Bending in Beam - Copy

8/12/2019 Bending in Beam - Copy

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MARA University of Technology

Faculty of Mechanical Engineering

Programme : Bachelor of Mechanical Engineering (Hons)

Course : Applied Mechanics Lab

Course Code : MEC 424

Lecture : Sir Syazwan Bin Abdul Latip

Laboratory Report

Title of Experiment:

BENDING IN BEAM

No Name Student Id No. Signature

1 MOHAMMAD HANIS IRSYADUDDIN (2012249314)

2 JOHAN BIN IDRIS (2012426554)

3 MUHAMAD FAIZ HAIKAL BIN AZIZAN (2011676466)4 MOHAMAD NAZRIEEN BIN ROSLAN (2012832524)

Laboratory session: Lecture verification:

Date of submission: Lecture verification:


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ABSTRACT

In this lab, the method of deflection is observed to determine the elastic modulus (E) of the

beam specimen. The lab will focus to the different types of the beam specimen by using mild

steel, aluminium and brass in which 0.45 mm, 0.56 mm and 0.6 mm respectively that havedifferent of width. The reason behind this testing was to better understand the deflection of

the beam when the load (W) was applied. The testing was done by clamping using load holder

and the centre point of the specimen beam was marked by using universal magnetic stand.

The value of the deflection was measure by using dial gauge when the load applied

continuously. Measurement of the deflection was recorded and then later compared with their

theoretical value.

This experiment was discovered using deflection measurement, an examination of the

relationship between deflection and materials properties will be shown along with a

comparison of the materials based on their strength and deflection, both theoretical and

experimental. Every different type of materials have a different elastic curve/Modulus young

(E) and the properties of each material. Such as, mild steel with 210 Gpa (E), aluminium with

70 Gpa (E) and brass with 104.1 Gpa (E). Aluminium has the lowest value of Modulus young

and this clearly shows that aluminium is softer than mild steel and brass. The load given to the

beam is proportionally with the deflection.


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TABLE OF CONTENTS

NO TITLE PAGE

1 Title

2 Abstract

3 Table of content

4 List Of Table

5 List Of Figures

6 Introduction

7 Objective

8 Theory

9 Apparatus

10 Experimental Procedure

11 Results

12 Discussion

13 Conclusion

14 References

15 Appendix

LIST OF TABLES

Table: Experimental data, sample observation

LIST OF FIGURES

Set up of apparatus


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OBJECTIVES

1) To determine the elastic modulus (E) of beam specimen by method of deflection.

2) To compare the analytical and experimental values of the stress in the stress in beam.

3) To become acquainted with various items of structural testing equipment.

4) To ascertain the coefficient of elasticity for steel, brass, and aluminum.


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Figure 1: Elastic Curve

Deflections are most often caused by internal loadings such as bending moment and axial

force. Bending is one of the engineering mechanics, characterizes the behavior of a slender

structural element subjected to an external load applied perpendicularly to a longitudinal axisof the element. Bending of beams is a frequently encountered loading situation in practice. A

slender member subject to traverse loads is termed as a beam under bending. At any cross-

section, the traverse loads generate shear and bending moment to maintain equilibrium. The

bending causes a change in curvature of the beam and induces tensile and compressive

stresses in the cross-section of the beam. Maximum stresses are achieved in layers furthest

from the neutral axis, the layer at which strain is zero.

Bending also the main point to ensure the building material chosen for a structure will besafely . People do nt want to work in a building in which the floor beams deflect an excessive

amount, even though it may be in no danger of failing. Consequently, limits are often placed

upon the allowable deflections of a beam, as well as upon the stresses.

When loads are applied to a beam their originally straight axes become curved. Displacements

from the initial axes are called bending or flexural deflections. The amount of flexural

deflection in a beam is related to the beams area moment of inertia I, the single applied

concentrated load P, length of the beam l, the modulus of elasticity E, and the position of the

applied load on the beam. The amount of deflection due to a single concentrated load P is

given by:

Where k is a constant based on the position of the load, and on the end conditions of the beam
http://en.wikipedia.org/wiki/Engineering_mechanicshttp://en.wikipedia.org/wiki/Structuralhttp://en.wikipedia.org/wiki/Structural_loadhttp://en.wikipedia.org/wiki/Structural_loadhttp://en.wikipedia.org/wiki/Structuralhttp://en.wikipedia.org/wiki/Engineering_mechanics


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THEORY

Pure bending

R 2=(R-y) 2 + (L/2)

R 2=R 2-2Ry+y 2+L2/4

Therefore: 2Ry=L 2/4

R=L 2/8y

M=W(x)

I=bh 3/12

As the beam is in static equilibrium and is only subject to moments (no vertical shear forces)

the forces across the section (AB) are entirely longitudinal and the total compressive forces

must balance the total tensile forces. The internal couple resulting from the sum of (.dA .y)

over the whole section must equal the externally applied moment.

E/M = M/I


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This can only be correct if (ya) or (y.z.y) is the moment of area of the section about the

neutral axis. This can only be zero if the axis passes through the centre of gravity (centroid)

of the section.

The internal couple resulting from the sum of (.dA .y) over the whole section must equal the

externally applied moment. Therefore the couple of the force resulting from the stress on

each area when totalled over the whole area will equal the applied moment

From the above the following important simple beam bending relationship results


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It is clear from above that a simple beam subject to bending generates a maximum stress at

the surface furthest away from the neutral axis. For sections symmetrical about Z-Z the

maximum compressive and tensile stress is equal.

max = y max . M / I

The factor I /y max is given the name section Modulus (Z) and therefore

max = M / Z

Values of Z are provided in the tables showing the properties of standard

steel sections

Deflection of Beams

Below is shown the arc of the neutral axis of a beam subject to bending.

For small angle dy/dx = tan = The curvature of a beam is identified as d /ds = 1/R

In the figure is small and x; is practically = s; i.e ds /dx =1

From this simple approximation the following relationships are derived.


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Integrating between selected limits. The deflections between limits is obtained by further

integration.

It has been proved ref Shear - Bending that dM/dx = S and dS/dx = -w = d2

M /dxWhere S = the shear force M is the moment and w is the distributed load /unit length of

beam. Therefore

If w is constant or a integratatable function of x then this relationship can be used to arrive at

general expressions for S, M, dy/dx, or y by progressive integrations with a constant ofintegration being added at each stage. The properties of the supports or fixings may be used

to determine the constants. (x= 0 - simply supported, dx/dy = 0 fixed end etc )

In a similar manner if an expression for the bending moment is known then the slope and

deflection can be obtained at any point x by single and double integration of the relationship

and applying suitable constants of integration.


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APPARATUS

Vernier calliperTwo support stands,

2 load hangers,

known loads, 2N

Dial Gauge

Aluminium Beam

Brass Beam Mild steel Beam


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PROCEDURE

1) The centre of the beam is marked on each side of this point mark off distances off.

2) The beam that was tested was tightly clamped at one end.

3) Good care was taken to make sure that the aluminum beam acted like a clamped free

beam which had no angular deformations at the root of the beam.

4) A hanging platform was then attached at the other end of the beam that slid over the

beam so that we would be able to apply a load there.

5) Dial gauge at the centre and set at zero.

6) 2N load is set at both load hangers at x(150mm).

7) The load is added until 16N.

8) The reading is recorded and all procedure is repeated using brass and mild steel.

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Bending in Beam - Copy