AAE 352, CRN 52120, Fall 2016
Homework #2; Due on Wednesday, September 7
Solve the following problems. This HW is for your own benefit and is necessary to properly learn
the material. You may work in teams and turn in one assignment per team. Write all te

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: 151.
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TORSION
.1 Tension OF UNIFORM ems
Torque is an important load on aircraft structures. The resulting shear stresses
and twist angle are to be determined.
There are two main approaches for solving the tors

3000 lb 30"
4000 lb 20" 10" 30"
Problem 2-4: The structure shown in the figure is an idealization of an engine mount. Find the internal forces in the 5 two-force members. The supports on the right (at C and E) are pinned.
34.641" 60
Rcy
A B C
Rcx
y x
D
E

AAE 352, CRN 52120, Fall 2016
Homework #2
Problem 1:
The members of the truss are assumed to be pin connected. If
member AC is a rod made of Ti 6-4 (E = 16500 ksi) of 3inch
diameter, determine the maximum allowable load P that can be
supported by the trus

Mechanics of Aircraft structures C.T. Sun
2.3
Consider the displacement field in a body: u = 0.02x + 0.02y 0.01z cm v= + 0.01y 0.02z cm w = -0.01x + 0.01z cm Find the locations of the two points (0,0,0) and (5,0,0) after deformation. What is the change of

Mechanics of Aircraft structures
C.T. Sun
2.8
A state of hydrostatic stress is given by
0
[ ij ] = 0
0
0
0
0
0
0
0
Show that on any surface the force (or stress vector) is always perpendicular to
the surface and that the magnitude of the stress vector is

Mechanics of Aircraft structures C.T. Sun
4.1
A uniform beam of a thin-walled angle section as shown in Fig. 4.19 is subjected to the bending M y ( M z = 0 ). Find the neutral axis and bending stress distribution over the cross-section.
Figure 4.19
Thin-w

Me a '6
AAE 352, CRN 52120, Fall 2016
i Homework #4; Due on Wednesday, September 21
Problem 1
For the following system (shown as an axially loaded bar in (a) and the nite element used to
model the bar in (b) it is made of two uniform, linearly elastic mat

Mechanics of Aircraft structures C.T. Sun
5.5
Find the shear flow for the three-stringer section shown in Fig. 5.33 for
Vz = 5000 N and V y = 0 . Given shear modulus G = 27GPa , find the twist
angle per unit length. Also determine the shear center. Is the

Mechanics of Aircraft structures C.T. Sun
3.1
Show that there is no warping in a bar of circular cross-section.
Solution: (a) Saint-Venant assumed that as the shaft twists the plane cross-sections are warped but the projections on the x-y plane rotate as

Mechanics of Aircraft structures C.T. Sun
5.1
Find the flexural shear flow produced by the transverse shear force Vz = 1000N in the beam with the thin-walled section given by Fig. 5.30.
Figure 5.30
Thin-walled section with a side cut
Solution: (a) Assume

Problem 4-2
AAE352-Problem set #4 Solution to Problem 2 The configuration shown has four rod elements connected to three node points. Node 1 is fixed (u1=0). Node moves only in the horizontal direction and has three of the four elements attached to it. Al

Problem 3-3 A rocket weighs 50,000 lb. and has a pitch mass moment of inertia of 10,000,000 lb-sec2-in at the instant shown. At an altitude of 1000 feet a jet vane malfunction causes a force F=20,000 lb. to be applied as shown.
a) Find the vehicle load fa

AAE 352 Homework #6 Due: October 24, 2011
Problem 1 (a) A panel has a fixed width, b, and length, L. The thickness is h. The moment of inertia for calculating the bending stress is I = bh3/12. The maximum bending moment applied to the beam is Mmax. If the

Mechanics of Aircraft structures C.T. Sun
2.15
Write the strain energy density expression in terms of stress components by using (2.95) for isotropic solids and show that the Poisson's ratio is bounded by -1 and 0.5.
Solution: From equation (2.95), we hav

AAE 352 S08 HW #3 Solutions 2.1
Mechanics of Aircraft structures C.T. Sun
Consider a unit cube of a solid occupying the region 0 x 1 , 0 y 1, 0 z 1 After loads are applied, the displacements are given by u = x
v = y
w=0 (a) Sketch the deform

AAE 352 S08 HW #5 Solutions 2.9
Mechanics of Aircraft structures C.T. Sun
An isotropic solid with Young's modulus E and Poisson's ratio is under a state of hydrostatic stress as given in Problem 2.8. Find the corresponding strain components.
0 0

Mechanics of Aircraft structures C.T. Sun
3.5
The two-cell section in Fig.3.35 is obtained from the single-cell section of Fig.3.36 by adding a vertical web of the same thickness as the skin. Compare the torsional rigidity of the structures of Figs. 3.35

Mechanics of Aircraft structures C.T. Sun
5.14
Show that the shear center for the section of Fig. 5.36 is at a distance a ( a + b ) e= (a + b)(1 + ) to the left of stringer 1.
Figure 5.36
Four-stringer thin-walled section
Solution: (a) Assume that the thi

Mechanics of Aircraft structures C.T. Sun
7.1
The truss structure consists of two bars connected by a pin-joint (which allows free rotation of the bars). The other ends of the bars are hinged as shown in Fig. 7.26. A weight W is hung at the joint. Find th

AAE 352 S08 HW #4 Solutions 2.5
Mechanics of Aircraft structures C.T. Sun
A cantilever beam of a rectangular cross-section is subjected to a shear force V as shown in Fig. 2.17. The bending stress is given by
Mz I where M = -V ( L - x ) . Assume a

AAE 352 S08 HW #1 Solutions 1.1
Mechanics of Aircraft structures C.T. Sun
The beam of a rectangular thin-walled section (i.e., t is very small) is designed to carry both bending moment M and torque T. If the total wall contour length L = 2( a + b)

1.
2.
3.
Unstable critical point: x = 4
Spout: Along the equilibrium solution x(t) = 4
Solution: If x0 > 4 then
I1 = Idt; ]n(x4) = t+C; C = ln(xo-4)
x4 .
x4 = (xo4)e'; x(t) = 4+(x04)e'.
Typical solution curves are shown in the gure on the left below.
Stab