Design of Steel Structures (CE-801) Unit 4 Notes

1. CONNECTIONS

Bolted Connections

Types: Lap joint, Butt joint (single/double cover), Tee joint, Framed connection (clip angles), Seated connection (seat angle + web cleat).
Bolt Grades: 4.6 (f_u = 400 MPa, f_y = 240 MPa), 8.8 (f_u = 800 MPa, f_y = 640 MPa), Fe 410 (f_y = 410 MPa).

Strength Calculation:
- Tensile strength: $$\displaystyle T_b = \frac{0.9 f_u A_{nb}}{\gamma_{mb}} $$
- Shear strength (bearing type): $$\displaystyle V_{sb} = \frac{f_u A_{sb}}{\gamma_{mb}} $$ or $$\displaystyle V_{pb} = \frac{2.5 k_b d t f_u}{\gamma_{mb}} $$
- Where $$\displaystyle A_{nb} = \frac{\pi}{4} d^2 $$, $$\displaystyle A_{sb} = \frac{\pi}{4} d^2 $$, $$\displaystyle k_b = \min\left(\frac{e}{3d_0}, \frac{p}{3d_0} - 0.25, \frac{f_u}{f_u}\right) $$
Failure Modes:
1. Bolt shear
2. Bolt tension (combined shear + tension)
3. Bearing failure (crushing of plate around bolt)
4. Splitting failure (edge shear)
5. Net section failure (tension across net area)
Design Parameters:
- Minimum pitch: $2.5d$
- Minimum edge distance: $1.7d$
- Gauge length: distance between bolt lines
- Staggered bolts: reduce net area but increase shear lag.
Bearing-type vs. Friction-type (HSFG):
- Bearing: bolts bear on holes, slip allowed.
- Friction-type: high-strength bolts tightened to slip-critical; no bearing, uses $$\displaystyle T_{sf} = \frac{k_2 n f_u A_{nb}}{\gamma_{mb}} $$ with slip factor $$\displaystyle k_2 $$.
Design of Joints:
- Lap joint: check net section, shear, bearing.
- Butt joint: cover plate design for shear and bearing.
- Tee joint: flange in tension, web in shear.

[!TIP] For staggered bolts, net area $$\displaystyle A_{net} = \left[ b - (n-1)p - n d_h \right] t + \text{additional shear lag deduction} $$.

Welded Connections

Types:
- Fillet weld: side, end, all-around. Throat thickness $$\displaystyle t = 0.707 \times \text{leg size} $$.
- Groove weld: butt, corner, edge, V-groove, U-groove. For thick plates.
Fillet Weld Design:
- Size: minimum $3$ mm, max $$\displaystyle t_{min}/2 $$ for single, $$\displaystyle t_{min}-2 $$ mm for double.
- Effective throat: $$\displaystyle t_e = 0.7 \times \text{leg size} $$.
- Effective length: $$\displaystyle l_{eff} = \text{length} - 2 \times \text{root} $$, min $4 \times \text{leg size}$.
- Strength: $$\displaystyle R = \frac{f_u A_w}{\sqrt{3} \gamma_{mw}} $$, $$\displaystyle A_w = l_{eff} \times t_e $$.
Groove Weld: depth of groove, reinforcement (max 3 mm), soundness (NDT).
Shop vs. Site: Shop welding (controlled, better quality); site welding (weather dependent, accessibility).
Applications: Lap joint (overlap limited to 4t), butt joint (full strength), tee joint (fillet welds).

Pin Connections

Definition: Hinged joint allowing rotation, used in trusses, bridges.
Types: Clevis pins, turnbuckles, pinned joints.
Advantages: Simple, allow rotation, easy assembly.
Limitations: Not for moment transfer, wear, maintenance.

2. TENSION MEMBERS

Types of Sections: Single/double angles, I-sections, channels, tubular sections.
Design Considerations:
- Net Area: $$\displaystyle A_{net} = (g - n d_h) t $$ for plates; for angles, effective net area $$\displaystyle A_{ne} = A_{net} \times \text{reduction factor } \beta $$ (IS 800 Table 5.3).
- Shear Lag: Reduction due to non-uniform stress; $$\displaystyle \beta = 1 - \frac{\bar{x}}{l_1} \left(1 - \frac{\bar{x}}{l_1}\right) $$ for angles.
- Stress Reversal: Wind loads; design for both tension and compression (use smaller capacity).
Block Shear Failure:
- Mechanism: Tension along one line, shear along another (corner rupture).
- Strength (IS 800):

$$T_{bs} = \left( \frac{A_{gn} f_u}{\gamma_{m1}} + \frac{A_{tn} f_y}{\gamma_{m0}} \right) \quad \text{or} \quad \left( \frac{A_{tn} f_y}{\gamma_{m0}} + \frac{A_{gn} f_u}{\gamma_{m1}} \right)$$

whichever is smaller, where $$\displaystyle A_{gn} $$ = gross area in tension, $$\displaystyle A_{tn} $$ = net area in shear.

Lug Angles:
- Purpose: Reduce connection length, accommodate bolts, avoid excessive stagger.
- Design: Lug angle size ≥ main angle; check strength of lug and its connection.
- Sketch: Single/double lug, with/without gusset.
Connections:
- Welded to gusset: fillet welds on three sides, overlap ≤ 4t.
- Bolted: back-to-back angles, tack bolts at intervals.
Factors Affecting Strength: End fixity (reduces effective length), member length (buckling), eccentricity (moment), type of loading (axial vs. eccentric).

[!TIP] For double angles with gusset on one side, effective net area is reduced due to shear lag; use IS 800 Table 5.3.

3. COMPRESSION MEMBERS (COLUMNS)

Types: Solid (I, channel, tube), built-up (laced, battened).
Laced Columns:
- Design Steps:
  1. Effective length $$\displaystyle L_e = K L $$ (K=1.0 for hinged ends).
  2. Slenderness ratio $$\displaystyle \lambda = \frac{L_e}{r} $$.
  3. Design axial load: $$\displaystyle P_d = \frac{A_g f_y}{\gamma_{m0}} \times \text{reduction factor for } \lambda $$ (IS 800 Table 5.2).
  4. Lacing bars/angles: inclined at 40°–60°, check for buckling and shear.
  5. Bolted connections: eccentricity in lacing, strength $$\displaystyle V = \frac{f_u A_{nb}}{\gamma_{mb}} $$ for bolts.
- Single vs. Double Lacing: Double lacing for heavy loads; single for lighter.
- Channel Placement: Back-to-back (better moment of inertia) or toe-to-toe (less material).
Battoned Columns: Wider spacing of battens (≥ 60 cm); check for local buckling of components.
Column Splices:
- Types: Welded (full penetration), Bolted (end plates), Bearing (direct bearing on cap plate).
- Design: transfer axial load and moment; match column sections.
Axial Load Capacity:
- Euler buckling: $$\displaystyle P_{cr} = \frac{\pi^2 E I}{(K L)^2} $$
- IS 800: $$\displaystyle P_d = \frac{A_g f_y}{\gamma_{m0}} \times \frac{1}{\phi + \sqrt{\phi^2 - \lambda^2}} $$ where $$\displaystyle \phi = 0.5 \left[1 + \alpha (\lambda - 0.2) + \lambda^2\right] $$, $\alpha$ = imperfection factor.
Failure Modes: Overall buckling, local buckling (thin flanges/web), crushing (short columns).
Built-up Columns with Channels: Design lacing for shear, check slenderness of lacing members.
Circular Tubular Struts: Use Table 5.2 for $\phi$; $$\displaystyle r = \sqrt{I/A} $$; check diameter-to-thickness ratio.

[!TIP] For laced columns, effective length for lacing bars is $0.7 \times \text{panel length}$; check both buckling and shear strength.

4. BEAMS

Laterally Restrained vs. Unrestrained:
- Restrained: Lateral displacement prevented (e.g., by deck slab, bracing). No lateral-torsional buckling; full moment capacity $$\displaystyle M_d = \frac{Z_p f_y}{\gamma_{m0}} $$.
- Unrestrained: Susceptible to lateral-torsional buckling; reduced moment capacity $$\displaystyle M_d = \frac{Z_p f_y}{\gamma_{m0}} \times \text{reduction factor} $$ (IS 800 Table 5.4).
Design of Laterally Supported Beams:
1. Select trial section (ISB/ISHB).
2. Check moment capacity: $$\displaystyle M_u \leq M_d $$.
3. Check shear capacity: $$\displaystyle V_u \leq V_d = \frac{A_w f_y}{\sqrt{3} \gamma_{m0}} $$.
4. Check deflection (if required): $$\displaystyle \delta_{max} \leq \frac{L}{250} $$ (general), $$\displaystyle \frac{L}{360} $$ (plaster).
5. Check web buckling (if concentrated loads).
Beam Connections:
- Framed: Clip angle welded to beam flange, bolted to column; transfers shear.
- Seated: Seat angle supports beam bottom, web cleat; transfers shear and moment.
- Design for end reactions: bolt shear, bearing, weld strength.
Composite Beams: Steel beam + RC slab; shear connectors (studs); effective width $$\displaystyle b_e = L_0/4 + b_0 $$ (IS 11384).
Deflection Limits:
- General beams: $L/250$ (live load), $L/360$ (total load).
- Gantry girders: $L/500$ (vertical), $L/1000$ (lateral under crane surge).
Gantry Girders:
- Profile: I-section with reinforced web (vertical stiffeners at supports and under crane wheels).
- Design: UDL from crane load, check moment, shear, deflection, local buckling under wheel loads.

[!TIP] For laterally unrestrained beams, provide lateral bracing at intervals $$\displaystyle L_{cr} = \frac{\pi r}{\sqrt{f_y / E}} $$ to restore full capacity.

5. ROOF TRUSSES AND PURLINS

Roof Truss Components (10 key):
1. Top chord: Compression member.
2. Bottom chord: Tension member.
3. Diagonals (web): Tension/compression.
4. Gusset plates: Connect members at joints.
5. Purlins: Horizontal members supporting roof covering.
6. Bracing: Wind bracing (portal, diagonal), sway bracing.
7. Ridge beam: Apex support (sometimes).
8. Eaves: Lower chord connection to supports.
9. Apex: Top joint.
10. Sag rods: Tension rods to prevent purlin sag.
Types of Roof Trusses: King post (central vertical), Queen post (two verticals), Fink (economical for short spans), Scissor (vaulted ceiling), Pratt (diagonals in tension), Howe (diagonals in compression), Warren (no verticals).
Purlin Design:
- Load Calculation:
  - Dead load: weight of sheeting + purlin self-weight.
  - Live load: as per IS 875.
  - Wind load: pressure/suction on sloping surface ($$\displaystyle P_z = C_p \times q_z $$).
  - Load per purlin = (load intensity) × (spacing) × (slope correction).
- Spacing: Truss spacing (6 m typical), purlin spacing (1–1.5 m).
- Section Selection: I-sections (ISB) or angles; simply supported between trusses.
- Design: Bending moment $$\displaystyle M = \frac{w L^2}{8} $$, shear $$\displaystyle V = \frac{w L}{2} $$; select section for $$\displaystyle M_d $$, $$\displaystyle V_d $$.
Wind Load on Trusses: Pressure coefficients for leeward/windward; suction on leeward side increases tension in bottom chord.

[!TIP] For purlins on slope, resolve loads perpendicular to purlin axis; use $$\displaystyle w_{perp} = w \cos\theta $$.

6. PLATE GIRDERS

Design Steps:
1. Depth: $$\displaystyle h = L/10 $$ to $L/12$ (span L).
2. Flange Design:
  - Width $$\displaystyle b_f = 0.3 h $$ to $0.5 h$.
  - Thickness: based on bending stress $$\displaystyle \sigma = \frac{M}{Z} \leq f_y/\gamma_{m0} $$.
  - Flange area $$\displaystyle A_f = \frac{M}{f_y d} $$.
3. Web Design:
  - Thickness: based on shear $$\displaystyle t_w \geq \frac{V_u}{0.6 f_y d} $$; also check buckling (stiffeners if $$\displaystyle h/t_w > 400 \varepsilon $$).
4. Stiffeners:
  - Transverse: at supports, under concentrated loads.
  - Vertical: if $$\displaystyle h/t_w > 400 \varepsilon $$.
  - Bearing stiffeners: at supports and load points.
5. Splices:
  - Flange splice: full strength, welded or bolted.
  - Web splice: shear transfer.
Elements: Flanges (top/bottom), web, stiffeners (transverse/vertical), splices, end bearings (rockers, guided).
Welded Plate Girder: UDL loading; fabrication: flame cutting, welding sequence to avoid distortion.

[!TIP] Web buckling stress $$\displaystyle \tau_{cr} = \frac{k \pi^2 E}{12(1-\nu^2)} \left(\frac{t_w}{h_w}\right)^2 $$; provide stiffeners if shear stress > $$\displaystyle \tau_{cr} $$.

7. FOUNDATIONS AND BASE PLATES

Slab Base (Unstiffened):
- Design:
  - Base plate thickness: $$\displaystyle t = \sqrt{\frac{2.5 W}{f_y d}} $$ (W = load, d = smaller dimension of plate).
  - Weld to column: fillet weld around column flange/web.
  - Bearing pressure on concrete: $$\displaystyle p = \frac{W}{A_p} \leq \text{allowable bearing stress of concrete} $$.
- Concrete pedestal: M20/M25, size based on spreading load.
Gusseted Base:
- Base plate + gusset plates; column load distributed via gussets.
- Design: gusset thickness, weld to column and base plate.
Grillage Foundation:
- Design: I-sections in top and bottom layers, web plates; load distributed through top flange.
- Check: bearing on soil ($p \leq R$), shear in grillage beams.
- Typical: 2–3 layers, each layer orthogonal.
Base Plate Types:
1. Slab base (simple, for light loads).
2. Gusseted base (heavy loads, eccentric loading).
3. Grillage base (very heavy loads, poor soil).

[!TIP] Base plate area $$\displaystyle A_p \geq \frac{W}{0.4 f_{ck}} $$ for concrete pedestal; provide 100 mm projection beyond column edge.

8. FAILURE MODES AND ADVANCED CONCEPTS

Block Shear Failure:
- Mechanism: Tensile failure along one line, shear along another (corner rupture). Common in angles, I-sections with bolt holes.
- Calculation: $$\displaystyle T_{bs} = \min\left( \frac{A_{gn} f_u}{\gamma_{m1}} + \frac{A_{tn} f_y}{\gamma_{m0}}, \frac{A_{tn} f_y}{\gamma_{m0}} + \frac{A_{gn} f_u}{\gamma_{m1}} \right) $$.
- Path: Tension on gross section, shear on net section (or vice versa).
Shear Lag:
- Concept: Non-uniform stress distribution in tension members with flanges or angles; outer fibers carry more stress.
- Effect: Reduces effective net area; use reduction factor $\beta$ (IS 800 Table 5.3).
- Example: In double angles, $$\displaystyle \beta = 1 - \frac{\bar{x}}{l_1} \left(1 - \frac{\bar{x}}{l_1}\right) $$.
Bolted Joint Failures (with sketches):
1. Bolt shear: Bolt fails across shank.
2. Bolt tension: Bolt fails in tension (combined shear+tension).
3. Bearing failure: Crushing of plate around bolt hole.
4. Net section failure: Tension fracture across net area.
5. Splitting failure: Edge shear tear-out.
Distinctions:
- Laterally Restrained vs. Unrestrained Beams: Restrained has full moment capacity; unrestrained susceptible to lateral-torsional buckling.
- Working Stress Design (WSD) vs. Limit State Design (LSD):
  
  | WSD | LSD | |---|---| | Stresses ≤ allowable | Factored loads ≤ design strength | | Factor of safety on material | Partial safety factors on loads ($$\displaystyle \gamma_f $$) and materials ($$\displaystyle \gamma_m $$) | | Elastic range | Inelastic range allowed | | IS 800: 1997 | IS 800: 2007 |

9. MATERIAL PROPERTIES AND DESIGN CODES

Steel vs. Cast Iron/Wrought Iron:

| Property | Steel | Cast Iron | Wrought Iron | |---|---|---|---| | Ductility | High | Brittle | Moderate | | Strength | High | High compressive, low tensile | Low | | Weldability | Good | Poor | Fair | | Corrosion | Moderate | Good | Good | | Advantages of Steel: High strength-to-weight, ductility (energy absorption), weldability, formability, recyclable.
Steel Grades (IS 2062):
- Fe 250: $$\displaystyle f_y = 250 $$ MPa, $$\displaystyle f_u = 410 $$ MPa (mild).
- Fe 410: $$\displaystyle f_y = 410 $$ MPa, $$\displaystyle f_u = 500 $$ MPa (high strength).
- Fe 550: $$\displaystyle f_y = 550 $$ MPa, $$\displaystyle f_u = 600 $$ MPa.
IS 800 (Limit State Design):
- Partial Safety Factors:
  - Materials: $$\displaystyle \gamma_{m0} = 1.1 $$ (yield), $$\displaystyle \gamma_{m1} = 1.25 $$ (ultimate), $$\displaystyle \gamma_{mb} = 1.25 $$, $$\displaystyle \gamma_{mw} = 1.25 $$.
  - Loads: $$\displaystyle \gamma_f $$ = 1.5 (dead), 1.5 (live), 1.2 (wind) – combinations as per Table 5.
- Load Combinations: $1.5(DL+LL)$, $1.2(DL+LL+WL)$, etc.
Timber Grouping (IS 883: 1994):
- Based on Modulus of Elasticity (E) and Extreme Fiber Stress (σ).
- Groups: I (high E, high σ), II, III (low E, low σ).
- Assign grade stress by multiplying characteristic values by modification factors (load duration, moisture, etc.).

10. MISCELLANEOUS TOPICS

Advantages of Bolted Connections over riveted/welded:
- Site work: no skilled labor, no heat.
- Reusable: dismantling possible.
- Inspection: easy to check tightness.
- No distortion (unlike welding).
Types of Welds:
- Fillet: L-shaped, most common (90°).
- Groove: V, U, J, butt, corner – for full penetration.
- Plug/Slot: for connecting overlapping plates, transfer shear.
- Difference Fillet vs. Groove: Fillet = triangular throat, no preparation; Groove = prepared edges, full depth.
Sketches of Bolted Connections:
- Lap joint: single/double row.
- Butt joint: single/double cover.
- Tee joint: flange-to-web.
- Framed: clip angle.
- Seated: seat angle + web cleat.
Efficiency of Bolted Joints:

$$\eta = \frac{\text{Strength of joint}}{\text{Strength of unperforated plate}} \times 100\%$$

For lap joint: $$\displaystyle \eta = \frac{(b - n d_h) t f_y}{(b t f_y)} \times 100\% $$ (considering net section).

Design Examples Integration:
- Tension member with wind reversal: Design for max tension (DL+LL+WL) and compression (wind only); use smaller capacity.
- Composite beam: Effective width $$\displaystyle b_e = L_0/4 + b_0 $$; shear connectors; transformed section.
- Assumptions: Self-weight = 0.3–0.5 kN/m² for roofs; end conditions: pinned/restrained; load factors as per IS 800.

[!TIP] In combined problems, always check both load cases (e.g., wind on/off) and take governing design.

Account

Design of Steel Structures (CE-801) - Unit 4 Short Notes