Design of Steel Structures (CE-801) - Unit 5 Short Notes

UNIT 5: DESIGN OF STEEL STRUCTURES - SHORT NOTES

1.0 CONNECTIONS

1.1 Bolted Connections

• Types:

  • Lap Joint: Plates overlap. Simple, but eccentric load path.

  • Butt Joint: Plates edge-to-edge. Uses single/double cover plates. More efficient.

  • Tee Joint: Flange of one member perpendicular to web/flange of another.

  • Framed Connection: Beam web connected to column flange/web with angles (seated or framed).

  • Seated Connection: Beam rests on seat angle on column.

  • Splice: Used to join members end-to-end (column/truss splice).

• Bolt Types & Grades (IS 1367):

  • Black Bolts (Grade 4.6): Low strength, used in bearing-type connections. $$\displaystyle f_u = 400 $$ MPa, $$\displaystyle f_y = 240 $$ MPa.

  • High Strength Friction Grip (HSFG) Bolts (Grade 8.8, 10.9): High strength, used in slip-critical connections. Tightened to develop friction.

• Failure Modes of Bolted Joints (Very Frequent):

  1. Shear failure of bolt: Bolt fails in shear across its shank.

  2. Bearing failure of plate: Crushing of plate material around bolt hole.

  3. Net section failure (Tension failure of plate): Plate tears along the line of bolt holes under tension.

  4. Edge shear-out / Block shear failure: A combination of shear along a line of bolts and tension along the last row. Critical for tension members.

  5. Splitting of plate: Tensile stress causes plate to split, common in small plates with few bolts.

• Design Concepts:

  • Bearing Type (Nominal Clearance): Load transferred by bearing on hole. Slip permitted. Design based on bolt shear & plate bearing.

  • Friction Type (Slip-critical): Load transferred by friction between faying surfaces. No slip allowed. Design based on bolt tension & slip resistance.

• Design Strength of Bolts (IS 800:2007):

  • Shear Strength (single bolt): $$\displaystyle V_{sb} = \frac{f_u}{\gamma_{mb}} A_{sb} n_b $$

    where $$\displaystyle A_{sb} = \frac{\pi d^2}{4} $$ (for full shank), $$\displaystyle n_b $$ = number of shear planes (1 for single shear, 2 for double shear).

  • Bearing Strength (per bolt): $$\displaystyle V_{pb} = \frac{2.5 k_b d t f_u}{\gamma_{mb}} $$

    where $$\displaystyle k_b = \min\left( \frac{e}{3d_0}, \frac{p}{3d_0} - 0.25, \frac{f_{ub}}{f_u} \right) $$, $e$ = edge distance, $p$ = pitch, $$\displaystyle d_0 $$ = hole dia.

  • Tensile Strength (per bolt): $$\displaystyle T_{db} = \frac{0.9 f_u A_{sb}}{\gamma_{mb}} $$

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

• Key Terminology:

  • Pitch (p): Distance between centers of bolts in a row (along load direction).

  • Gauge (g): Distance between rows of bolts (perpendicular to load).

  • Edge Distance (e): Distance from center of bolt to plate edge.

  • Staggered Bolts: Alternate bolts in adjacent rows offset to increase net section.

1.2 Welded Connections

• Types of Welds:

  • Fillet Weld: Triangular cross-section. Used in lap, tee, corner joints. Most common.

  • Groove Weld: Used in butt joints. Types: Square, V, U, J, Bevel.

  • Seam Weld: Continuous row of spot welds.

  • Slot Weld: Fillet weld in a slot.

• Fillet Weld Design (IS 800):

  • Throat Thickness ($$\displaystyle t_t $$): Minimum distance from root to face. $$\displaystyle t_t = 0.7 \times \text{Size (s)} $$ for equal leg fillet.

  • Effective Length ($$\displaystyle l_{eff} $$): Actual length minus 2×size (for end returns).

  • Design Strength:

    • Parallel to weld axis: $$\displaystyle F_w = \frac{f_u}{\sqrt{3} \gamma_{mw}} l_{eff} t_t $$

    • Perpendicular to weld axis: $$\displaystyle F_w = \frac{f_u}{\gamma_{mw}} l_{eff} t_t $$

  • Minimum Size: To avoid excessive heating. $$\displaystyle s_{min} = \max( \text{plate thickness}, 6\text{mm}) $$.

  • Maximum Size: $$\displaystyle s_{max} = \text{thickness of thinner plate} $$ (for fillet weld).

• Advantages over Riveting: No hole drilling, full efficiency, better aesthetics, quieter.

• Disadvantages over Bolting: Inspection difficult, requires skilled labor, residual stresses, cannot be disassembled.

1.3 Pin Connections

• Definition: Connection using a pin (bolt) passing through aligned holes in connected parts.

• Components: Pin, Pin Plate (thick plate to distribute load), Bushing (sleeve to reduce bearing stress).

• Types in Structures: Truss joints (pin-jointed), Column bases (base plates with anchor pins), Gantry girder connections.

• Design Considerations: Check pin in shear & bearing, pin plate in bearing & tension, connected element for bearing & net section.

1.4 Special Failure Modes & Concepts

• Block Shear Failure (Very Frequent):

  • Mechanism: A plate segment tears out along a path combining shear along a line of bolts and tension along the last bolt row.

  • Design Equation (IS 800): $$\displaystyle T_{db} = \frac{A_{g} f_y / \gamma_{m0} + 0.9 A_{tn} f_u / \gamma_{m1}}{1} $$ OR $$\displaystyle \frac{A_{tn} f_u / \gamma_{m1} + A_{gv} 0.6 f_u / \gamma_{m0}}{1} $$ (whichever is smaller).

    where $$\displaystyle A_{tn} $$ = net area in tension, $$\displaystyle A_{gv} $$ = gross area in shear path.

  • Critical for: Tension members with staggered bolts, gusset plates.

• Shear Lag & Net Section:

  • Concept: In tension members (especially angles, tees), stress is not uniform across gross section. Outer fibers carry more load, inner fibers less. This reduces effective area.

  • Net Area ($$\displaystyle A_{net} $$): Gross area minus area of bolt holes. For single angle, $$\displaystyle A_{net} = (b - d_0)t + (t \times \text{leg length if welded}) $$.

  • Effective Net Area ($$\displaystyle A_{n,eff} $$): $$\displaystyle A_{n,eff} = \beta \cdot A_{net} $$, where $\beta$ = shear lag factor (from IS 800 Table 5.3.1). Depends on connection type (welded, bolted with single row, etc.).

• Lug Angles:

  • Purpose: To provide additional bolts away from the main member's heel, improving connection strength and reducing eccentricity in tension member connections to gusset plates.

  • Application: Used when connection to gusset plate requires more bolts than can be placed on the main member's leg (e.g., double angle tension member).

  • Sketch: Small angle (lug) welded to back of main angle, with bolts through both lug and gusset.

  • Design: Lug angle designed for tension; its bolts and weld designed for force in lug.

2.0 TENSION MEMBERS

2.1 Types & Selection

• Single Sections: Angles (most common), Tees, Channels, I-sections.

• Built-up Sections: Double Angles (back-to-back, toe-to-toe), Double Channels, I-section with plates.

2.2 Design Considerations

• Design Strength ($$\displaystyle T_{db} $$): Minimum of:

  1. Yielding of Gross Section: $$\displaystyle T_{dg} = \frac{A_g f_y}{\gamma_{m0}} $$

  2. Rupture of Net Section: $$\displaystyle T_{dn} = \frac{0.9 f_u A_{net}}{\gamma_{m1}} $$

  3. Block Shear Failure: As above.

• Effect of Bolt Holes: Deduct hole area ($$\displaystyle d_0 \times t $$) from gross area for net area. Staggered holes increase net area.

• Effect of Welds: Weld metal replaces base metal. Net area calculated by deducting hole area or considering effective throat area of weld.

• Reversal of Stresses (Wind): Use double angles (back-to-back) to avoid bending due to eccentric load on single angle. Check slenderness ratio ($$\displaystyle \lambda = l_{eff}/r_{min} $$).

2.3 Design of Connections

• Welded to Gusset: Design weld to develop full tensile strength of member. Weld on all sides of angle (three sides typical). Check weld strength $$\displaystyle \geq T_{db} $$.

• Bolted to Gusset: Design bolts (shear, bearing) and check net section of angle and gusset plate. Use lug angles if bolt rows > 2 on gusset.

• Use of Lug Angles: When main member cannot accommodate required number of bolts in one/two rows.

2.4 Design Problems (Typical Steps)

1. Calculate design load ($$\displaystyle T_u $$).

2. Select trial section (angle/channel). Calculate $$\displaystyle A_g $$, $$\displaystyle r_{min} $$, $\lambda$.

3. Check slenderness limit ($$\displaystyle \lambda_{max} = 400 $$ for tension members).

4. Compute $$\displaystyle T_{dg} $$, $$\displaystyle T_{dn} $$, $$\displaystyle T_{db} $$ (block shear).

5. Adopt section if $$\displaystyle T_{db} \geq T_u $$.

6. Design connection:

   • Bolted: Determine number/size of bolts, pitch, edge distance. Check bolt shear, bearing, net section of member & gusset.

   • Welded: Determine weld size/length. Check weld strength.

3.0 COMPRESSION MEMBERS (Columns & Built-up Sections)

3.1 Buckling & Slenderness

• Euler's Buckling Load: $$\displaystyle P_{cr} = \frac{\pi^2 EI}{(K L)^2} $$, where $K$ = effective length factor.

• Slenderness Ratio ($\lambda$): $$\displaystyle \lambda = \frac{K L}{r} $$, where $$\displaystyle r = \sqrt{I/A} $$.

• Section Classification (IS 800): Based on width-to-thickness ratio ($b/t$ or $d/t$). Classes: Plastic (Class 1), Compact (Class 2), Semi-compact (Class 3), Slender (Class 4). Plastic/Compact sections have higher $$\displaystyle f_{cd} $$.

3.2 Design Strength of Axially Loaded Members

• Design Stress ($$\displaystyle f_{cd} $$): Obtained from buckling curve (a, b, c, d) based on section class & $\lambda$. From IS 800 Table 7.1.2.

• Design Axial Load Capacity: $$\displaystyle P_{d} = \frac{A_g f_{cd}}{\gamma_{m0}} $$ (for Class 1,2,3). For Class 4 (slender), use effective area $$\displaystyle A_{eff} $$.

3.3 Built-up Compression Members

• Laced Columns (Frequent):

  • Purpose: Economical for heavy loads; use smaller sections with lacing.

  • Types: Single lacing (one diagonal system), Double lacing (two diagonal systems, more rigid).

  • Lacing Members: Usually flat bars or angles. Design as compression/tension diagonals of a truss.

  • Effective Length of Lacing: $$\displaystyle L_{eff} = \text{length between connections} $$ (for single lacing) or $0.7 \times \text{length}$ (for double lacing).

  • Spacing of Lacing: $$\displaystyle l_1 \leq 50 \omega $$ (where $\omega$ = slenderness ratio of main column) or as per code.

  • Design Steps:

    1. Design main members (channels/angles) for axial load.

    2. Design lacing bars for compression/tension from shear force ($$\displaystyle V = 0.02 P $$ approx).

    3. Design lacing connections (riveted/bolted/welded).

    4. Check for shear deformation of lacing.

• Battened Columns:

  • Batten Plates: Flat plates connecting main members. Designed for shear and bending moment from shear force ($V$) and moment ($$\displaystyle M = V \times \text{distance} $$).

  • Spacing: Batten shall be provided at intervals not exceeding $$\displaystyle 50i_{min} $$ (least radius of gyration of main member).

  • Distinction: Lacing uses slender members (bars/angles), Batten uses rigid plates. Lacing is lighter, batten is stiffer.

3.4 Column Bases & Splices

• Slab Base (Grillage Foundation):

  • Components: Base plate, anchor bolts, weld to column, grillage (top & bottom layers of I-sections in concrete).

  • Design Steps:

    1. Calculate factored load $$\displaystyle P_u $$.

    2. Determine base plate area: $$\displaystyle A_{bp} = P_u / (0.45 f_{ck} \text{ or soil bearing capacity}) $$.

    3. Check base plate thickness for bending: $$\displaystyle t_{bp} = \sqrt{\frac{6M}{f_{sd} b}} $$ where $M$ = moment on projection.

    4. Design weld (column to base plate).

    5. Design grillage I-sections for compression.

• Gusseted Base:

  • Used when base plate is small or moments exist.

  • Components: Base plate, gusset plates (triangular), stiffeners, column connection (welded/bolted), concrete pedestal.

  • Design: Gussets designed for tension from anchor bolts or moment. Similar to slab base but with gussets taking tension.

• Column Splice:

  • Types: Flange splice, Web splice, Full-depth splice.

  • Design: For axial load & moment. Flange splice plates designed for flange force. Web splice for shear. Bolted or welded.

4.0 BEAMS & GIRDERS

4.1 Laterally Supported vs. Unsupported Beams (Very Frequent)

• Lateral Torsional Buckling (LTB): Instability of beam under bending when lateral support is inadequate. Top flange in compression tends to move laterally, causing twist.

• Laterally Supported (Restrained) Beam:

  • Compression flange is laterally restrained at intervals.

  • Conditions for support: At supports, under concentrated loads, at points of inflection.

  • Design: Check only for bending strength and shear strength. No LTB check.

• Laterally Unsupported (Unrestrained) Beam:

  • Compression flange free to move laterally over a significant length.

  • Design: Must check for LTB in addition to bending/shear. Design bending strength reduced by buckling factor ($$\displaystyle C_{b} $$, $$\displaystyle f_{cd} $$).

4.2 Design of Beams

• Section Selection: Based on maximum bending moment ($M$) and shear force ($V$). Use I-sections or channels.

• Web Stiffeners:

  • Vertical Stiffeners: Prevent web buckling under shear or concentrated loads.

  • Horizontal Stiffeners (Longitudinal): Prevent web buckling under compressive stress from bending.

• Web Crippling: Local failure of web under concentrated load/end reaction. Prevented by bearing stiffeners.

• Deflection Limits (IS 800):

  • Dead load + imposed load: $L/250$

  • Imposed load only: $L/350$

  • Roofing: $L/200$

  • Gantry girder: $L/500$ (vertical), $L/250$ (lateral)

4.3 Plate Girders (Frequent)

• Components: Flanges (top/bottom plates), Web (vertical plate), Stiffeners (Transverse, Longitudinal), Splices (flange, web), End bearing stiffeners.

• Design Philosophy: Built-up I-section for large spans (>~20m). Economical depth: $d/h \approx 0.4$ to $0.5$ (h = span).

• Design Steps:

  1. Preliminary: Estimate depth ($d \approx L/15$ to $L/20$), flange width ($$\displaystyle b_f \approx d/3 $$), web thickness ($$\displaystyle t_w \approx d/100 $$ to $d/150$).

  2. Web Design: Check shear strength ($$\displaystyle V_{wd} = \frac{A_{vw} f_{yw}}{\sqrt{3} \gamma_{m0}} $$). If $$\displaystyle V > V_{wd} $$, provide transverse stiffeners.

  3. Flange Design: Check bending strength ($$\displaystyle M_{fd} = \beta b_{eff} t_f^2 f_{yw} $$). Also check for flange buckling (local).

  4. Transverse Stiffeners: Design for shear force ($$\displaystyle V_s = V - V_{wd} $$). Check buckling of stiffener itself.

  5. Longitudinal Stiffeners: If web depth > $2000$ mm or shear stress high, provide. Design as column (compression from shear).

  6. Splices: Flange splice (moment), web splice (shear). Design plates/welds for forces.

  7. End Bearing Stiffeners: Provide at supports to distribute load and prevent web buckling.

4.4 Gantry Girders

• Profile: Usually I-section with heavy web (often with additional plates). Sometimes built-up plate girder.

• Design Considerations:

  • Crane Loads: Vertical (static + impact), Horizontal (braking, skewing).

  • Fatigue: Repeated crane loads cause fatigue. Check fatigue stress range.

  • Deflection Limits: Very strict due to crane operation.

    • Vertical deflection under crane load: $L/500$

    • Lateral deflection under horizontal load: $L/250$

  • Web Buckling under Wheel Loads: Provide bearing stiffeners under crane wheels.

5.0 ROOF TRUSSES, PURLINS & FLOOR SYSTEMS

5.1 Roof Trusses

• Common Types: King Post, Queen Post, Fink, Howe, Pratt (most common for industrial), Warren (with/without verticals), Fan, Gang-Nail (prefabricated).

• Components & Functions (Any Ten):

  1. Top Chord: Compression member (rafter).

  2. Bottom Chord: Tension member (tie).

  3. Principal Rafter: Sloping top chord member.

  4. Principal Tie: Bottom chord member.

  5. King Post: Central vertical compression member in King Post truss.

  6. Queen Post: Two vertical compression members in Queen Post truss.

  7. Strut: Compression web member.

  8. Tie: Tension web member.

  9. Panel Point: Joint where members meet.

  10. Purlin: Horizontal member supporting roof sheeting, rests on top chords.

  11. Sag Rod: Tension rod from bottom chord to purlin to prevent purlin sag.

  12. Knee Brace: Diagonal bracing between column and rafter to provide lateral stability.

  13. Portal Bracing: Diagonal bracing in end panels to resist wind.

• Truss Analysis: Simple method: Use method of joints/sections. Loads: Dead load (self-weight, sheeting), Live load, Wind load (normal/suction).

• Joint Connections: Welded (shop) for internal joints, Bolted (field) for splices. Gusset plates used at joints.

• Truss Splices: Usually in chords at panel points. Bolted or welded splice plates.

5.2 Purlins (Very Frequent)

• Function & Location: Horizontal members supporting roof sheeting, spanning between trusses on sloping roof. Also girts on walls.

• Types: Z-section (most common, can be nested), C-section, I-section, Angle sections.

• Design of Purlins:

  1. Load Calculation (on sloping surface):

     • Dead Load (DL): Sheeting weight + purlin self-weight.

     • Live Load (LL): As per code, reduced for slope.

     • Wind Load (WL): Pressure/suction on sloping area. $$\displaystyle w = p \times \text{spacing} \times \sec(\theta) $$.

     • Total UDL: $$\displaystyle w_u = 1.5(DL + LL) + 1.5 \text{ or } 0.9 \times WL $$ (as per limit state).

  2. Bending Moment & Shear: For simply supported span: $$\displaystyle M = w_u L^2 / 8 $$, $$\displaystyle V = w_u L / 2 $$.

  3. Section Selection: Choose Z/C/I section from steel tables. Check:

     • Bending Strength: $$\displaystyle M_{sd} \leq M_{d,allow} $$ (considering lateral torsional buckling if unsupported).

     • Shear Strength: $$\displaystyle V_{sd} \leq V_{d,allow} $$.

     • Deflection: $$\displaystyle \delta_{max} \leq L/200 $$ (roof).

  4. Connection to Truss: Bolted (with cleats) or welded. Cleats prevent lateral movement.

  5. Effect of Continuity: If purlin rigidly connected to truss, supports provide negative moment. Design for max of +ve/-ve.

5.3 Floor & Roof Systems

• Composite Beams: Steel beam with concrete slab (cast in-situ or precast) connected by shear connectors (studs). Slab acts as compression flange, increasing moment capacity.

• Corrugated Sheets: Used as decking (forms floor/roof) and sheeting (cladding). Loads transmitted to purlins/girts.

6.0 FOUNDATIONS & BASES

6.1 Slab Base (Isolated Footing)

• Design Steps:

  1. Calculate factored load $$\displaystyle P_u $$.

  2. Determine base plate area $$\displaystyle A_{bp} $$ from soil bearing capacity: $$\displaystyle A_{bp} \geq P_u / q_{allow} $$.

  3. Check base plate thickness for bending on projection $$\displaystyle m = (a - c)/2 $$ (where $c$ = column size). $$\displaystyle t_{bp} = \sqrt{\frac{3P_u}{f_{sd} a} \left( \frac{a}{2} - m \right)} $$.

  4. Design weld (column to base plate): Fillet weld size/length to transfer $$\displaystyle P_u $$.

  5. Check shear at column face (through base plate).

  6. Design anchor bolts (if tension due to overturning moment).

6.2 Grillage Foundation

• When Used: Heavy loads, poor soil.

• Components: Base plate, top & bottom grillages (layers of I-sections, usually 2-4 beams), transverse stiffeners, concrete envelope.

• Design:

  • Load from column distributed to grillage beams.

  • Design grillage I-sections for compression (considering buckling within concrete).

  • Design connections between grillage layers (welded/bolted).

  • Check bearing pressure on soil.

6.3 Gusseted Base

• Components: Base plate, gusset plates (triangular), stiffeners, column connection, concrete pedestal.

• Design: Similar to slab base but gussets take tension from anchor bolts or resist moment. Gusset thickness designed for tension.

7.0 MATERIAL PROPERTIES, DESIGN PHILOSOPHY & MISCELLANEOUS

7.1 Steel vs. Cast Iron & Wrought Iron

• Advantages of Steel: High strength-to-weight ratio, ductility (energy absorption), speed of construction, recyclability, malleability.

7.2 Design Approaches

• Working Stress Method (WSM): Stresses due to loads < allowable stress ($$\displaystyle f_{allow} = f_y / FS $$). Elastic design.

• Limit State Method (LSM): Ensures probability of failure is within acceptable limits. Considers:

  • Ultimate Limit State (ULS): Strength, stability, fatigue (factor $$\displaystyle \gamma_{m0}, \gamma_{m1} $$).

  • Serviceability Limit State (SLS): Deflection, vibration (no partial safety factors).

  • IS 800:2007 is based on LSM.

7.3 Structural Systems & Components (Industrial Building)

• Main Frames: Columns & Rafters (primary load-bearing).

• Purlins: Roof support (between trusses).

• Girts: Wall support (between columns).

• Bracing:

  • Portal Bracing: In end panels of roof truss.

  • Diagonal Bracing: In walls/roof planes.

  • Knee Bracing: Between column & rafter.

  • Sag Rods: Tension rods from bottom chord to purlin to prevent purlin sag.

7.4 IS Codes & Sections

• IS 800:2007: General construction in steel - Code of practice.

• Steel Tables: Use SP 6(1) for I-sections, SP 6(2) for angles, channels, etc. Provides $$\displaystyle A_g $$, $$\displaystyle I_{xx}, I_{yy}, r_{xx}, r_{yy}, Z_{pe} $$, etc.

[!TIP] EXAM FOCUS AREAS (From Past Papers):

1. Bolted Connections: Failure modes, design strength of bolts (shear/tearing), efficiency, cover plates.

2. Tension Members: Net area, block shear, lug angles, design of welded/bolted connections to gusset.

3. Laced Columns: Design of lacing bars, connections, effective length.

4. Purlins: Load calculation on slope, section selection, connection.

5. Bases: Slab base & grillage foundation design steps.

6. Beams: Distinction between laterally supported/unsupported, plate girder components.

7. Block Shear: Derivation/explanation, design equation.

8. Weld Design: Fillet weld throat, effective length, strength.