Design Guide 9.
- Explain the role of warping in the torsional behavior of thin-walled open sections and how it contributes to the overall stress state.
- Under what typical structural conditions might torsion become a significant design consideration that cannot be ignored?