8
NAME ME 544
The maximum shear stress theory of failure is based on the shear stress occurring
on certain planes oriented relative to the principal axes. The distortion energy
theory of failure has a similar representation, called the octahedral shear
10.
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12.
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_ hlAE 544
States of Stress, Strain, and Energy at a Point
(hune
Derive an equation by which the normal stress, on, on any plane defined
by direction cosines, l,m,n, can be calculated from the six stress
components gx av, 02, TXY sz Ty
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.
+103 xmu.m:. 2. Homm. >a<m=oma nm.nc.:m
Hmc 0._._._.:.Uz._.:_. c>r00rdm om. 92:23. <>E>Ekm 7. m
on an: mua m. A: mu Amh m. m. qv m. w: m:
+ + + .+ -.ww:
H. A; e: m. . Q: m: 9. EH em 6: o: 9.
aw. M. a:
3. . WEN. AM: I Ema l .\._V.
. HH. | W
Mechanical Design and Failure Prevention
MAE 544: A first-level graduate course
Prerequisites: None required; the usual undergraduate background is assumed for solid mechanics, materials,
and mechanical design
Text: Failure of Materials in Mechanical Desi
MAE 544
II. STRUCTURE OF MATTER
The objective is to derive macros conic mechanical pmpejes from our understanding of the
micrgsirncture of materials.
A. There are many particles in matter. The ATOM is level at which the greatest understanding of
mechanica
MAE 544
DISLOCATION THEORY
1. Metallic gmaml lattice defects
Point defects:
vacancy, interstitial atom of the same or different kind, foreign substitutional atom
Line defect: IS a dislocation, i.e. a series of adjoining point-defects along a line
Surface
FORM DESIGN
MAE 441 Notes and Problems
The objective of form design is to use heuristics to select geometric congurations, proles, and crosssections of
structural elements (parts), as contrasted to making these determinations using a quantitative stress a
MAE 544
PRINCIPAL SHEAR STRESSES
Principal shear stresses are the non-zero extreme values of the shear stress 7' on an arbitrarily
oriented face at a point where stresses occur. Since the expression for
2 .
2 1s much less complex than the one
7' 20162 + 0
MAE 544
KINDS OF PRIMARY BONDING NOTES
Ionic
Electrons migrate from one atom to another causing a charge difference. The migration
arises because some atoms attract electrons more than others; this tendency is measured by
electronegativity.
The cohesi
NAME
A sign weighing 1780 N is
supported by a steel pipe as shown in
Fig. A. The maximum horizontal
wind force is estimated to be 400 N.
a.) Identify the critical point that
would be used in determining the size
of the pipe. Show its location in a
crossse
w, Indicate which of the following lengthy phrases complete the sentence with
accurate information.
Transverse shear stress
arises from a gradient in moment from the top to the center of a beam.
arises from a gradient in moment along the length of a beam.
NAME MAE 544
Mohrs circle is based on a twodimensional stress
transformation, not on a threedimensional one.
Therefore, Mohrs circle does not work as a geometric
model for obtaining 01, 0'2, and 0'3 from the six stress
components. To tie the cubic equatio
NAME MAE 544 7
A 2-inch diameter steel shaft has the hub of a gear attached to it by a shrink t that exerts a
radial pressure of 20,000 psi on the shaft. The sha is also subjected to a bending moment of
25,000 in-lbf and a torsional moment of 20,000 inlbf
Review of Load and Stress Analysis of a Heavily Loaded Part
General Procedure
1. Calculate external reaction loads from externally applied loads.
2. At a critical cross-section determine the 6 components of internal loading.
3. Reduce these to the FOUR re
NAME MAE 544
The results of a. certain nite element solution provide the stress components
ox = 816 psi, 0y = 477 psi, dz = 53,700 psi
7'33; = 92 psi, Ty: = 6,280 psi, 7' = 62 psi.
IE
a) Find the principal normal stresses and the surfaces on which they
NAME MAE 544
Determine the topological character (geometric shape) of that extremum point on the on surface which is
associated with the middle value of principal normal stress.
Hint: Use eqn (4-13) in Collins, but describe the state of stress using princ
Ag- Fr 5
TM MW= (Ha I'm;
' W M46 3
: two-q = lion/aw.
-WW a 3 I700 A/M.
Notice (i) that four parallel edges of the element are at right
angles to the pipe axis and are parallel to the tangent plane
at the critical point and (ii) that
MAE 544
OBJECTIVE OF EMBODIMENT
is
to nd some index of Failure Inducing Tendency (FIT) for each mode of failure and relate
this to material strength
Failure Mode Index of FIT
Fracture of brittle materials -
Plastic deformation (yielding)
III.
(5
ME 544 Problem
Problem 3-3 from Marin:
At the critical element in a member the stresses produced are arx=33000 psi,
03283200 psi, 0Z=10g000 psi 7x37: ZYZr-O, tar: 3,7700 psi.
Determine the principal stresses and the maximum shear stress.
Lecture 3 Orbital Mechanics I
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Lecture 7 Thermochemistry 1
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1.1 Fundamental Concepts
Rocket engines are a particular class of device that make use of the Jet Propulsion Principle [1.1].
Rocket engines are fundamentally reaction engines. They rely on the conservation of m
Lecture 5 Nozzle Thermodynamics
The Physics Underlying Converging-Diverging Nozzle Geometry
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nozzle converging-diverging? In order to address this quest
Lecture 4 Orbital Mechanics 2
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with an emphasis on maneuvers and operations while orbiting a single planet. Recalled that in that lecture
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K
Lecture 2 Fundamentals of Launch Vehicle Mission Design
2.1 Trajectory Characteristics
In this section we will consider the trajectory of a vehicle ascending from the Earths surface to
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