EXPERIMENT NO.: 06
Objective

To determine diametrical deflection of a circular bar subjected to diametrical loading.
Introduction
Diametrical deflection of a circular bar subjected to diametrical loading is an important concept in
mechanical and civil engineering. When a circular bar is subjected to a load applied along its
diameter, it undergoes deflection, which is critical to determining its mechanical behavior and
overall strength. This deflection can affect the structural integrity of a mechanical system or a civil
structure, and it is therefore essential to calculate it accurately to ensure the safety and reliability
of the system or structure.
The diametrical deflection of a circular bar is influenced by several factors, including the diameter
and length of the bar, the material properties, and the magnitude and location of the applied load.
The deflection is proportional to the load applied and the length of the bar, while inversely
proportional to the diameter of the bar and the modulus of elasticity of the material. Accurately
calculating the diametrical deflection of a circular bar requires a thorough understanding of the
mathematical formulas and equations that govern this behavior.
The diametrical deflection of a circular bar is also influenced by the type of loading. In the case of
diametrical loading, the load is applied along the diameter of the bar, which causes the bar to
deform in a specific manner. This type of loading can be found in various mechanical systems and
civil structures, and understanding the diametrical deflection behavior of circular bars subjected to
diametrical loading is crucial to ensuring their optimal design and safe operation.
Theory
The diametrical deflection of a circular bar subjected to diametrical loading can be determined by
analyzing the bending behavior of the bar using basic mechanics of materials principles. The
deflection of the bar can be calculated using the following theory and formulas:
The bending moment: The bending moment at any point along the bar is given by the equation:
𝑀 = 𝐹 ∗ 𝐿/4
Where M is the bending moment, F is the applied load, and L is the length of the bar. This equation
assumes that the load is applied at the midpoint of the bar, resulting in equal deflection on both
sides.
The stress distribution: The stress distribution in a circular bar under diametrical loading is given
by the equation:
𝜎 = 𝐹 / (𝜋 ∗ 𝑑 ∗ 𝑡)
Where σ is the stress, F is the applied load, d is the diameter of the bar, and t is the thickness of
the bar. This equation assumes that the load is uniformly distributed over the cross-sectional area
of the bar.
The bending stress: The bending stress is calculated using the following formula:
𝜎_𝑏 = 𝑀 ∗ 𝑐 / 𝐼
Where σ & b is the bending stress, M is the bending moment, c is the distance from the neutral
axis to the point where the stress is being calculated, and I is the moment of inertia of the crosssectional area of the bar.
The curvature of the bar: The curvature of the bar is determined by the following equation:
κ = σ-b / E
Where κ is the curvature, σ-b is the bending stress, and E is the modulus of elasticity of the
material.
The deflection of the bar: The deflection of the bar at any point is given by the equation:
𝛿 = (𝐹 ∗ 𝐿^3) / (48 ∗ 𝐸 ∗ 𝐼)
Where δ is the deflection, F is the applied load, L is the length of the bar, E is the modulus of
elasticity of the material, and I is the moment of inertia of the cross-sectional area of the bar.
Methodology
Apparatus






Curved bar apparatus
Ring
Vernier Calipers
Meter rod
Dial Indicator Gauge
Weight and weight pans
Procedure
Following are the steps that are involved in performing the above experiment.







Check the zero error and least count of the measuring devices.
Measure the width and height of circular bars with the Vernier caliper. Also measure the
diameter of the circular ring with the meter rod.
Position and fix the dial indicator gauge on the ring to get the desired the deflection.
Level the whole apparatus using the levelling screws at the bottom and level indicator.
Apply a small load by adding a weight on the hanger.
Note the deflections in the central gauge
Keep adding weights with regular increments and note the dial gauge reading for each
successive addition.


Note the dial gauge readings while unloading the weights one by one.
Calculate the mean deflection
Observations & calculations
Discussion
The diametrical deflection of a circular bar subjected to diametrical loading can be a critical factor
in the design of structures such as bridges, towers, and other load-bearing components.
Understanding the behavior of the bar under such loading conditions can help engineers to ensure
that the structure is safe and able to withstand the expected loads.
In this experiment, the diametrical deflection of a circular bar under diametrical loading was
analyzed using basic mechanics of materials principles. Theoretical formulas were used to
calculate the bending moment, stress distribution, bending stress, curvature, and deflection of the
bar.
During the experiment, it is important to ensure that the load is applied uniformly and at the
midpoint of the bar. Any deviations from these conditions can affect the accuracy of the results.
Additionally, it is important to take careful measurements of the bar's dimensions and to use
appropriate units and conversions in the calculations.
Conclusion
The experiment to determine the diametrical deflection of a circular bar subjected to diametrical
loading was successful in analyzing the behavior of the bar under this type of loading condition.
Theoretical formulas and mechanics of materials principles were used to calculate the bending
moment, stress distribution, bending stress, curvature, and deflection of the bar.
The results of the experiment demonstrated that the diametrical deflection of a circular bar is
directly proportional to the load applied and the length of the bar. It was also observed that the
deflection decreases as the diameter of the bar increases and the material's modulus of elasticity
increases.
The experiment highlighted the importance of considering material properties, cross-sectional
area, and location of the applied load in the design of load-bearing structures. By using the results
of this experiment, engineers can ensure that the structures they design can withstand the expected
loads and deflection limits.
.