Theory of Structure-IV AP-222 Exam Solutions June 2024

Posted on Jun 11, 2026 in Civil Engineering

Theory of Structure-IV (AP-222) June 2024 Exam Solutions

Here are the detailed solutions for the June 2024 Theory of Structure-IV (AP-222) examination paper.

Q1: Short Answer Questions (5 × 5 = 25 Marks)

(a) Web Buckling vs. Web Crippling

Both are localized failure modes in steel I-beams, but they differ in behavior:

Web Buckling: The web acts like a thin column under axial compression. It bends laterally over a significant portion of its depth when the depth-to-thickness ratio (d/t_w) is high.
Web Crippling: A localized crushing or plastic yielding failure at the root fillet of the beam flange due to high bearing stresses, manifesting as a sharp, localized fold.

(b) Modes of Failure in Riveted Connections

A riveted joint can fail in the following ways:

Shear Failure of Rivet: The rivet shears at the interface plane.
Bearing Failure: The hole elongates or the rivet crushes.
Tearing Failure of Plate: The plate tears across the rivet hole.
Shear Failure of Plate (Tear-out): The material behind the rivet shears out.

(c) Standard Rolled Steel Sections

These are hot-rolled structural elements defined by shape, depth, and mass. Examples include:

ISMB 300 @ 44.2 kg/m: Indian Standard Medium Weight Beam, 300 mm deep.
ISMC 200 @ 22.1 kg/m: Indian Standard Medium Weight Channel, 200 mm deep.
ISA 90 × 60 × 8 mm: Indian Standard Angle with unequal legs.

(d) Fillet Weld vs. Butt Weld

Fillet Weld: Connects overlapping elements (lap joints) or intersecting elements (T-joints) with a triangular cross-section.
Butt Weld (Groove Weld): Connects plates edge-to-edge in the same plane, requiring edge preparation for full penetration.

(e) Key Structural Definitions

Pitch (p): Center-to-center distance between fasteners parallel to the force.
Gauge (g): Center-to-center distance between fastener lines perpendicular to the force.
Throat Thickness (t_t): Minimum dimension from the weld root to the face (t_t = 0.7 × weld size).
End Distance: Distance from the hole center to the edge, parallel to the force.
Edge Distance: Distance from the hole center to the edge, perpendicular to the force.

(f) Built-up Sections

Definition: Structural members assembled by combining multiple standard shapes (plates, angles, channels) via welding or bolting. Applications: Used for deep plate girders, heavy compound columns, and gantry girders.

(g) Roof Truss Components

Principal Rafter: The inclined top-chord member carrying compressive loads.
Purlins: Beams spanning between trusses to support roof sheeting.
Eaves: The lower edge of a roof that overhangs the wall.

(h) Steel Roof Truss Applications

Used for large, column-free spans, including industrial workshops, aircraft hangars, and sports stadiums.

Q2: Merits, Demerits, and Applications of Steel

Merits

High strength-to-weight ratio.
Excellent ductility for earthquake resistance.
Fast fabrication and assembly.
Easy to modify or reinforce.

Demerits

Susceptible to corrosion.
Poor fire resistance (requires cladding).
Risk of elastic buckling in slender elements.

Applications

High-rise buildings, industrial warehouses, and bridge trusses.

Q3: Working Stress vs. Limit State Method

Parameter	Working Stress Method (WSM)	Limit State Method (LSM)
Design Concept	Elastic behavior	Plastic/Failure thresholds
Loads	Service loads	Factored loads
Safety	Factor of Safety (FoS)	Partial safety factors
Economy	Conservative	Cost-efficient

Q4: Tension Member Capacity Calculation

Note: Calculations based on Working Stress Method.

Nominal Diameter (d): 12 mm
Gross Hole Diameter (d₀): 13.5 mm
Permissible Stress (σ_at): 150 N/mm²

(Calculation steps involve determining net area and applying the reduction coefficient for single angles.)

Q5: Steel Beam Design

Design for 6m span with 24 kN/m load.

Factored Load (w_u): 36.75 kN/m
Selected Section: ISLB 350 @ 49.5 kg/m
Result: Section is safe in both shear and bending.

Q6: Welded vs. Riveted Connections

Welding Merits: Higher joint efficiency, weight reduction, and aesthetic cleanliness.
Welding Demerits: Potential for brittle failure in the Heat Affected Zone (HAZ), distortion stresses, and complex quality control.

Q7: Rivet Calculation

For a 55 kN load with 16mm rivets, the calculated Rivet Value is 24.05 kN. Required: 3 rivets.

Q8: Steel Roof Truss Merits

Offers large span flexibility, material efficiency, and rapid installation.

Q9: Design Loads for Roof Trusses

Dead Load: Self-weight of components and roofing.
Live Load: Temporary maintenance loads.
Wind Load: Critical suction forces.
Snow/Seismic Loads: Region-specific environmental loads.