Design of Steel Structures (CE-801) - Unit 2 Short Notes

UNIT 2: DESIGN OF STEEL STRUCTURES - SHORT NOTES

1.0 INTRODUCTION & MATERIAL PROPERTIES

1.1 Advantages of Structural Steel over Cast Iron & Wrought Iron

• High Strength & Ductility: High yield stress ($$\displaystyle f_y $$) and ultimate stress ($$\displaystyle f_u $$) with significant plastic deformation before failure.

• Uniformity & Predictability: Homogeneous, isotropic material properties; consistent quality.

• High Strength-to-Weight Ratio: Enables long spans and lightweight structures.

• Ductile Failure: Gives visible warning (buckling, deformation) before collapse, unlike brittle cast iron.

• Fabrication & Erection: Easy to cut, drill, bolt, weld; prefabricated; rapid on-site assembly.

• Reusability & Recyclability: Can be dismantled and reused; 100% recyclable.

• Cast Iron: Brittle, weak in tension, not weldable, heavy.

• Wrought Iron: Low strength, expensive, labor-intensive production (obsolete).

1.2 Mechanical Properties (Key for Design)

• Yield Stress ($$\displaystyle f_y $$): Stress at which permanent deformation begins. Design basis in LSM.

• Ultimate Stress ($$\displaystyle f_u $$): Maximum stress material can withstand.

• Modulus of Elasticity ($E$): ~200 GPa for steel. Used in deflection and buckling calculations.

• Poisson's Ratio ($\nu$): ~0.3.

• Partial Safety Factor ($$\displaystyle \gamma_{m0} $$): 1.1 (IS 800:2007) for $$\displaystyle f_y $$ in LSM.

1.3 Grades of Steel (IS 2062)

2.0 CONNECTIONS (HIGH FREQUENCY)

2.1 Bolted Connections

• Types:

  • Lap Joint: Single/double, simple, but eccentric.

  • Butt Joint: Single cover, double cover (reduces eccentricity, preferred).

  • Tee Joint: Beam to column flange.

  • Framed Connection: Beam web connected to column flange/web (seated).

  • Seated Connection: Seat angle supports beam bottom flange.

• Bolt Types & Grades:

  • Black Bolts (Grade 4.6): $$\displaystyle f_u = 400 $$ MPa, $$\displaystyle f_y = 0.6 f_u = 240 $$ MPa. Bearing type.

  • HSFG Bolts (Grade 8.8, 10.9): High strength, slip-resistant (friction type). Tightened to proof load.

• Failure Modes of Bolted Joints:

  [!TIP] EXAM TIP: Sketch & explain each. Order of design: Bolt shear → Bearing → Net section.

  1. Bearing Failure of Plate: Crushing of plate around bolt hole. Controlled by bearing strength.

  2. Net Section Failure of Plate: Tearing along net section ($$\displaystyle b_{net} = p \cdot t $$). Controlled by tensile strength.

  3. Bolt Failure: Shear rupture of bolt shank or tension rupture of bolt.

  4. Edge Failure (Shear-out): Plate tears out between bolt row and edge. Prevent by $$\displaystyle e_{min} \geq 1.25d $$ (IS 800).

• Design Strength of Bolts:

  • Shear Strength (Single Bolt): $$\displaystyle V_{sb} = \frac{f_u}{\sqrt{3} \gamma_{mb}} \cdot A_{sb} \cdot n_s $$

    • $$\displaystyle A_{sb} = \frac{\pi}{4} d^2 $$ (shank area), $$\displaystyle n_s $$ = number of shear planes.

  • Bearing Strength: $$\displaystyle F_b = 2.5 k_b d t f_u / \gamma_{mb} $$

    • $$\displaystyle k_b = \min\left( \frac{e}{3d_0}, \frac{p}{3d_0} - 0.25, \frac{f_{ub}}{f_u}, 1 \right) $$

  • Tensile Strength: $$\displaystyle T_{tb} = \frac{0.9 f_u A_{sb}}{\gamma_{mb}} $$

• Design of Bolted Joint:

  1. Calculate design force per bolt.

  2. Check shear, bearing, and tensile capacities.

  3. Determine pitch (p) and gauge (g) from standard tables (IS 800: Table 19).

  4. Ensure edge distance ($e$) and end distance ($$\displaystyle e_e $$) $\geq 1.25d$ (minimum).

  5. Check net section of plate.

• Efficiency of Bolted Joint: $$\displaystyle \eta = \frac{\text{Strength of joint with holes}}{\text{Strength of solid plate}} \times 100\% $$. Governed by net section failure.

• Bearing Type vs. Friction Type (Slip-resistant):

  | Feature | Bearing Type (Black Bolt) | Friction Type (HSFG) | | :--- | :--- | :--- | | Mechanism | Bearing + shear | Friction resistance | | Hole Tolerance | Normal (1.5-2 mm clearance) | Tight (0.2-0.3 mm clearance) | | Slip | Allowed at service load | No slip at service load | | Use | General, statically loaded | Dynamic, seismic, fatigue |

2.2 Welded Connections

• Types:

  • Fillet Weld: Triangular, most common. Effective throat thickness $$\displaystyle t_e = 0.7 \times \text{leg size} $$.

  • Groove Weld: Butt, corner, edge, V/U-grooves. For full strength.

• Shop vs. Site Welding: Shop (controlled, quality) vs. Site (weather dependent, access).

• Design Strength of Fillet Weld:

  • Per unit length: $$\displaystyle f_w = \frac{f_u}{\sqrt{3} \gamma_{mw}} $$ (IS 800:2007)

  • Total Strength: $$\displaystyle R_t = f_w \times l \times t_e $$

  • $l$ = effective length (≥ 4 × leg size, minus 2 × root gap).

• Design of Welded Joints for Tension Members:

  • Weld Strength ≥ Tensile Strength of Member.

  • Overlap (l): $$\displaystyle l \geq \text{max}(t_1, t_2) + 40 $$ mm (IS 800: Cl. 10.5.2.2).

  • Weld on three sides (two sides + end) is more efficient than two sides only.

• Advantages over Riveted/Bolted: No holes → no stress concentration, rigid, economical, better fatigue.

• Disadvantages: Requires skilled labor, inspection difficult, residual stresses, brittle fracture risk.

2.3 Pin Connections

• Definition: Hinged connection allowing free rotation. Pin is a high-strength steel rod.

• Characteristics: Simple, accommodates movement, used where moment is zero or minimal.

• Common Types: Pinned column base, bridge truss joints (pin-connected), gantry girder ends.

2.4 Lug Angles

• Purpose: Used in tension member connections when gusset plate is narrow or member is long. Provides additional bolts away from end.

• Application: Single angle tension member connected to gusset plate.

• Sketch:

  DiagramSEARCH: "lug angle connection steel structure"

  • Lug angle (small angle) welded to main angle.

  • Bolts placed on lug, away from critical section.

3.0 TENSION MEMBERS (HIGH FREQUENCY)

3.1 Design Strength of Tension Members

• Gross Section Yielding: $$\displaystyle T_{dg} = A_g f_y / \gamma_{m0} $$

• Net Section Rupture: $$\displaystyle T_{dn} = (0.9 A_{net} f_u) / \gamma_{m1} $$

  • $$\displaystyle A_{net} = \text{gross area} - \text{area of holes} $$.

  • For staggered holes, use reduced net section formula.

• Design Strength: $$\displaystyle T_d = \min(T_{dg}, T_{dn}, T_{db}) $$ (Block Shear)

3.2 Factors Affecting Strength

• Net Area: Holes reduce area; pitch, gauge, stagger.

• Shear Lag: Reduction in effective net area for single angle or flange of T-section.

• Block Shear: Combined tension on net section and shear on gross section.

3.3 Block Shear Failure (IS 800:2007)

• Mechanism: Rupture along a "block" (tension on net section + shear on gross section).

• Formula: $$\displaystyle T_{db} = \frac{(A_{gn} f_y / \gamma_{m0}) + (0.9 A_{tn} f_u / \gamma_{m1})}{1.25} $$

  • $$\displaystyle A_{gn} $$: Gross area in shear.

  • $$\displaystyle A_{tn} $$: Net area in tension.

• Critical for: Angles, Tees, channels with bolt holes near web/flange junction.

3.4 Design of Single Angle Tension Members

• Reversed Stresses (Wind): Design for compression in the other direction.

  • Use effective length $$\displaystyle L_{eff} = L $$ (for wind only, no gravity).

  • Check slenderness ratio $$\displaystyle \lambda = L_{eff} / r_{yy} $$ (about minor axis).

  • Use single angle section tables (IS 800: Table 10) with reduced design strength.

• No Reversal: Design only for tension (yielding/rupture).

3.5 Design of Double Angle Tension Members (Struts)

• Back-to-Back: Long legs connected (common), short legs connected.

• Tack Bolts: Required at intervals (≤ 600 mm) to hold angles together.

• Gusset Plate Connection: Welded or bolted.

• Design Steps:

  1. Calculate design load $T$.

  2. Select trial double angle section.

  3. Calculate design tensile strength considering shear lag.

     • For long legs connected: $$\displaystyle A_{net} = 2(A_g - t \times \text{no. of holes}) $$

     • For short legs connected: $$\displaystyle A_{net} = 2(A_g - 2t \times \text{no. of holes}) $$ (both legs affected).

  4. Check $$\displaystyle T_d \geq T $$.

  5. Design connection (bolts/weld) to gusset.

3.6 Shear Lag Concept

• Definition: Non-uniform stress distribution in tension members with disconnected flanges/legs.

• Effect: Effective net area $$\displaystyle A_{net,eff} < A_{net} $$.

• Formula (Single Angle): $$\displaystyle A_{net,eff} = A_{net} \cdot \beta $$

  • $$\displaystyle \beta = 1 - \frac{\bar{x}}{2b_c} $$ (for long leg connected)

  • $\bar{x}$: distance of CG from connected leg, $$\displaystyle b_c $$: width of connected leg.

• Diagram:

  DiagramCANVAS: "Shear lag in single angle tension member. Show stress concentration at connection, lower stress at free tip. Label connected leg, free leg, CG, stress distribution curve."

3.7 Efficiency of Bolted Joint

• $$\displaystyle \eta = \frac{T_{dn}}{T_{dg}} \times 100\% = \frac{A_{net} f_u}{A_g f_y} \times \frac{\gamma_{m0}}{\gamma_{m1}} \times 100\% $$.

• For Fe 410: $$\displaystyle \eta \approx \frac{A_{net}}{A_g} \times \frac{410}{250} \times \frac{1.1}{1.25} \approx 1.44 \frac{A_{net}}{A_g} $$.

4.0 COMPRESSION MEMBERS (HIGH FREQUENCY)

4.1 Types

• Rolled I-Sections: ISHB, ISMB, ISLB. Most efficient.

• Built-up Sections:

  • Laced Columns: Two channels/angles back-to-back with lacing.

  • Battened Columns: Two channels/angles with batten plates.

4.2 Buckling Modes

1. Flexural Buckling: About minor/major axis (most common).

2. Torsional Buckling: For open sections with low torsional stiffness.

3. Flexural-Torsional Buckling: For singly symmetric sections (channels, angles) under axial load.

4.3 Slenderness Ratio & Effective Length

• $$\displaystyle \lambda = \frac{L_{eff}}{r} $$ (for both axes, use max).

• $$\displaystyle L_{eff} = K \times L $$ (K depends on end conditions).

  • Hinged-Hinged: K=1.0

  • Fixed-Fixed: K=0.7

  • Fixed-Free: K=2.0

• IS 800:2007: Use non-dimensional slenderness ratio $$\displaystyle \lambda_{nn} = \sqrt{\frac{f_y}{f_{cr}}} $$ for design curves.

4.4 Design of Laced Columns

• Single Lacing: Lacing in one direction. Angle sections in tension (usually).

• Double Lacing: Lacing in both directions (X-type). Angles in alternate compression/tension.

• Design of Lacing:

  • Tension Lacing: Check $$\displaystyle T_{dlacing} \geq \text{force in lacing} $$.

  • Compression Lacing: Check buckling (slenderness limit $\leq 50$ for single, $\leq 80$ for double).

  • Connection: Welded or bolted to chords. End connections must resist shear + moment.

• Spacing: $S \leq 40 \times \text{least radius of gyration of chord}$ and $$\displaystyle \leq \frac{L}{2} $$.

4.5 Design of Battened Columns

• Batten plates (flat plates) placed alternately on both sides.

• Batten Design: Check for bending and shear.

• Batten Thickness: $$\displaystyle t_b \geq \frac{l_b}{50} $$ (IS 800: Cl. 7.7.2).

• Batten Width: $$\displaystyle b_b \geq \frac{a}{2} $$ (a = distance between centroids of chords).

4.6 Column Splices

• Welded Splice: Full strength weld. Flanges and web welded.

• Bolted Splice: Flange plates and web plates with bolts. Used for site splicing.

• Purpose: Maintain continuity, transfer axial load & moment.

4.7 Plastic, Compact, Semi-Compact, Slender Sections (IS 800:2007)

• Based on width-to-thickness ratios ($b/t$, $$\displaystyle d/t_w $$) compared to limits ($$\displaystyle \lambda_p, \lambda_r $$).

• Plastic: Can develop plastic moment ($$\displaystyle M_p $$) before local buckling.

• Compact: Can develop yield moment ($$\displaystyle M_y $$) before local buckling.

• Semi-Compact: Local buckling occurs before yield moment, but after elastic buckling.

• Slender: Local buckling occurs at stress < yield.

• Design Implication: Use appropriate design stress ($$\displaystyle f_{cd} $$) from Table 5 (IS 800) based on section class.

5.0 BEAMS (HIGH FREQUENCY)

5.1 Laterally Restrained vs. Unrestrained Beams

• Laterally Restrained: Compression flange fully restrained against lateral movement (by slab, deck, bracing). No Lateral Torsional Buckling (LTB). Design for bending & shear only.

• Laterally Unrestrained: Compression flange free to move laterally. Susceptible to LTB. Design must consider LTB.

• Conditions for Lateral Restraint: Concrete slab on top, profiled deck with shear connectors, transverse bracing at intervals.

5.2 Design Steps for Laterally Supported Beams

1. Calculate $$\displaystyle M_u $$, $$\displaystyle V_u $$.

2. Select trial I-section.

3. Check bending strength: $$\displaystyle M_{cd} = \beta_b Z_p f_{cd} $$ (plastic) or $$\displaystyle \beta_b Z_e f_{cd} $$ (elastic). $$\displaystyle \beta_b $$ = 1.0 for fully restrained.

4. Check shear strength: $$\displaystyle V_{cd} = A_w f_{cd} / (\sqrt{3} \gamma_{m0}) $$.

5. Check deflection (if required).

6. Check web buckling (if concentrated load) → provide vertical stiffeners.

5.3 Plate Girders

• Elements:

  DiagramSEARCH: "plate girder components labelled"

  • Web: Carries shear, thin (subject to buckling).

  • Flanges: Carries bending moment.

  • Stiffeners:

    • Vertical: Prevent web buckling (under shear/compression).

    • Horizontal (Longitudinal): Prevent flange buckling into web.

    • Bearing Stiffeners: At supports (concentrated load).

• Design Considerations:

  • Depth: Usually 1/10 to 1/20 of span.

  • Flange Width/Thickness: Check local buckling (class 1/2).

  • Web Thickness: Check shear and buckling.

• Stiffener Design: Based on sub-panel of web. Use effective area concepts.

5.4 Gantry Girders

• Profile: I-section with top flange extended as cantilever (to resist lateral load from crane).

• Section Selection: Based on maximum bending moment (from crane load + self-weight).

• Deflection Limits (IS 800):

  • Vertical Deflection: $L/500$ (under crane load).

  • Lateral Deflection: $L/1000$ (under crane lateral force).

• Crane Load Considerations: Impact factor (25-50%), repeated loading (fatigue check).

5.5 Beams with RC Slabs (Composite Action)

• Definition: Steel beam + concrete slab act together as a composite beam.

• Mechanism: Shear connectors (studs) transfer shear, prevent slip.

• Benefit: Increased moment capacity (plastic stress distribution in slab in compression).

• Design: Use transformed area method or plastic theory (IS 11384).

6.0 FOUNDATIONS & BASES (HIGH FREQUENCY)

6.1 Slab Base (Un-gusseted Base)

• Components: Base plate, anchor bolts, fillet welds.

• Design:

  1. Bearing Pressure: $$\displaystyle p = \frac{P}{A_{base}} \pm \frac{M}{Z_{base}} \leq f_{bc} $$ ( allowable bearing on concrete).

  2. Base Plate Thickness: Based on yield line theory.

$$t_p = \sqrt{\frac{2.5 P}{f_y \times \text{perimeter of column}}}$$

3.  **Weld Design:** Fillet weld to transfer axial load & moment.

6.2 Gusseted Base

• Components: Base plate, gusset plates, stiffeners, anchor bolts.

• Use: For heavy loads or eccentric loading.

• Design for Axial Load with Eccentricity:

  1. Calculate pressure distribution (linear if $$\displaystyle e < \frac{B}{6} $$).

  2. Design base plate for bending (thickness).

  3. Design gusset plates & stiffeners for compression/tension from eccentricity.

  4. Design anchor bolts for tension (if uplift).

6.3 Grillage Foundation

• Purpose: Distribute heavy column load to larger soil area.

• Elements: Top flange (under base plate), cross beams, bottom flange (on concrete).

• Design with I-Sections:

  1. Assume load distribution (45° spread).

  2. Design top flange (I-section) for bending.

  3. Design cross beams (I-section) for bending.

  4. Check bearing pressure on soil $$\displaystyle < \text{allowable} $$.

  5. Provide concrete block to hold grillage.

7.0 ROOF TRUSSES & PURLINS (HIGH FREQUENCY)

7.1 Roof Trusses

• Common Types:

  DiagramSEARCH: "pratt warren fink king post queen post roof truss"

  • Pratt: Diagonals in tension (downward slope).

  • Warren: No verticals, diagonals alternating.

  • Fink: For steep roofs, web subdivided.

  • King Post: Central vertical in tension.

  • Queen Post: Two central verticals.

• 10 Components (Sketch & Explain):

  1. Top Chord: Compression member (rafter).

  2. Bottom Chord: Tension member (tie).

  3. Web Members: Diagonals/verticals (tension/compression).

  4. Joints: Typically gusset plates (welded/bolted).

  5. Purlins: Horizontal members supporting roof covering.

  6. Rafters: May be separate or part of top chord.

  7. Bracing: Portal/roof bracing for stability.

  8. Gusset Plates: Connect chords/webs at joints.

  9. Anchor Bolts: Fix truss to supports.

  10. Sleeves: For splicing chords at site.

7.2 Purlins

• Function: Horizontal members supporting roof sheeting (corrugated sheets), spaced along truss slope.

• Placement: On rafters (sloping), at regular c/c spacing (1-2 m).

• Design Loading:

  • Dead Load: Weight of sheeting + purlin self-weight.

  • Live Load: Maintenance access.

  • Wind Load: Suction (uplift) or pressure. Critical for design.

  • Load Calculation: Loads are normal to roof slope. Resolve into perpendicular and parallel components. Design for bending about major axis.

• Design as Simply Supported Beam: Span = purlin spacing.

  1. Calculate UDL (total load).

  2. Calculate $$\displaystyle M_u $$, $$\displaystyle V_u $$.

  3. Select I-section (usually C-section or Z-section).

  4. Check bending & shear.

  5. Check deflection (L/200 for purlins).

• Spacing: Based on sheeting type and span. Typically 1.0-1.8 m.

8.0 SPECIAL TOPICS & CONCEPTS

8.1 WSM vs. LSM (IS 800:2007)

8.2 Shear Lag (Diagrammatic)

See 3.6 above.

DiagramCANVAS: "Rectangular bar with central bolt. Show uniform stress in gross section, but stress lines 'lag' behind in net section near hole. Label 'disconnected' portion where stress is lower."

8.3 Block Shear Failure (Detailed)

• Path: Tension rupture along net section + shear rupture along gross section.

• Formula (IS 800:2007): $$\displaystyle \boxed{T_{db} = \frac{(A_{gn} f_y / \gamma_{m0}) + (0.9 A_{tn} f_u / \gamma_{m1})}{1.25}} $$

• Critical for: Angles, Tees, channels with bolt lines near web-flange junction.

• Check: $$\displaystyle T_{db} < T_{dn} $$ (net section) often governs.

8.4 Failures of Bolted Joints (with Sketches)

See 2.1.3. Sketches should show:

1. Bearing: Punching shear around bolt hole.

2. Net Section: Tear along line of holes.

3. Bolt Shear: Bolt breaks across shank.

4. Edge Shear-out: Plate tears out from edge to nearest bolt.

8.5 Timber Grouping (IS 883:1994) - Low Frequency

• Based on Modulus of Elasticity (E) and Extreme Fiber Stress in Bending ($$\displaystyle \sigma_b $$).

• Groups: I, II, III (I = strongest, III = weakest).

• Application: Select timber grade for structural members based on required strength/stiffness.

9.0 DESIGN EXERCISES & CALCULATIONS (PROBLEM MAPPING)

• 9.1 Bolted Joint Design: Lap/Butt joint. Calculate number of bolts (strength check), pitch/gauge (IS 800: Table 19), edge distance.

• 9.2 Welded Joint Design: Fillet weld size & length. Overlap for tension members.

• 9.3 Single/Double Angle Tension Member: Consider shear lag, net area, reversed stresses.

• 9.4 Laced/Battened Column: Design lacing/batten members, check slenderness of chords & lacing.

• 9.5 Laterally Supported/Unsupported Beam: Check LTB for unsupported (use $$\displaystyle M_{cr} $$ formula or Table 10). For supported, check bending/shear/deflection.

• 9.6 Plate Girder: Design web thickness (shear), flange area (bending), stiffeners (web buckling).

• 9.7 Gantry Girder: Select I-section with top cantilever. Check deflection limits (L/500 vertical, L/1000 lateral).

• 9.8 Purlin Design: Calculate wind load (suction/pressure), resolve loads, design as simply supported beam.

• 9.9 Base Plate (Slab/Gusseted): Slab base: thickness from yield line. Gusseted: design gusset & stiffeners for moment.

• 9.10 Grillage Foundation: Determine load spread, design top flange & cross beams (I-sections), check soil bearing.

• 9.11 Seat/Framed Connection: Design seat angle (bending) and bolts (shear) for beam reaction.

• 9.12 Column Splice: Design flange & web splice plates and bolts for axial load & moment.

FINAL EXAM STRATEGY: For design problems, always state assumptions, draw sketch with dimensions, show calculations step-by-step, and box final answer (e.g., "Required bolt diameter = 20 mm").