Mechanics- School of PE Flashcards
Mechanics
Name the 7 different points on a stress strain diagram
Mechanics
Chunk of steel acts like a spring. Explain
I you move a spring to far it changes shape and no longer behakes the same. For example, if you stretch a slinky to far it does not go back to its orional shape.
Mechanics
Explain the graph used for explaining the relationship of a spring when a load is being applid to it.
If you take a spring and stretch it a distance, delta using a force, and measure the amount of force it takes to stretch it by a given delta, you end up with a slope, and that slope is called k.
Mechanics
What does E stand for on the stress vs strain diagram
Youngs Modulas
or Modulas of Elasticity
Mechanics
What is Toughness in Mechanics of Material
It is the area under the stress vs strain curve
Mechanics
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Mechanics
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Mechanics
Explain pressure inside a vessel.
What is this called
Creates Tensile stress Hoop Stress on outside of vessel
Called Hoop Stress (Same whether pressure is inside or outside of vessel)
Mechanics
What does tensile hoop stess failure look like?
gash running down longitudinal axis of vessel
Mechanics
Explain Pressure on outside of pressure vessel.
What is it called.
Creates a Compressive Hoop Stress on outside of pressure vessel
Hoop Stress (Same same for internal pressure and external pressure being applied to a pressure vessel)
Mechanics
Explain Equations for Hoop Stress for a Pressure Vessel.
Same equation for both Tensil a Compressive Hoop Stress. Only diference is that Compressive is negative.
Add Picture from Camera
Mechanics
Equations for Hoop Stress in a thin walled tank.
What are the condition for using these equations?
Refer to Picture
Thin Walled equations can be used when: Cylinder Wall < or = 1/10 th Inside Radius
p= insdie radius
D= outside diameter
t= thickness of wall
Mechanics
Are youi more likely to see a Hoop Stress Failure or a Axial Stress Failure?
About 2 times more likely to see a Hoop Stress Failure.
We usually calculate the Axial Stress to determine how much stress is going to be on the cicumferential welds. If we have to keep the end cap of the tank from blowing of, we know we have a certain weld area needed, and need to make to joint stronf enough to handle all the axial stresses.
Mechanics
Explain Why we use Mohtrs Circle, and What it is used for-
For any given part, no matter what combination of axial stress and shear stress is applied to it, you can tilt your head to the right frame of reference and summarize what is going on in terms of only axial stress (or only shear stress). Can enven be used in 3-d. There is always some oreientation that youi can summarize what is going on in terms of only axial stress (or only shear stress).
Theory (Refer to attached Picture):
- Apply Shear Force to top and side
- Shear Force is added to opposite side in opposite direction for equilibrium
- Material tends to deform
- Materials follows poisons ratio
- Look at interior part and notice that it elongates as if an axial stress is applied
- Shift frame of reference so you are only looking at the axial stress being applied (or shear stress); Other stress cancels out
- In other words, it may look like origionally like shear stress, but once you rotate it to the right frame of reference, it now looks like axial stress.
- The angle for your frame of reference is theta (Mohrs Circle allows us to find 2 theta)
Mechanics
What are the 2 things that need to be calculated to draw Mohrs Circle.
Provide both Equations
- Radius (r = τmax)
- CENTER Point (σo)
- σx = axial stress in x direction
- σy = axial stress in y direction
Mechanics
What is the angle of reference for Mohrs Circle?
Ancle of Reference is θ
Mohrs Circle shows 2θ, so if asked for the angle of reference, it is half of this value.
Mechanics
Maximum Shear stress for Mohrs Circle =
τmax = R
refer to picture for equation
Mechanics; Mohrs Circle
When looking at a maximumum Noral Stress for Brittle Material, a material fails when (Used to predict failure)?
First need to rotate frame of reference to eliminate the Shear Stress (If combined stresses; Mohrs Circle)
When the largest stress (+ σ; Because Tensile) is greater then the Tensile Strength
OR
When the largest stress (- σ, Because compressive) is less then the Compressivle Strength
Remember that stress in compression is negative
Mechanics; Mohrs Circle
Provide 3 dimensional Equation for Hooks Law for strain and for Shear.
Refer to Picture
Probably no problems on FE in 3 dimension
Think about how material deforms in Mohrs Circle
Mechanics; Mohrs Circle
The maximum Normal Stress that a metal fails (for predicting failure);
Provide the equation for maximum shear stress theory:
Explain
For Ductile material we tend to look at the maximum amount of shear.
Worried about Shear Max being greater then 1/2 the yield in tensile strength
Mechanics; Mohrs Circle;
What theory is good for mederatly ductil to ductile materials for determining the max normal stress (static loading failure ) of a material?
What is it called?
Explain-
Distortion Energy (Von Mises Stress); Equation good for 3-D
Tells how much energy you can put into a meterial withour destroying it
Calculation are based off the principle stresses ( σ1, σ2, σ3 )
In the example shown ► σ1 = -48 & σ2 = 30;
σ1 is usually the larger value, but doesn’t matter when you stick in equation; get same answer)
In this example, the problem has already been shifted to the right frame of reference, so there is no shear to eliminate
Mechanics
Provide the Torsion equation for a thin walled shell
Refer to Picture
The interal arrows in the wall is the shear flow (Circled in Bule)
Mechanics
Explain the following in terms of slopes and areaas for drawing graphically
Load
Shear
Momemt
We know when we see a deriviative it it the slope and when we we an integration it usually means an area
Load is the slope of shear
Shear is the slope of the Moment
Shear is the Area under the load
Moment is the Arrea under the Shear
Mechanics
Equation for Bending Stress of a beam
Explain how stresses are developed in beam
C is half the thickness of the beam.
Top of beam is in tension
Bottom is in compression
Middle of Beam bending stress is Zero
Max Bending Stress is at edges/surfaces (Outside edge) of beam
Mechanics
Equation for Shear Stress in a Beam
Explain how Shear is developed in Beam
Refer to Picture
How difficult it will be to shear is summariezed by I (momemt of Inertia)
b is the distance from center to any arbitraty point on the beam
Max Shear is in center of Beams
Zero shear at surface/edges of beam
Mechanics
Equation for Beam Columns (Axially Loaded Beams)
ADDING AXIAL STRESS AND BENDING STRESS TOGETHER
Mechanics
Provide Eulers Formula
What is it used for?
Refer to Picture
Used for Columns
Mechanics
What is the Equaltion for Elastic Strain Energy-
Explain
Elastic Strain Energy is the amount of energy required to strain something (Same as calculation spring energy)
Talking about eleastic region; It is the area under this region when graphed
Mechanics
When a beam is symmetric, what is the shear in the middle (along the length) of the baem?
Shear is zero
