Beam Deflection Experiment

• This lab focuses on measuring beam deflection under different loading scenarios and comparing these measurements to theoretical calculations.
• The experiment examines how support conditions and beam materials affect deflection.

Objective

• Measure beam deflection under various loading conditions.
• Compare measured deflections to theoretical calculations.
• Investigate the impact of different support conditions and beam materials on beam deflection.

Equipment

• Beam apparatus supporting simple, cantilever and fixed supports.
• Dial gauge indicator.
• Weights and weight hangers.
• Steel, aluminum, and brass beams of varying cross-sections.
• Micrometer or caliper for measuring beam dimensions.

Theory

• Beam deflection relies on material properties, cross-sectional geometry, load applied, and support conditions.

Formulas for Common Beam Configurations:

• Simply Supported Beam (point load at midspan): $\delta = \frac{PL^3}{48EI}$
• Cantilever Beam (point load at the free end): $\delta = \frac{PL^3}{3EI}$
• Simply Supported Beam (Uniformly Distributed Load): $\delta = \frac{5wL^4}{384EI}$
• $\delta$ is deflection at point of interest.
• $P$ is point load.
• $w$ is uniformly distributed load (force per unit length).
• $L$ is beam length.
• $E$ is modulus of elasticity of the beam material.
• $I$ is area moment of inertia of the beam's cross-section

Area Moment of Inertia

• The area moment of inertia ($I$) for a rectangular beam is given by: $I = \frac{bh^3}{12}$
• $b$ is the width of the beam.
• $h$ is the height of the beam.

Procedure

1. Measure Beam Dimensions

• Use a micrometer or caliper to measure the width ($b$) and height ($h$) of each beam specimen.
• Record these measurements in Table 1.

2. Material Properties

• Record the modulus of elasticity ($E$) for each beam material (steel, aluminum, brass) from a material property table or reference book in Table 1.

3. Simple Support with Point Load

• Set up the beam apparatus for simple supports. Measure and record the span length ($L$) in Table 2.
• Place a weight hanger at the midspan of the beam.
• Position the dial gauge indicator at the midspan to measure deflection.
• Apply a known weight ($P$) to the hanger. Record the weight in Table 2.
• Record the deflection ($\delta$) indicated by the dial gauge in Table 2.
• Repeat steps 3.4 and 3.5 for different weights.
• Repeat steps 3.1 to 3.6 for different beam materials.

4. Cantilever Beam with Point Load

• Set up the beam apparatus as a cantilever. Measure and record the span length ($L$) in Table 3.
• Apply a known weight ($P$) to the free end of the beam. Record the weight in Table 3.
• Record the deflection ($\delta$) indicated by the dial gauge in Table 3.
• Repeat steps 4.2 and 4.3 for different weights.
• Repeat steps 4.1 to 4.4 for different beam materials.

5. Data Analysis

• Calculate the theoretical deflection for each loading condition using the appropriate formula from the Theory section. Record these calculations in Tables 2 and 3.
• Compare the measured deflections with the theoretical deflections and Calculate the percentage difference between them.

Data Tables

• Tables are provided to record beam properties, simple support/point load data, and cantilever beam/point load data.
• These tables help to organize measured and theoretical deflection values, along with percentage differences.

Discussion Points

• Identify error sources during the experiment.
• Compare deflection characteristics across beam materials.
• Analyze the impact of varying loads on the deflection of beams.
• Discuss limitations of chosen theoretical formulas.
• Suggest improvements for accuracy in experiment execution.

Conclusion

• Experimental findings summarize comparisons between measured and theoretical deflections as well as effects tied to beams and support conditions.
• Summarize the limitations of the theoretical models used.