Objectives & Theory
Core Objectives
- Determine reaction forces, max bending stress, and shear stress.
- Compare experimental reactions with theoretical values.
- Analyze shear force & bending moments under concentrated loads.
Key Equations
For a simply supported beam with load $F$ at distance $x$ from Support A:
Interactive Derivations
Visualizing the mechanics behind the math.
Imagine the beam is made of many thin layers (laminae). When bent, the layers fan out. The Neutral Axis (NA) stays the same length.
- Top layers compress (shorter)
- Bottom layers elongate (longer)
- Strain ($\epsilon$) $\propto$ Distance ($y$)
1. σ = E · ε = -E(y/ρ)
2. ∫ σ · y dA = M // Moment Equilibrium
3. ∫ -E(y²/ρ) dA = M
4. Since ∫ y² dA = I // Area Moment of Inertia
To balance the changing bending moment ($dM/dx$), horizontal shear forces must exist between layers.
"Imagine a stack of papers. Bend them, and they slide over each other. That sliding is Shear."
1. ΔF = (dM)·Q / I // Force diff on cut area
2. Shear Flow q = dF/dx = (dM/dx)·Q/I
3. Shear Stress τ = q / t
5.0 Experimental Procedure
1. Measure the beam dimensions: length (L), width (b), and depth (d) using vernier calipers or measuring tape.
2. Calculate the second moment of area (I) for the rectangular cross-section: I = bd³/12.
3. Mount the beam on simple supports with known span length. Ensure the supports allow free rotation.
4. Set up the dial gauge at the center of the beam (midspan) to measure deflection.
5. Apply incremental loads at the center and record the corresponding deflection readings.
6. Plot load vs. deflection graph and compare with theoretical predictions.
7. Calculate bending stress and shear stress at critical sections using measured data.
5.1 Safety Measures
The following safety precautions must be observed when conducting beam deflection testing to prevent injury and equipment damage.
1 Personal Protective Equipment (PPE)
- • Always wear safety glasses to protect eyes from sudden beam failure or flying debris.
- • Wear closed-toe shoes with non-slip soles in the laboratory.
- • Keep long hair tied back and avoid loose clothing near the equipment.
2 Equipment Safety
- • Inspect the beam for cracks or defects before mounting.
- • Ensure supports are stable and properly positioned before applying loads.
- • Apply loads gradually and incrementally - never shock load the beam.
3 Load Application
- • Stand clear of the beam when applying or removing loads.
- • Do not exceed the maximum allowable load for the beam specimen.
- • Watch for signs of excessive deflection or unusual sounds indicating failure.
4 General Laboratory Safety
- • Keep the work area clean and organized.
- • Never leave loaded beams unattended.
- • Report any equipment malfunction immediately to the instructor.
- • Know the location of emergency stop buttons and first aid kits.
⚠️ Important: Students who fail to follow safety procedures may be asked to leave the laboratory. Safety violations will be reported to the academic supervisor.
6.0 Results
Present your beam deflection test results in a clear and organized format. All tables and figures must include units, labels, and proper numbering.
1. Tabulate measured beam dimensions (L, b, d) and calculated properties (I, A).
2. Record the load-deflection data for all incremental loads applied.
3. Plot the load vs. deflection graph with experimental and theoretical curves.
4. Calculate bending stress at maximum load: σ = My/I where M = PL/4 at midspan.
5. Calculate maximum shear stress at supports: τ_max = (3V)/(2A) for rectangular section.
6. Compare experimental deflection with theoretical prediction: δ = PL³/(48EI).
7. Calculate percentage error between experimental and theoretical values.
7.0 Discussion
Please login and complete all discussion items below. Your responses will be included in your lab report.
Sources of Error
Identify and discuss at least three potential sources of error in this experiment and their impact on the results.
Theoretical vs. Experimental Comparison
Compare your experimental deflection results with theoretical predictions. Explain any discrepancies observed.
Material Behavior and Assumptions
Discuss the validity of assumptions made in the theoretical analysis (e.g., homogeneous material, small deflections, linear elastic behavior).
Practical Applications
Describe real-world engineering applications where beam deflection analysis is critical.
8.0 Laboratory Datasheet
Record your experimental measurements and calculations. Data is auto-saved locally.
Table 1: Beam Specifications
| Parameter | Symbol | Measured Value | Unit |
|---|---|---|---|
| Beam Length (Span) | L | mm | |
| Beam Width | b | mm | |
| Beam Depth | d | mm | |
| Young's Modulus | E | MPa | |
| Second Moment (I = bd³/12) | I | mm⁴ | |
| Cross-sectional Area | A | mm² |
Table 2: Load-Deflection Experimental Data
| No. | Load P (N) | Dial Reading (mm) | Deflection δ (mm) | Theoretical δ (mm) | % Error |
|---|
Virtual Simulation
Log in to interact with the experiments and record your data.
Post-Lab Assessment
4 QuestionsLogin to take the Quiz
Official Lab Record
Review your scores and generate a complete lab report. Your report will include game performance, quiz results, datasheet data, and discussion responses.
Game Score
0 pts
Quiz Score
0%
Report will include:
(Game + Quiz Combined)
📝 Important: Students must refine their formal report using Microsoft Word and attach the generated PDF as supporting documentation in their final submission.
MEQ491 Laboratory Report Rubric
Self-audit your report before submission. Scroll horizontally to view details.
| Item | Excellent (9-10) | Good (7-8) | Satisfactory (5-6) | Poor (3-4) | Very Poor (0-2) |
|---|---|---|---|---|---|
| 1. Appearance & Organisation | All sections in correct order, well formatted, very readable. Pages/diagrams intact, neat layout. Minor spelling/grammar slips only. Front cover completed; tape/ring bound with custom cover. Single PDF. | Sections ordered; formatting generally good. Readable, no torn pages. Some spelling issues. Missing one front-page detail. Tape/ring bound. | Sections present but rough formatting. Some torn pages. Multiple errors. Missing two non-title details. Stapled without binding or cover missing branding. | Sections out of order, messy formatting, torn inserts. Frequent errors, white-out used. Missing >2 details. Stapled poorly. | Meets most “Poor” conditions or absent submission. |
| 2. Objectives & Theory | All objectives clearly rephrased in original sentences. Detailed paragraph linking to prior knowledge. Incorporates relevant external research. | Objectives identified though phrasing could be clearer. Prior knowledge included. Partial paraphrasing. | Objectives partly identified/loosely stated. Heavy reliance on manual text. Some prior knowledge. | Objectives unclear or missing. Minimal relevant prior knowledge. Theory copied verbatim. | Content absent. |
| 3. Apparatus & Procedures | Complete equipment list with labelled diagrams. Numbered, step-by-step procedure (own words). Safety tips highlighted; safety report with photo included. | Vital items listed. Procedure mostly paraphrased, diagrams where needed. Safety report attached (missing photo). | Partial equipment list. Steps unclear, unnumbered, or copied. Required diagrams absent. | Equipment missing. Procedure unusable/confusing. No diagrams. | Content absent. |
| 4. Results, Calculations & Graphs x2 | Accurate, well-organised data showing trends. Figures numbered/captioned. Units present; complete calc walk-through with examples. | Correct data but trends less obvious. Minor figure issues; units included. Few calcs missing. | Some data missing/disorganised. Figures incomplete; units occasionally missing. Several calcs absent/incorrect. | Most data missing/unreliable. Figures poorly constructed. Calcs largely absent/wrong. | Content absent. |
| 5. Discussion x2 | Answers every question clearly. Explains trends, links to theory. Discusses errors, impacts, and mitigation. | Misses one question; remaining answers clear. Minor gaps in interpretation. Notes errors. | Misses two questions or inconsistent. Partial understanding. Errors mentioned without depth. | Misses multiple questions. Little/incorrect interpretation. No meaningful error discussion. | Content absent. |
| 6. Conclusions | Summarises data underpinning conclusions. States if objectives achieved, comments on validity. Addresses errors and proposes improvements. | Missing one “Excellent” element. | Missing two “Excellent” elements. | Missing three or more elements. | No conclusion provided. |
| 7. References | >9 sources (journals/books/media). 30% recent (<5 yrs). Formatted as specified. | 6-8 sources from varied media. Manual formatting observed. | 3-5 sources drawn from two media types. Formatting not fully compliant. | 1-2 sources cited. Formatting ignored. | No references. |