SCEE08002 Structural Mechanics 2 Laboratories Assignment UK

Overview

1. Three Laboratory Exercises:
   • Composite action in a beam.
   • Torsion of a shaft.
   • Membrane stresses in a pressure vessel.
2. Tasks Overview:
   • Data collection (in lab sessions).
   • Analysis (independent study time).
   • A single report submission at the end of semester 1.

Marking Criteria

Exercise 1: Composite Action in a Beam

Data Collection

1. Setup:
   • Apparatus investigates Euler’s Beam Theory (refer to Figures 1.1 and 1.2).
   • Test two beam types:
     • Bonded (steel + aluminium glued).
     • Unbonded (steel + aluminium not glued).
2. Procedure:
   • Zero the strain gauge.
   • Incrementally load weights (30N to 150N) and record strain data for each strain gauge.
3. Report Content:
   • Two Tables:
     • One for bonded beam.
     • One for unbonded beam, showing weight and strain gauge readings.

Analysis

1. Tasks:
   • Write an expression for the force FFF in terms of weight WWW, dimensions mmm, and nnn.
   • Write an expression for the bending moment MMM at mid-span.
   • Plot strain vs. vertical position for the 150N load for both beams and theoretical predictions.
2. Report Content:
   • Two tables (moment and strain gauge readings).
   • One graph (experimental vs. theoretical strain).
   • Explanation of behavior differences between bonded and unbonded beams.

Exercise 2: Torsion of a Shaft

Data Collection

1. Setup:
   • Apparatus measures rotation response to torque.
   • Test aluminium and steel bars at two lengths (300mm and 160mm).
2. Procedure:
   • Record shaft rotation for different weights (0.25kg and 0.5kg).
   • Measure lever arm and shaft diameters.
3. Report Content:
   • Table showing rotation readings for each setup.
   • Notes on lever arm and shaft diameters.

Analysis

1. Tasks:
   • Convert weights to torque.
   • Estimate shear modulus for materials based on rotation vs. torque plots.
2. Report Content:
   • Table (mass, torque, rotation, length).
   • Graphs (rotation vs. torque for all setups).
   • Calculations and error discussion.

Exercise 3: Membrane Stresses in a Pressure Vessel

Data Collection

1. Setup:
   • Thin-walled cylinder (aluminium) subjected to internal pressure.
   • Strain gauges measure strain in axial and tangential directions.
2. Procedure:
   • Record strain readings for:
     • Closed condition: Bi-axial stress.
     • Open condition: Uni-axial stress.
3. Report Content:
   • Table showing strain for both conditions.

Analysis

1. Tasks:
   • Predict longitudinal and hoop stresses.
   • Draw Mohr’s circle for each condition.
   • Calculate yield pressure and theoretical hoop strain.
   • Compare predictions with experimental strains.
2. Report Content:
   • Mohr’s circle (theoretical).
   • Yield pressure calculation.
   • Hoop and longitudinal strain calculations.
   • Comparison and error discussion.

Key Figures and Tables

Beam Test Setup (Figures 1.1 & 1.2):

• Dimensions and strain gauge positions.
• Loading beam ratio.

Torsion Test Equipment (Figure 2.1):

• Rotating and fixed chucks.
• Lever arm details.

Pressure Vessel Setup (Figure 3.2):

• Hydraulic pump, manometer, and strain gauge arrangement.

Material Properties Tables:

• Young’s modulus:
  • Steel: 200 kN/mm².
  • Aluminium: 70 kN/mm².
• Pressure Vessel:
  • Outer diameter: 75mm.
  • Wall thickness: 2.5mm.

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