{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

gm1_4_notes

# gm1_4_notes - Lecture M1 Slender(one dimensional Structures...

This preview shows pages 1–5. Sign up to view the full content.

Lecture M1 Slender (one dimensional) Structures Reading: Crandall, Dahl and Lardner 3.1, 7.2 This semester we are going to utilize the principles we learnt last semester (i.e the 3 great principles and their embodiment in the 15 continuum equations of elasticity) in order to be able to analyze simple structural members. These members are: Rods, Beams, Shafts and Columns. The key feature of all these structures is that one dimension is longer than the others (i.e. they are one dimensional). Understanding how these structural members carry loads and undergo deformations will also take us a step nearer being able to design and analyze structures typically found in aerospace applications. Slender wings behave much like beams, rockets for launch vehicles carry axial compressive loads like columns, gas turbine engines and helicopter rotors have shafts to transmit the torque between the components andspace structures consist of trusses containing rods. You should also be aware that real aerospace structures are more complicated than these simple idealizations, but at the same time, a good understanding of these idealizations is an important starting point for further progress. There is a basic logical set of steps that we will follow for each in turn. 1) We will make general modeling assumptions for the particular class of structural member In general these will be on: a) Geometry b) Loading/Stress State c) Deformation/Strain State 2) We will make problem-specific modeling assumptions on the boundary conditions that apply (idealized supports, such as pins, clamps, rollers that we encountered with truss structures last semester) a.) On stresses b.) On displacements 3) We will apply an appropriate solution method: a) Exact/analytical (Unified, 16.20) b Approximate (often numerical) (16.21). Such as energy methods (finite elements, finite difference - use computers) Let us see how this works: Applied at specified locations in structure

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Rods (bars) The first 1-D structure that we will analyzes is that of a rod (or bar), such as we encountered when we analyzed trusses. We are interested in analyzing for the stresses and deflections in a rod. First start with a working definition - from which we will derive our modeling assumptions: "A rod (or bar) is a structural member which is long and slender and is capable of carrying load along its axis via elongation" Modeling assumptions a.) Geometry L = length (x 1 dimension) b = width (x 3 dimension) h = thickness (x 2 dimension) Cross-section A (=bh) assumption: L much greater than b, h (i.e it is a slender structural member) (think about the implications of this - what does it imply about the magnitudes of stresses and strains?) b.) Loading - loaded in x 1 direction only Results in a number of assumptions on the boundary conditions
Similarly on the x 2 face - no force is applied s 21 = s 12 = 0 s 32 = s 23 = 0 s 22 = 0 on x 1 face - take section perpendicular to x 1 and c.) deformation s 31 = 0 s 32 = 0 s 33 = 0 s 12 = 0 s 13 = 0 s 11 dA = P A s 11 dx 2 dx 3 = P s 11 = P bh = P A

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Rod cross-section deforms uniformly (is this assumption justified? - yes, there are no
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern