ARCH 252 - STRUCTURES 1 High Moment of Inertia Beam Design Project
Jordan Davis Professor Parker Fall 2012 10/28/12
TABLE OF CONTENTS
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
MODEL PICTURE AND DESCRIPTION
N u m b e r o f 1 / 1 6 i n x 1 /4 i n B a s s w o o d U s e d : 1 6
T y p e o f G l u e U s e d :
W e i g h t :
B u c k e t : . 79 1 l b s
M y B e a m : 2 0 . 74 1 l b s
Deflection:
My Beam: .444in
L o a d S u p o r t e d :
Sobo Premium Craft Glue
Co n t r o l B e a m : 1 3 . 5 1 5 l b s
Co n t r o l B e a m : . 2 67 5 ' '
19.95lbs
000
TEST SETUP DIAGRAM
001
CALCULATIONS: C e n t r o i d Cross Section
.6875’’
.375’’
Component
∆A
X
∆AX
Y
∆AY
.258in2
.1875in
.0484in3
.3438in
.0887in2
X=
∆AY ∆A
X= .1875in
Y=
∆AY ∆A
Y= .3438in
002
CALCULATIONS: Moment of Inertia Cross Section
.6875’’
.375’’ bH3/12
Hb3/12
Ixc
dy
Ady2
Iyc
dx
Adx2
.01015in4
0in
0in
.00302in4
0in
0in
+
+
Ix= .01015in4
Iy= .00302in4
003
CALCULATIONS: Calculated Deflection Cross Section
∆= PL 48EI 3
(19.95lbs)(22in) ∆= 48(1,460,000psi)(.01015in4) 3
.6875’’
∆= .2986in
.375’’
004
CALCULATIONS: Control Beam Calculated Delfection Cross Section
∆= PL3 48EI (12.72lbs)(22in) ∆= 48(1,460,000psi)(.00521in4) Ix= bH3/12 3
.6875’’
∆= .371in
.375’’
005
CALCULATIONS: Percent Error For Both Beams Control Beam: % error = ((|experimental Δ - calculated Δ|) ÷ calculated ∆) × 100 % error = ((|.2675in - .371in|) ÷ .371in) × 100 % error = 27.8 % error
My Beam: % error = ((|experimental Δ - calculated Δ|) ÷ calculated ∆) × 100 % error = ((|.444in - .2986in|) ÷ .2986in) × 100 % error = 48.6 % error
006
SUMMARY:
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%
007
DISCUSSION:
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.
008