Deflection of Beam Experiment: Apparatus, Procedure, Observation Table and Calculations

What is the Deflection of Beam Experiment?

The deflection of beam experiment measures how a beam bends under applied transverse loads. It is a foundational Strength of Materials (SOM) lab experiment performed in B.Tech Mechanical and Civil Engineering programmes. The objective is to verify theoretical deflection formulae and determine the flexural rigidity (EI) of the beam material.

Two configurations are typically tested: a simply supported beam with a central point load, and a cantilever beam with an end load.

Aim of the Experiment

• To determine the deflection of a simply supported beam at the mid-span under a central point load
• To determine the deflection of a cantilever beam at its free end under an end load
• To verify theoretical deflection values against experimental readings
• To determine the Young’s Modulus (E) of the beam material

Theory and Formulae

The deflection of a beam depends on the load, span, cross-section, and material. The key formulae are:

Simply Supported Beam — Central Point Load

δ = WL³ / 48EI

Where:
δ = deflection at mid-span (mm)
W = applied load (N)
L = span length (mm)
E = Young’s Modulus (N/mm²)
I = second moment of area (mm⁴)

Cantilever Beam — End Point Load

δ = WL³ / 3EI

Second Moment of Area for Rectangular Section

I = bd³ / 12
Where b = breadth, d = depth of the beam cross-section.

Apparatus Required

• Deflection of beam apparatus (FortitestX-06) with knife-edge supports
• Steel, aluminium, and brass beam specimens (rectangular cross-section)
• Dial gauge (0.01 mm least count) with magnetic stand
• Weight hanger and calibrated weights (100 g to 1000 g)
• Vernier calliper
• Steel rule / measuring tape
• Graph paper and calculator

Experimental Procedure

Simply Supported Beam

1. Measure the cross-section dimensions (breadth b and depth d) of the beam using a Vernier calliper at three positions; take the average.
2. Set the knife-edge supports apart at the required span (L). Note the span length.
3. Place the beam on the supports and position the weight hanger at the mid-span.
4. Mount the dial gauge at the centre of the beam and zero the reading.
5. Apply loads in increments of 100 g (0.981 N). Record the dial gauge reading after each increment.
6. Continue loading up to the maximum safe load (typically 500 g for a 600 mm span steel beam).
7. Unload in the same increments and record readings to check for elastic recovery.
8. Repeat for aluminium and brass beams.

Cantilever Beam

1. Clamp one end of the beam firmly in the support fixture. Measure the effective length L from the fixed end to the point of load application.
2. Hang the weight hanger at the free end and zero the dial gauge.
3. Apply loads in increments and record deflection at each step.

Observation Table

Simply Supported Beam — Material: Mild Steel | Span: 600 mm

Breadth (b) = ___ mm | Depth (d) = ___ mm | I = bd³/12 = ___ mm⁴

Calculations

Step 1: Calculate I = (b × d³) / 12 for each beam material.

Step 2: Calculate theoretical deflection using δ = WL³ / 48EI (simply supported) or δ = WL³ / 3EI (cantilever). Use the standard E values: Steel = 200 GPa, Aluminium = 70 GPa, Brass = 100 GPa.

Step 3: Plot Load (W) vs Deflection (δ) graph. The slope gives WL³ / 48EI, from which experimental E can be back-calculated.

Step 4: Calculate percentage error = [(Theoretical − Experimental) / Theoretical] × 100.

Expected Results

• The Load vs Deflection graph is linear, confirming elastic behaviour under the applied loads.
• Experimental deflection values agree within ±5% of theoretical values.
• Steel deflects least for the same load; aluminium deflects more; brass is intermediate — consistent with their E values.

Precautions

• Ensure the beam does not yield during loading — check that deflection returns to zero after unloading.
• Zero the dial gauge after positioning but before applying load.
• Apply loads gently to avoid impact.
• Measure beam dimensions at the section under maximum bending moment.

Viva Questions

1. What is the significance of flexural rigidity (EI)?
2. Why does a cantilever deflect more than a simply supported beam for the same load and span?
3. What is the Euler-Bernoulli beam theory assumption?
4. How does the moment of inertia change if beam depth is doubled?
5. Define neutral axis and its significance in bending.