beam bending_introductory presentation

8/6/2019 Beam Bending_Introductory Presentation

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Lab 2: FundamentalConcepts

Beam Bending


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Goals

Understand the principles of Stress-Strain

To make measurements for cantileverbeam bending and compute the deflectionof different materials and shapes.

To understand how engineers compare

different materials. To understand why cross-sectional shapeis important in design


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Characterization of Stiffness andStrength of Materials

L

L

P

P

Strain: L

L=

Stress: A

P =

A

P

Units of stress:

)Pa(m

N)psi(

in

lb22

or

The tension test:


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Stress-Strain Curve

In the elastic (linear) portion of the stress-strain curve: E = (Hookes Law)

Modulus of Elasticity (slope of - ) curve)(Material Stiffness )

+

Strain

+

+

Ceramic

Steel

Aluminum

Stre

ss

Plastic

Elastic

Yield Stress

Yield Stress


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Yield Stress is the limit of the elasticregion. Materials that are loaded withinthe elastic region will return to their

original dimensions upon unloading Typical values:

Steel Aluminum Copper Titanium

Modulus of Elasticity 29x10 6 10.1x10 6 17x10 6 16.5x10 6(psi)

Yield Stress 36,000 - 14,000 - 10,000- 25,000-(psi) 100,000 73,000 53,000 120,000

Stress-Strain


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Structural components are designed todeform (change dimensions) when used.For Example:

The top floorof the Searstower inChicago cansway 6inches due tothe forceapplied bythe wind

Stress-Strain


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The tip of the wings of a Boeing 747 Jumbo jet deflect up 14 feet as the aircrafttake off.

Stress-Strain


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Stress-StrainStress Strain Experienced in bridges.

u will get information regarding this in your bridge competi


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Bending of a CantileverBeam

Experimental setup:

F

L

Weights

Dial indicator s


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The deflection of the beam depends on: The load F . More deflection with larger load.

The length of the beam. The deflection of theend increases with the length.

Material stiffness. Higher stiffness producesless deflection.

The geometry of the cross section. Highermoment of inertia (defined in the next slide),results in less deflection.

Bending of a Cantilever Beam


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Theoretically, the deflection of the beam atthe location of the dial indicator is given by

( ) s L I E

s F = 36

2

Where E is the modulus of elasticity of the beams material, and I is the momentof inertial of the cross section.

Bending of a Cantilever

Beam


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b

h

b2

b1

h2 h

1

Rectangular Box

3

12

1hb I

rect =

3

22

3

1112

1

12

1hbhb I

box=

Moment of Inertia of a CrossSection

In the lab we will set up three cantilever beams and we willcompare their deflection. Two of the beams have the samecross section geometry (rectangle), but one is made of steeland the other is made of aluminum. The third beam is madeup of aluminum with a smaller cross sectional area than thefirst two beams, but with a box cross section.


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For each of the three beams (steelrectangular, aluminum rectangular,aluminum box):

1. Clamp the beam and position the dialindicator such that:

L = 12.5 in. and s = 11.5 in.Refer to setup shown on the next slide

2. Load (by placing 2.5 lb weights in thebucket) incrementally (5 increments) up

to:

In Lab


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In Lab

Setup

DialIndicator:Make sureindicatoris in an uprigposition

Clamps:Clamp the L-shapedBeam and theCantilever beam tothe edge of thetable

Make suremagnet isturned ON

Bucket: Place weights inthe bucket


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In Lab

Setup

DialIndicator:Make sureindicatoris in an uprightposition

Clamps

L= 12.5 in

s = 1 1 . 5

i n


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NOTE: The deflection measured in the lab is greaterthan theory predicts. This is mainly due tohow the beams are clamped. The clampedend is not a true fixed end as assumed bytheory, and the beam is not perpendicular tothe side of the table.

ASSUMED BEAM ACTUAL BEAM


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Worksheet A(located in procedure)

Steel Beam

AluminumBeam

AluminumBox

E , Modulusof Elasticity

(psi)

29x106

10.1x10 6

10.1x10 6

Width, b(in.)

Height, h(in.)

Wall Thickness

(in.)

I, Momentof Inertia

(in 4)

N.A

N.A


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Worksheet A - Example

Steel rectangular:

Load F (lbs)

Deflection

Theoretical, (in)

Deflection

Experimental , (in)


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Lab ReportingRequirements

Write an individual lab memoSee procedure for discussion questions andreview grading guidelines for pointdistribution.Due in Lab 3.Note: Pay special attention to memorequirements. If you receive less than a 90%on this memo, you will be required to rewritethe memo and resubmit it in Lab 5.


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Important: Memo GradingGuidelines Sample Grading Guide

beam bending_introductory presentation

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