ARCH 252 - STRUCTURES 1

High Moment of Inertia Beam Design Project

Jordan davis

Professor Parker

fall 2012

10/28/12

000. Model Picture And Description

001. Test Setup Diagram

002. CalCulations: Centroid

003. CalCulations: Moment of Intertia

004. CalCulations: Calculated Deflection

005. CalCulations Control Beam Calculated

Deflection

006. Percent Error for Both Beams

007. Summary

008. Discussion

TABLE OF CONTENTS

Number of 1/ 16 in x 1/4 in Basswood Used : 16

Type of G lue Used : Sobo Prem ium C raft G lue

We ight : Bucket : . 79 1 lbs My Beam : 20 .74 1 lbs Cont ro l Beam : 13 .5 15 lbs

Def lect ion : My Beam : . 444 in Cont ro l Beam : . 2675 ' '

Load Supor ted : 19 .95 lbs

MODEL PICTURE AND DESCRIPTION

000

TEST SETUP DIAGRAM

001

CALCULATIONS: C e n t r o i d

002

.375’’

.6875’’

Component ∆A X ∆AX Y ∆AY

.258in2 .1875in .3438in .0887in2.0484in3

∆A ∆AX= Y=

∆AY∆AY

Y=X= .3438in.1875in

Cross Section

CALCULATIONS: MoMent of inertia

003

Ixc dy Ady2 Iyc dx Adx2

.375’’

.6875’’

Cross Section

bH3/12 Hb3/12

.01015in4 0in 0in 0in0in .00302in4

+

Ix= .01015in4 Iy= .00302in4

+

CALCULATIONS: CalCulated defleCtion

004

.375’’

.6875’’

Cross Section∆= PL3

48EI

∆= 48(1,460,000psi)(.01015in4)

(19.95lbs)(22in)3

∆= .2986in

CALCULATIONS: Control BeaM CalCulated delfeCtion

005

.375’’

.6875’’

Cross Section∆= PL3

48EI

∆= 48(1,460,000psi)(.00521in4)

(12.72lbs)(22in)3

Ix= bH3/12

∆= .371in

CALCULATIONS: PerCent error for Both BeaMs

006

Control Beam:

My Beam:

% error = ((|experimental Δ - calculated Δ|) ÷ calculated ∆) × 100

% error = ((|experimental Δ - calculated Δ|) ÷ calculated ∆) × 100

% error = ((|.2675in - .371in|) ÷ .371in) × 100

% error = 27.8 % error

% error = ((|.444in - .2986in|) ÷ .2986in) × 100

% error = 48.6 % error

CALCULATIONS: PerCent error for Both BeaMs SUMMARY:

007

Moment of Inertia (Ix ) = .01015in4

Experimental Deflection: .444in

Control Beam Experimental Deflection: .2675in

Calculated Deflection: .2986in

Calculated Control Beam Deflection: .371in

Percent Error for Control Beam: 27.8%

Percent Error for My Beam: 48.6%

DISCUSSION:

008

A few factors that would cause varying results can be the individual strength of each individual piece of basswood. The basswood’s Young Modulus differentiates from piece to piece, therefore not being a constant. The gauge could be rounding or simplifying the deflection giving us a different measurement. There could be weaknesses in the basswood such as: knots, cracks, chips, or any other inhibitions that could lower the strength of the beam. The glue could also affect the calculation since we did not account for the extra weight. The cross section may not be uniform all the way through the entire length of the beam, therefore causing inaccuracies in the calculated answer.