AAE 221 Aerospace Structures II Spring 2004 Chapter 2.1 Beam Bending and Extension 0. Obtain the bending moment and shear force diagrams for the following cases, where P is a force, M0 a moment and w a force per unit length. In (i) the pin joint acts like
AE 221 Aerospace Structures II Spring 2004 Chapter 2.2 Beam Torsion Solution 1. Relevant information Mt = 400 N*m Length = 4 m E = 70,000 N/mm2 = .3 a = .02 m b = .0125 m
70000 N E = = 26923 = 36923 10 6 Pa 2 2(1 + ) 2(1 + .3) mm
The torsional co
AAE 221 Aerospace Structures II Spring 2004 Chapter 2.1 Beam Bending and Extension Solutions
1. (a) The Youngs modulus of the three sections are
E1 = 3 10 7 E 2 = E3 = 1 10 7
First, the Youngs modulus of aluminum is chosen to be the reference mo
AE 221 Aerospace Structures II Spring 2004 Chapter 1 Review Solution To learn more about Matlab commands and their arguments, type help and then the command that you need help with. For example, if you want to find out what linspace does, enter help linsp
AE 221 Spring 2004 FINAL EXAM Solutions
1. (i) Components sxy and sxz are tractions components on the lateral surfaces of the bar and must therefore be zero there. So their variation with the height of the bar cannot be as significant (since they have to
AE 221 Spring 2004 EXAM #2 Solutions
1. (i) A statically determinate structure is one in which the force and moment reactions (and internal resultants) can be obtained from equilibrium alone (i.e., by solving SF = 0 and SM = 0). This considerably simplifi
AE 221 Spring 2004 EXAM #1 Solutions
1. The is an extension and a bending problem in this case. Since the beam is of homogeneous
and symmetric cross-section Iyz = 0, thus uncoupling the y and z bending problems.
( EAu) = - f x = 0
u(0) = 0
AE 221 Spring 2004 Structures II Chapter 4 Introduction to Buckling
For an electronic chip design a conducting film (modulus E) of thickness t and width w is deposited on a much thicker silicon substrate. The deposit did not bond to the substrate over
AAE 221 Structures II Spring 2004 Chapter 3.2 Analytical solutions of static problems using energy methods
1. Consider the beam problem illustrated in fig. 1.
fig. 1 The beam is homogenous and symmetric, has length L, a moment of inertia I and a Youngs mo
AAE 221 Structures II Spring 2004 Chapter 3.1 Work and potential energy principles
1. Using PVW, find the equilibrium position of the two masses subjected to the effect of an external force F and of gravity (see fig. 1).
fig. 1 2. Using PVW, solve the fol
AAE 221 Aerospace Structures II Spring 2004 Chapter 2.3 Beam Shearing
1. Consider the homogenous C-channel cantilever beam shown in Figure 1. The beam is of length L, and its cross-section is of uniform (small) thickness t. The dimensions of the beam can
AAE 221 Aerospace Structures II Spring 2004 Chapter 2.2 Beam Torsion 1. An uniform beam with elliptical cross-section is submitted to a twisting moment of 400 Nm. The length of the beam is 4m. The beam is made of aluminum (E = 70,000 N/mm2), = 0.30). The
AE 221 Aerospace Structures II Spring 2004 Chapter 1 Review Practice Problems Using the package(s) of your choice (Mathematica, Maple, Matlab, Gnuplot, ), solve the following problems, which are typical of those you will face in AE 221. 1.
0 for x < x0 Pl
AAE 221 Aerospace Structures II Spring 2004 Chapter 4 Introduction to Buckling Solution 1. We can neglect y effects and assume s y = 0 .
From the beam equation, w' '+
4p 2 EI P w = 0 , we get Pcr = . EI S2
In addition, s x = s y = 0 (plane stress in x-y p
AAE 221 Aerospace Structures II Spring 2004 Chapter 3.1 Work and Potential Energy Principles Solution 1. Consider the free body diagrams below. The circular object on the left represents the upper mass while the circular object on the right represents the
AAE 221 Structures II Spring 2004 Chapter 2.3 Beam shearing 1. First the location of the centroid and the moments of inertia must be found
1 1 z i Ai = 98t 2 A The moments of inertia are y cm =
2 2 t 1 2 25t ( 2.5t ) + 48t 2 = 6.62t
25t t 3