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 = A + B But we are out of equations to Break-down how much force is At A and how much is at B This is one of those Statically Indeterminate Things.

Material Properties to the Rescue Blow the bottom support out and let the loaded bar Just 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 to Cancel the displacement Now you have B Now we can use our statics equation = 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 of Block 1 Well lets see – Nothing – so P1=0 What force is yanking on the bottom of Block 2 Looks like 600 KN so P2 = 600 What force is yanking on the bottom of Block 3 Well pretty clearly Block 2 is hanging on Worth about 600 KN so P3 = 600 Throw in Block P4 – has 600 KN From below plus 300 KN for a Total of 900 KN

Estimate some Deformations P M A=400X10^-6 M 600KN δ= 600*0.15/(400X10^-6 * E) = /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 R B

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 small Geometry from one force Won’t change anything for the Next force. We can just Put them over the top of Each other. Actually that’s what we did When we printed physical Compression over thermal Expansion or solved the Statically indeterminate problem

Remember – Each Force Stretches in Its Direction and Thins things down in the other directions Force in X direction stretched In X direction, but the pulls In Y and Z thinned it down Principle of Superposition