Role of Axial Compressive Force in Bending of Beam

Aim

·         Aim of this lab work is to understand the role of axial compressive force in bending of beam

Objective

·         Find the deflection of beam with vertical supports

·         Fins the deflection of beam with oblique support

·         Calculate modulus of elasticity of beam with vertical support

·         Calculate deflection of beam with oblique support

Introduction

Beam is one of the most important structural members as it is used in a lot of structures used in daily life. Structures like building, vehicles and even furniture has beam to support its functional structures. There many different types of beams main classified on the basis of their shape and support placement type.

Shapes of Beam

Beam can be of any shape as needed but there some very common shapes that are used in daily life structures. Some of them are as follow

1.      I beam

2.      T beam

3.      Square beam

4.      Rectangular beam

5.      Circular beam

Beam type on support placement

Beam provides support to the structure of the body and for that they them self need some support from ground of the other member of that body. Based on the placement of the support a beam have following are the classes of the beams.

1.      Simply supported beam

2.      Overhanging beam

3.      Cantilever beam

Bending moment

When a force is applied to the beam then that beam under the influence of that beam try to rotate at its fixed point also called pivot point of the beam. This rotating effect of the beam is called bending moment of beam. This bending moment can be calculated as follow

Where

M is moment

F is force applied

d is the displacement from the pivot point

Bending stresses

Beam provides support to any structure by taking its load and provides resist against that load. When a certain load is applied on the beam then that load tries to bend it. Due to this stresses are produce in beam called the bending stresses. Bending stresses can be calculated by the help of following formula

Where

M is bending moment

C is distance from neutral axis

I is moment of inertia

Deflection of beam

When a load is applied to the beam then bending stresses are produce in beam and as a result of those bending stress deflection is produce in beam. Deflection of beam is the displacement of beam from its initial position. Deflection of simply supported beam can be calculated as follow.

Where

 beam deflection

F force applied

E modulus of elasticity

I second moment of the inertia

L length of beam

Procedure

Following is the procedure to perform the experiment for finding the deflection of beam

1.      First of all setup the apparatus which involve fixing the ends of the aluminium beam between one fix and one change able end of the apparatus and placing hanger at the centre of the beam

2.      Second step is to check the apparatus of any error and remove them if there are any

3.      Third step is to add weight of 10 N on hanger and note the reading of beam deflection

4.      Fourth step is to repeat the step three for weights up to 100 N

5.      After 100 N weight has been applied then remove the weight in the manner they were added and not the deflection for each step

6.      Repeat the same procedure for oblique end attachment

Results

Force on beam	Loaded deflection mm oblique	Unloaded deflection  mm oblique	Loaded deflection mm vertical	Unloaded deflection  mm vertical	Average deflection oblique	Average deflection mm vertical
0	350	351	351	350.5	0	0
5	351	352.5	352	351	1	1
15	354	354.5	354	352.5	4	3
25	356	356.5	355	354.5	6	4
35	358	358.5	357	356	8	6
45	361	361	359	357	11	8
55	363	363.5	361	359.5	13	10
65	366	366	363	361	16	12
75	368	368	364.5	363	18	13.5
85	371	371.5	366	364.5	21	15
95	373.5	374.5	367.5	366.5	23.5	16.5
105	377	377	369	369	27	18

Calculations

Reaction at support

 Bending moment at A

Bending moment at B

Deflection Equation

The theoretical value of aluminium modulus of elasticity is about 68 to 70 GPa whereas the above value for modulus of elasticity is only 6.5 GPa. This difference can be due to the type of experiment used because this method for calculating required experimentally calculating the deflection of beam when a particular load is applied. Application of load, reading the deflection and placement of load is all done manually by operator. Any mistake made during experiment will result is incorrect calculation for modulus of elasticity.

Compressive force

Compressive load when load is 5 N

Discussion

After the setting up the apparatus, loads were applied to beam for both arrangements of ends this for vertical and oblique end type. Deflection was recorded for both types for each weight from 10 to 100 N. when graph of deflection against loading was made the graph of oblique and vertical end was same initially but as the load was increased the graph of oblique end show more increase in deflection as compared to vertical end. High deflection value of oblique end as compared to the vertical end shows that the compressive axial load has great effect on the deflection of beam. So it must be considered during the designing of item where they are present.