Structural Integrity & Materials Selection

Structural integrity

• the ability of a structure to support a designed load without bending, collapsing, or breaking

Structural failure

the loss of structural integrity,

• created when the material is stressed to its strength limit, thus causing fracture or excessive deformations.
•  

Common types of failure:

1. Fracture:

Brittle vs. Ductile

(a) Very ductile, soft metals (e.g. Pb, Au) at room temperature, other metals, polymers, glasses at high temperature.
(b) Moderately ductile fracture, typical metals
(c) Brittle fracture, cold metals and ceramics.





*brittle fracture → rapid run of cracks through  stressed material.  
*very little plastic deformation
*No warning → worst type of fracture
*Amorphous microstructures (glass) produce shiny brittle fracture surfaces



In crystalline materials:
 transgranular fracture - travels through the grain of the material

  intergranular fracture - crack traveling along the grain boundaries
 2. deformation 

Elastic Deformation:

 - object returns to its original shape

 - Not permanent





Plastic Deformation:

- object becomes permanently deformed

3. Fatigue

The weakening of a material caused by repeatedly applied loads.

 

 

* microscopic cracks form around small discontinuities at the surface & near grain boundaries. 

* cracks eventually reaches a critical size, then suddenly propagates through the remainder of the solid.

 

 

 

 

Fatigue life depends on:

 

• Temperature
• surface finish
• atomic microstructure

 

 

Things to avoid:

 Sharp corners & bends - make everything smooth!

 

 

Example:  90° corner:

Use the probe to point out where the max stress is:

 

 

 

Same loading force, comparison of max stress with and without fillet:

 

 

 

1.411 vs. 0.58 → stress along 90° corner is ~ 2.5 times larger than the stress along the fillet. 

 

 

 

Find where stress is concentrating on your bridge for various loading conditions, then redesign joints to more homogeneously distribute the load.

 

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Fatigue rules of thumb:

 

It can be hard to measure, and get repeatable results on. 

Fatigue usually applies to tensile stresses but can also occur under compressive loads.

 

↑stress = shorter life.

Damage is cumulative & usually permanent.

 

 

Design Criteria:

 

Localized failure should not cause immediate or even progressive collapse of the entire structure.

 

 

 

 

 http://gawker.com/thousands-of-bridges-in-u-s-could-collapse-if-only-sin-509937766

 

 

Test for "critical" spots on your bridge.

Run a FEA sim where you apply a forces to critical spots (at supports and joints).

 

 

Modal Analysis

 

Earthquake? Wind? Vibrating machinery? Vibrating cars & trucks?

 

Modal Analysis solves for natural vibrational tendencies of a structure in the form of mode shapes and frequencies.

 

 

 

https://www.youtube.com/watch?v=Ug2u7sTWrcw&feature=youtu.be

 

 

 

Try just applying one fixed constraint, and then run the simulation without any other applied forces.

 

Use the animate tool to watch it vibrate!

 

 

Display the position of your center of gravity, and notice the influence of the center of gravity on the vibrational patterns in your bridge:

 

View → Center of Gravity

 

 

 

 Notice how everything vibrates around the center of gravity. 

 

 

Further Reading:
Mechanical resonance
Skim through:
List of bridge failures

Think about the main causes of bridge failure, and then decide how to modify your bridge to avoid these types of failures.

Find the mass, volume, center of mass etc. of your part:

 

 

 

 

The larger the volume, the more expensive it is to make. 


What on your bridge is over-designed?  Where can you remove a little bit of material to reduce costs?



 

 

 

 

 

 

 

 

 

 

  

Arch Bridges, Drawing with Equations in Inventor, Stress analysis including gravity

Skim through this Link:

Rules of thumb for creating arches:For Circular arches - avoid flattened arches

pg 26:   1/9< rise/span=H/L <1/6 (1/4, 1/3)

     rise/span ~ 1/7.5

Statics of arches link

Supporting Forces:
Consider a simple truss structure

The load in the compression element increases to infinity as the angle decreases to zero:

Taller bridges have smaller loads in each member.

Rule of thumb:  keep H/L ~ 1/7.5

If H/L does not exceed 1/7.5, what is "H" for your given L?

example:
for a bridge using only one arch to span 1000m:
L = 1,000m (0.62 niles)

H = (1/7.5)*1000 = 133.333m  (437.445 ft)

Use Excel or Mathematica to test out your equation! 

Use the 2D equation to create the arch with Inventor: link

Start a sketch:

Read instructions under sketch→line→ equation curve

Decide on bridge dimensions, then enter equation:

Offset your line to create a 2D area to extrude:

Create a bridge!
Note - I extruded an extra long arch, then cut the road out of the center of it so that it is symmetrical on both sides & in the center.

You can also import excel points:

Use the first sheet, A1 = units, A2, B2, C2 = (x,y,z)


Gravity Stress Analysis:

The bridge has to support it's own weight as well as the added loads that are applied to it.  Add a gravitational load.

After you see the FEA results with gravity, create a ball, and open up your bridge in an assembly.

Constrain the bridge to the ground plane, and the balls to move up and down.

Once you have all of your constraints in place...

Simulate a ball falling on your bridge:link

Open up an assembly, include a ball and your bridge.  Start playing around with the dynamic simulations!

One good tutorial:
https://www.youtube.com/watch?v=504xOZcfcbM

Environment →Dynamic Simulation

Look at the menu on the left hand side.
Add and remove joints

 Be sure you are in construction mode, or you cannot change anything!

 Create spatial constraints on your ball to move it from being grounded, to being mobile.

Either Convert constraints or

Insert Joint → Spatial →select ball, and then bridge

 Open up all of the options (+) under Grounded, and mobile groups, standing joints, force joints etc. and have a loot around.

Don't forget to add gravity!

 Right click on your bridge, and ground it if it is not grounded automatically. 

Output Grapher →open it and have a look around!

Simulation Settings → decide if you want to automatically create constraints in your dynamic simulation based off of the constraints you created in your assembly...

FEA & Bridges

FEM  Finite Element Method:

Breaks large complex geometries into small connected elements in order to analyze things like strength properties.

Connect nodes with springs:

 Simple linear spring force:

Simple Stress Strain diagram:

Materials behave like simple linear springs within their elastic region.

Some example problems relating Young's Modulus to spring forces:
https://notendur.hi.is/eme1/skoli/edl_h05/masteringphysics/11/youngsModulus.htm


Failure Criteria:

von Mises criterion
- reasonable estimation of fatigue failure, especially in cases of repeated tensile and tensile-shear loading
 States that failure occurs when the energy of distortion reaches the same energy for yield/failure in uniaxial tension. Mathematically, this is expressed as,

principle stresses:

http://demonstrations.wolfram.com/MohrsCircleAndFailureCriterionForPlanarStressStates/


Review Mechanics of Materials notes:
 http://engr1304.blogspot.com/2014/03/mechanics-of-materials.html


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Bridges!

Create a bridge in Inventor (or import it from CAD into Inventor)
**Make this as one single part rather than an assembly.  We will do more with constraints on our next project.

 Create a loading blocks where forces can be applied:

Environment → Stress analysis

Assign a material to your bridge:

Apply fixed constraints:

 Apply a load:

Add mesh
Play around with the mesh settings, create a tighter mesh in high stress areas.  Update the mesh by right clicking on the red lightning bolt in your files.

Do the stress analysis!
Generate a report
Experiment with the probes
Investigate different directions of stress and strain

Civil ENGR & materials design unit

Bridge Project:
* Create Bridge (30 points)
* Apply three different loads (30 points)
* Re-design Bridge to better support above loads (30 points)
* Compare 3 different building materials. (10 points)


Bridge Report and Presentation:
*Present your bridge to the class (30 points)
*Create a report detailing the above comparisons (70 points)

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1. Choose a large bridge to re-create and do a stress analysis on.
 - your recreation will not be exact, but you should use the general form & dimensions of  an existing bridge.
 
____/30 points for bridge

2. Apply 3 different loading conditions 
(____/ 30 points)

Loading Condition #1:
Assume the average person weighs about 150 pounds and occupies ~  2.5 square feet in a crowd...

Loading Condition #2:

Approximate wind loads with this simple formula:

Wind pressure (Psf) = .00256 x V^2
V = wind speed in mph (use a worst case scenario  of  112 mph → 32 lbs/sq ft)

Wind Load (Force) = Area * wind pressure * drag coefficient
Drag coefficient estimates:
1.2 for long cylinder tubes
.8 for short cylinders,
2.0 for long flat plates
1.4 for shorter flat plates


http://www.wikihow.com/Calculate-Wind-Load

http://ascelibrary.org/doi/abs/10.1061/%28ASCE%29BE.1943-5592.0000316?journalCode=jbenf2

Apply the wind force horizontally to your bridge.


Loading Condition #3
Choose the worst-case scenerio road train, get weights/lengths off of the wiki article:
http://en.wikipedia.org/wiki/Road_train

3. Redesign part of your bridge to better support each of the above loading conditions.

4. Show results for 3 different building materials.

Concrete
Steel - compare different types
http://en.wikipedia.org/wiki/I-beam