# Cantilever Column Load, Twisting Moment, Stress and Strain, Slope and Deflection

Cantilever Light beam

Table of Contents

Table of Contents2

1 . Introduction3

2 . Theory3

2 . you Bending Instant and Stresses3

2 . two Deflection and Slopes5

several. Equipment6

5. Procedures7

some. 1 Method 17

4. 2 Procedure 28

4. 3 Procedure 38

five. Results8

a few. 1 Comes from procedure 18

5. 2 Results from method 210

a few. 3 Results from procedure 312

6. Conversation and Error Analysis14

six. Conclusion15

1 ) Introduction

Within this lab a beam was tested to find the associations between fill, bending second, stress and strain, slope and the deflection in a cantilever beam that was the main aim. The main goal was to understand the fundamental concepts that have to be taken into account before designing and manufacturing a beam or using one as part of a design.

2 . Theory

The theory behind this laboratory can be grouped to two different issues, bending second and stress being the first, the second being incline and deviation. Each one is talked about below: installment payments on your 1 Bending Moment and Stresses

Picture [ 1 ]

Twisting moment is known as a moment created by a load applied to a surface area that causes it to fold. In the case of the lab the surface is the beam device applied towards the end of it. To be able to calculate the bending minute it is necessary to pull a Free Body Diagram indicating all the pushes applied after the beam. Picture one particular is the free of charge body picture of the column. F is a load applied, R is definitely the reaction from the clamps (the bar is fixed within the bench by two G clamps) and M is a bending moment. Since we must have balance and no pushes on the x-axis there are two equations we have to use the pursuing equations: If we resolve the vertical makes for the whole beam

ОЈFY=0в†”F-R=0 в†”

F=R (1) By taking occasions anti-clockwise regarding right hand side for the entire beam WL+ M=0 в†”

M=-WL (2)

Equation (2) is a bending second of the column (measured in Nm), as the equation (1) describes the sheer force. Picture [ two ]

For the bending pressure in the light it is useful to know the second moment of area (I) first. The form of the tavern is rectangle-shaped as mentioned on Determine 2

Iz=y2dA=-d2d2y2 bdy=by33-d2d2=bd324+bd324в†”

Iz=bd312 (3)

The Second instant of place is measured in mm4

The bending stress is Пѓx=ОµxE where Оµx is the stress and Elizabeth is the Young's modulus. (The stress is definitely measured in N/m2) There is a last equation that links bending pressure with bending moment. MI=Пѓxy=ER

2 . 2 Deflection and Slopes

In order to find the equations for slope and deflection it is necessary to use formula (1) and (2). It is known that Meters =-EId2vdx2. Therefore the twisting equation may be rewritten while -EId2vdx2=-Wx (x is a unique length of the light always smaller than the whole size L). In case it is integrated even as we will get the slope equation -EIdvdx=-W2x2+C1 (4) If we combine again (4) then we have deflection equation -EI=-W6 x3+C1x+C2 (5)

Simply by inserting boundary conditions to look for the constants of integration a final equations to get the light beam slope and beam deviation can be determined. At x=L: dv/dx=0 and v=0

4в†”0=-W2 L2+C1в†”

C1=WL22

5в†”0=-W6 L3+WL22 L+C2в†”

C2=-WL33

Hence 4 and 5 may be re-written because

Beam Incline: dvdx=W2EI(x2-L2) [m]

Beam Deflection: v=W6EI L-x2(2L+x) [m]

three or more. Equipment

The apparatus used through the lab program is the subsequent:

1) Along with

Used to put the equipment

2) Two G-Clamps

Positioned parallel to one another to hold strongly the column in place 3) One Aluminum Cantilever Column

The key subject from the experiment, with strain gauge attached both on top and bottom. The Young's Modulus of the beam is 70GPa. It was designated at 50mm intervals to facilitate the process....

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