Lab 4 beam deflection and analysis - prelab - Derek Zahratka
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Iowa State University *
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Apr 3, 2024
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AerE 322 Aerospace Structures Laboratory Prelab Lab 4 Beam Deflection and Analysis Section 3 Group 5 Date: 2/14/2024 Member: Derek Zahratka 1 Instructions: •
Replace the highlighted areas in yellow above with your own name, section and group numbers and correct dates, •
Watch the corresponding lab demo videos, review related materials in lecture notes, lab manual and other related documents, •
Provide your best answers to the following questions. Add pages as needed, •
Convert this Word answer sheet into pdf format and submit to Canvas. Apply the basic beam theory, which you learned in EM324 or the like, to directly solve for the deflections for the cantilever beam setup as shown in Fig. 1. Please note that, in the following references, “x grams load” or simply “x grams” should be interpreted as the “gravitational weight/force of x grams mass”. Here the quantity of x purely measures the mass itself
. 1.
(30 pts) Derive a general formula by using either method of superposition or discontinuity function method and show the following expression for deflections at 1/3 beam length measured from the free end, i.e. ? =
2
3
𝐿, ? = −
?
𝐸𝐼
14
81
𝐿
3
2.
(20 pts) Calculate the deflections in mm at 1/3 beam length measured from the free end for three beams of rectangular cross section subjected to loads at the free end. Let the beam length be 90cm and use E = 68.9 GPa (for Aluminum 6061-T6511 alloy). The beam cross sections and loads are as follows: (A)
12.8 x 6.4 mm (12.8 mm is the base and 6.4 mm is the height) rectangular cross-section with 100 grams load.
(B)
6.4 x 12.8 mm rectangular cross-section with 200 grams load.
(C)
12.8 x 12.8 mm square cross-section with 500 grams loads.
Load w
applied here
deflection y
measured here
1/3 L
1/3 L
1/3 L
x
y
E, I
Figure 1. Cantilever beam setup for Prelab
AerE 322 Aerospace Structures Laboratory Prelab Lab 4 Beam Deflection and Analysis Section 3 Group 5 Date: 2/14/2024 Member: Derek Zahratka 2 Total 50 points Answers:
AerE 322 Aerospace Structures Laboratory Prelab Lab 4 Beam Deflection and Analysis Section 3 Group 5 Date: 2/14/2024 Member: Derek Zahratka 3
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