More Applications of Linear Stress-Strain Relations (Credit for many illustrations is given to McGraw Hill publishers and an array of

internet search results)

Parallel Reading

• 3.4 Statically Determinate Structures

• 3.5 Statically Indeterminate Structures

• 2.13 Generalized Hooke’s Law

I Mentioned That Sometimes in Statics Problems we run out of

equations before we have answers

A

B

Looks like no brainer statics

0F z

300+600 = A + B

But we are out of equations toBreak-down how much force isAt A and how much is at B

This is one of those Statically IndeterminateThings.

Material Properties to the Rescue

Blow the bottom support out and let the loaded barJust hang there.

Calculate how much lengthening we will see.

Next Impose that the Ground Did not Disappear and will Push Up as

Necessary to Ensure 0 displacement

See how large the force B has to be toCancel the displacement

Now you have B

Now we can use our statics equation

600+300 = A + B

A General Comment On Solution Methods

• Look at the Problem• Look at What You Know• Look at What You Want to Know• Look for What Equations Apply• Plan your solution strategy before you start

number crunching

• Some people just start trying equations hoping that some miracle will suddenly pop out (it usually doesn’t)

Lets Do the Math

Chop our block into 4 pieces

What force is yanking on the bottom ofBlock 1

Well lets see – Nothing – so P1=0

What force is yanking on the bottom ofBlock 2

Looks like 600 KN so P2 = 600

What force is yanking on the bottom ofBlock 3

Well pretty clearly Block 2 is hanging onWorth about 600 KN so P3 = 600

Throw in Block P4 – has 600 KNFrom below plus 300 KN for aTotal of 900 KN

Estimate some Deformations

P2 0.15 M

A=400X10^-6 M

600KN

δ= 600*0.15/(400X10^-6 * E) = 225000/E

Add Up All the Deformations(P2, P3, and P4)

Now We Will Have the Reaction at the Base Reverse the Deformation

We Know the Supports Working Together Prevent Stretching Out

We Used Material Properties to Determine RB

Finish It Off With Statics

Statics Folks – Eat Your Heart Out

Assignment #5

• Problem 3.5-2

What Happens if I Try to Pull a Block Apart in 3 Directions at

Once?

Make it Easy to Solve

If the deformations are smallGeometry from one forceWon’t change anything for theNext force. We can justPut them over the top ofEach other.

Actually that’s what we didWhen we printed physicalCompression over thermalExpansion or solved theStatically indeterminate problem

Remember – Each Force Stretches in Its Direction and Thins things

down in the other directions

Force in X direction stretchedIn X direction, but the pullsIn Y and Z thinned it down

Principle of Superposition