Page 1 of 6
Assignment 1: Introduction to Structures
Marks awarded for ANSWERS only.
Use solutions template to enter in results and follow instructions provided in template file.
An additional one-page document is required for answering Question 4 (pdf only)
So, your submission consists of two files:
1) solutions spreadsheet;
2) response to Question 4 (pdf)
Question 0:
Your student number is used to assign the values of a and b.
Use the tables below with the last (n) and second last digit (m) of your student number to assign
values to a and b respectively.
Last digit n
| n | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| a | 3.5 | 4 | 4.5 | 5 | 5.5 | 6 | 6.5 | 7 | 7.5 | 8 |
Second last digit m
| m | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| b | 0.15 | 0.2 | 0.25 | 0.3 | 0.35 | 0.4 | 0.45 | 0.5 | 0.55 | 0.6 |
e.g.: Student number 2308705, a = 6 (from n = 5), b = 0.15 (from m = 0).
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Question 1 (30%)
For the following cross-sections and axes shown, all dimensions are in mm.
For each question, pay attention to the method required to be used for determining section properties,
and provide only the properties requested.
| (a) | Calculate the centroid location, xc, yc (in mm), relative to the origin O. Use the complete cross-section dimensions |
(b) Calculate Ix, Iy, Ixy (in mm4) at the centroid, C.
(i) Use thin-wall assumptions: use segment centrelines and ignore higher powers of t (t 2, t 3, etc.)
(ii) Use concentrated areas only: any concentrated area has no self second moment of area.
(Ignore the properties of the thin-wall segments)
a
O
Y
X
1.5a
5b
| b |
Y
X
C
xc
| 5 39 166 + a c |
x |
=
p
ö÷ø
æçè
+ +
=
395
14710
5.2
p
p
c ay
t = 3b
3a
t = 5b
t = b
8a
yc
10a
A2
4a
t = 5b
12a
A1 = 75b mm2
A2 = 150b mm2
A3 = 250b mm2
A4 = 100b mm2
t = 5b
A4
t = b
Y
X
C
x
| c | yc |
ax
c 23
232
= c ay
23
174
=
9a
A1
t = b A3
17a
10a
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(c) Calculate Imax, Imin (in mm4) and a (in degrees), the angle between the XY and principal axes.
(i) For a cross-section with the following values
Ix
= 7a3b mm4, Iy = 410a3b mm4, Ixy = -4480a2b2 mm4
(ii) For a cross-section with the following values
Ix
= 9a3b mm4, Iy = 723a3b mm4, Ixy = 0 mm4
(d) For the given cross-sections, select the most suitable orientation of the principal axes from
the following options.
(i) cross-section from Question 1 (a)
(ii) cross-section from Question 1 (b) (i)
A B C D E
Imin
Imin
Imax
Imax Imax
Imax
Imin
Imin
a
1.5a
5b
| b |
Imax
Imin
t = 3b
3a
t = 5b
t = b
8a
Page 4 of 6
Question 2 (20%)
The beam below is loaded with forces, moments and a distributed load, which all act through the beam
centroid.
State whether each statement is true (T) or false (F) regarding the beam internal forces and moments
Note: where values of force and moment are stated these should be interpreted as magnitudes
| (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) (ix) (x) |
The shear force in the y direction at (0,0,a) is zero The shear force in the x direction at (0,0,b) is zero The shear force in the y direction varies linearly from (0,0,b) to (0,0,a) Moment A at (0,0,L) does not cause torsion The torsion at the fixed support (0,0,0) is zero The force 2P at (0,0,a) does not cause torsion The bending moment around the x axis at (0,0,L) is A The bending moment around the x axis varies linearly from (0,0,c) to (0,0,b) The bending moment around the y axis at (0,0,a) is zero if A = P The bending moment around the y axis varies linearly from (0,0,a) to (0,0,0) |
y
z
P P
a b
w
d
L
A
c
2A
e P
2P
x
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Question 3 (30%)
Answer the following short-answer questions
(a) State the number of significant figures in the following numbers:
(i) 4002 (ii) 7 ´ 1010
(b) Convert the following to the specified ( length // mass // time ) unit system, using the values
of a and b from Question 0. Enter ONLY the values in the template, NOT the units.
| SI ® Imperial (ft // slug // s) | Imperial ® SI ( mm // tonne // s) | ||
| (i) (ii) (iii) (iv) |
4a kN 25a MPa 22a × 109 mm4 341a N mm |
(v) (vi) |
2.2a ft-lbf 80a lbs 995b ksi 995b Msi |
| (vii) (viii) |
| (c) (i) |
State whether each statement is true (T) or false (F) A typical aircraft fuselage structure would be capable of carrying torsion moments |
| (ii) | Shear strain can be expressed in units of either degrees or radians |
| (iii) (iv) (v) |
The use of zeroes after a decimal point are an indicator of accuracy A material point in equilibrium has 1 independent component of shear stress in the xz plane A negative normal strain can be considered to increase or decrease volume depending on the coordinate system used The Poisson effect does not apply to shear strains In a 2D stress state in the xy plane, sz, txz and tyz can be ignored even if they are non-zero Plane stress occurs for thin plates undergoing in-plane loading only In plane strain, one dimension is large enough so that strain in that direction are zero At the mid-plane of a plate in pure bending the stresses are minimum The maximum shear stress causes the material to rotate by the principal angle |
| (vi) (vii) (viii) (ix) (x) (xi) |
|
| (xii) (xiii) (xiv) (xv) |
The product second moment of area Ixy is found by multiplying Ix and Iy Typical metals show elastic-plastic behaviour in tension and shear but not in compression Sandwich materials typically use a high density core with non-structural cover plates An external load and the resultant internal stresses are always statically equivalent systems |
| (xvi) | A roller support acts like a contact boundary condition as it can produce a reaction force as a push response to a body but will not produce a pull force to hold a body from moving away The shear force diagram is always the slope of the bending moment diagram |
| (xvii) |
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(d) Calculate the reaction loads at A and B, with sign relative to the positive axes shown
Question 4 (20%)
What is a free body diagram? What are they used for? How are they useful for the structural analysis of
an aircraft?
Explain with use of at least one diagram and at least one example, no more than one page.
Attach your answer as a separate one-page document (pdf) with your spreadsheet submission.
(Tip: Treat this as an opportunity to get feedback on your discussion skills, considering this will form a
significant part of your assessment for the whole course. Don’t just dump in what you find in a Google
search or in a textbook. See if you can answer it in your own words as best you can, with a diagram that
makes sense to you and helps illustrate your argument)
Y
X
A B
P1 P2
P1 = 3a N
150 P2 = 20b N
275
175
dimensions in mm
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