Design of steel structures- Flexure members and foundations
- 1. Design of Steel Structures Unit 3 Flexure Members and Foundations
- 2. Introduction to Flexural Members • Flexural members are elements subjected primarily to bending moments. • Typical examples include beams, girders, rafters. • In steel structures, flexural members carry transverse loads and resist deflection, bending, shear, and sometimes torsion. • Behaviour is affected by: Section properties (Z, I, A) Material grade (yield strength fy) Support conditions and restraints
- 3. Types of Flexural Members in Practice • Rolled Sections: I-beams, channels, etc. • Built-up Sections: Plate girders, welded beams. • Encased Beams: Rolled steel beams encased in concrete. • Composite Beams: Steel and concrete working together. • Laterally Restrained Beams: Compression flange braced. • Unrestrained Beams: Compression flange free to move.
- 4. Stress Distribution in Flexural Members • Bending produces compression on one side and tension on the other. • Neutral axis passes through the centroid. • Stress = (M*y)/I → Linear variation across depth. • Design uses plastic or elastic section modulus (Zp or Ze).
- 5. Design Strength of Beams (Clause 8.2.1) For laterally restrained beams: :Design bending strength of the section (in kNm) : Section classification factor • = 1.0 for plastic and compact sections • < 1.0 for semi-compact sections (reduction in moment capacity) : Section modulus • Use Zp : Plastic modulus for plastic/compact sections • Use Ze : Elastic modulus for semi-compact sections fy : Yield strength of steel (MPa), per IS 2062 • : Partial safety factor for material strength (usually 1.10 as per Table 5 IS 800)
- 6. Laterally Restrained Beams • Compression flange is restrained against lateral buckling. • No reduction in bending strength. • Use full plastic or elastic moment capacity. • Ensure local buckling and shear do not govern design.
- 7. Laterally Unrestrained Beams Susceptible to lateral-torsional buckling (LTB). Effective length (LLT) increases due to unbraced length. Reduction in bending capacity: Where: • Md : Design bending strength under LTB • χLT : LTB reduction factor (from IS 800 Annex E) • Ze : Elastic section modulus of the cross-section • fy : Yield strength of material • γm0 : Partial safety factor = 1.10
- 8. Factors Influencing Lateral-Torsional Buckling • Length between restraints • Load position (top, bottom flange) • Section shape (I, box, T) • Warping rigidity • Torsional restraint at supports
- 9. Calculation of λLT (Annex E, IS 800: 2007) Use the following parameter: Where: • λLT : Non-dimensional slenderness ratio for LTB • βb : Classification factor (1.0 for plastic/compact) • Zp : Plastic section modulus • fy : Yield stress • Mcr : Elastic critical moment (depends on effective length, boundary conditions, torsion stiffness)
- 10. Shear Strength Check (Clause 8.4.1.1) Use parameters: • • Av= Shear area (generally web area) • For V > 0.6Vd , reduce Md • Web stiffeners may be required
- 11. Deflection Limits (IS 800 Table 6) Max deflection: • Beams: Span/250 • Cantilevers: Span/100 Check serviceability: Consider live + dead loads
- 12. Encased Beams • Beam fully/partially embedded in concrete • Improves: Fire resistance Load capacity Aesthetics • Design as composite section (IS 800 + IS 456)
- 13. Bolt Design in Beams (Cl. 10.3–10.4) Check for: • Shear strength • Bearing strength • Edge/end distances Where: • Vnsb : Nominal shear strength of bolt • fub : Ultimate tensile strength of bolt material (MPa) • Anb : Net area of bolt at thread root • γmb : Partial safety factor for bolts (usually 1.25) Use HSFG bolts in slip-critical joints
- 14. Welded Connections for Flexural Members • Common: Fillet & butt welds • Fillet weld strength: • Design for bending + shear continuity • Follow IS 816 + IS 800 Cl. 10.5
- 15. Web Bearing & Buckling (Cl. 8.6) • Bearing strength is given by: Where: • b: Width of load bearing • tw : Web thickness • fbw : Permissible bearing stress Use stiffeners if concentrated load is high or web is thin Check for concentrated loads also
- 16. Built-up Beams – Overview • Used when rolled sections are insufficient • Made from plates/welded I-beams • Must design: Component plates Connection stiffness Deflection and buckling Welded Plate Girders • Components: Flanges and web • Use transverse and longitudinal stiffeners • Design welds for shear continuity • Consider fabrication tolerance
- 17. Foundations in Steel Structures
- 18. Introduction to Steel Column Foundations • Column bases form the interface between steel columns and concrete foundations. • Primary functions include: • Transmitting axial loads, bending moments, and shear forces safely to the footing. • Providing anchorage and preventing uplift or overturning. Common types of steel column foundations: • Slab Base (for small axial loads) • Gusseted Base (for large axial loads and moments) • Grillage Foundation (for very large loads and heavy columns)
- 19. Column Bases Column bases transfer loads from steel columns to concrete foundations. Functions: • Spread column load to concrete • Provide anchorage • Resist bending and shear Types: • Slab Base • Gusseted Base • Grillage Foundation Slab Base – Structural Configuration • Consists of a thick steel base plate placed between the column and concrete footing. • Column is welded or bolted to the base plate. • Load is transferred primarily by bearing. • Anchor bolts provide lateral and uplift resistance.
- 20. Design of Slab Base – Load Transfer • Load is transferred by bearing from column to base plate, then to concrete. • Uniform pressure assumed under base: • Check: Area of base plate Bearing pressure ≤ Permissible stress of concrete
- 21. Slab Base Design – Plate Thickness Plate acts as cantilever beyond column face. Check bending of plate using: • M: Moment due to bearing pressure • fy: Yield stress of plate steel • b: Projection beyond column
- 22. Design of Slab Base – Step-by-Step Step 1: Compute factored axial load (P) on column. Step 2: Bearing capacity of concrete pedestal (as per IS 456): Step 3: Calculate required base plate area: Step 4: Choose plate size slightly larger than required area. Step 5: Design thickness of base plate using cantilever projection method: Where: w = bearing pressure a = projection beyond column face fy= yield strength of plate (MPa)
- 23. Welded Slab Base Connection – Design Details • Weld connects column base to base plate. • Type: Fillet weld or groove weld Weld must transfer: Axial load Bending moment (if any) Design weld strength: Where: fwd : design strength of weld Lw : effective weld length γmw : partial safety factor (usually 1.25)
- 24. Bolted Slab Base Connection Base plate is connected to pedestal using anchor bolts. Bolts resist: Uplift (tension) Shear Tension design of bolts: Shear design of bolts: Follow edge and pitch requirements per IS 800: Min. edge distance = 1.7 × bolt diameter Min. pitch = 2.5 × bolt diameter
- 25. Introduction to Gusseted Base • Used when heavy axial loads or moments are present. • Consists of: Base plate Gusset plates Angle cleats Anchor bolts • Provides better stiffness and load distribution. • More economical for large columns compared to increasing plate thickness.
- 26. Design Philosophy – Gusseted Base • Determine factored loads (axial + moment). • Select base plate size to ensure pressure ≤ permissible bearing pressure. • Design gussets and cleats to resist force using: Bolt/weld connection design Plate bending and shear checks • Bolt design: Where: • Vnsb : shear capacity of bolt • Vnpb : bearing capacity of bolt
- 27. Gusseted Base – Load Transfer • Axial load transferred through: Gussets to plate Plate to concrete • Moment resisted by: Eccentric gussets Bolted cleats • Ensure gussets are symmetrical for uniform load path. • Provide adequate fillet welds or HSFG bolts for high-strength transfer.
- 28. Introduction to Grillage Foundation • Used for columns carrying very heavy loads. • Distributes load over large area when SBC is low. • Made of rolled steel I-beams laid orthogonally in layers. • Beams encased in concrete. • No direct soil contact by steel.
- 29. Components of Grillage Foundation • Top Layer: Distributes load from column base. • Bottom Layer: Spreads load to concrete block. • Concrete Block: Transfers load to soil. • Anchor Bolts/Welds: Fix column base to top beams. • Spacing between beams as per IS 800 (minimum 75 mm). • Provide packing plates for uniform load transfer.
- 30. Design of Grillage Foundation • Calculate total load from steel structure. • Determine number and size of grillage beams: • Use bending equation: • Select beams from ISHB/ISMB tables. • Check deflection: • Provide sufficient concrete cover on all sides.
- 31. Summary and Best Practices Select foundation type based on: • Load level • Available area • Soil conditions Use IS 800 + IS 456 for safe design Always check: • Bending • Shear • Bearing • Welds/bolts Ensure proper construction: • Tight anchorage • Uniform bearing • Proper grouting
- 32. Any Query