IB structures ALL

What is shear flux

q=SAy/I and S is shear force NOT bending stress

When is S=dM/dx valid

For a slender beam

How does a couple affect a SFD

It does not

How does a couple affect a BMD

Step change

What is thin walled

t less than r/10

How to find shear stress tau from shear flux q

tau = q / thickness

What’s the major axis

The shorter cut, the bigger I

How to find I of parallelogram

Same as rectangle with same height and base

Where is the max shear

Always at the centroid

What is J

Polar second moment of area NOT EQUAL TO I

How to get J

Combine databook equations for elastic shaft and elastic tube

When you do equilibrium can you use stresses

NO use forces only

What does torque create

Pure shear

What are principal axes

Directions with zero shear (x intercepts of mohrs circles)

How to draw mohrs circles

Find stress and shear in two directions and plot as diameter

How do you do virtual work for an indeterminate structure

s.e equals F.d equals zero because there are no external forces in a self stress state

What are the steps to find indeterminate truss bar forces

Remove bars to make determinate, find tensions t0, find a state of self stress for each bar removed (make that bar force 1), t=t0+xs, get extensions with e=Ft, then do virtual work to find x

What is F in e=Ft

The flexibility matrix, L/AE down the leading diagonal and zero otherwise

What bars should you not remove for your indeterminate method

Any that create a mechanism

Making a cut removes how many redundancies

3

Adding a pin removes how many redundancies

1

What do we know about anti symmetry

Central moment zero and central deflection zero

What do we know about symmetry

Central rotation zero and central shear zero

How do you find Zp

Sum of area*distance to central area axis

What is the stress in a plastically deformed section

The yield stress everywhere

How many hinges need to form in an indeterminate structure for collapse

At least 2

How do you find collapse load

Work done = energy dissipated

What is energy dissipated at a plastic hinge

Plastic moment * angle

How do you find rotations in a collapsed portal frame

Find the IC

Make the IC rotate theta

Find the horizontal deflection of the top right hinge

Find the rotation of the rhs part

Find the deflections of the centre hinge

Find the rotation of the lhs part

Slab collapse- what are the hinge line rules

They cannot go into a wall, they must go through the point where the axes of rotation cross

How do you do ED=WD for slabs

Force x distance (or pressure x volume) = mp x L x angle

What is the energy dissipated by a slip line

Area x shear yield stress k x displacement

How do you find rotations (slabs)

Do a vector diagram of rotations. Find arrows from right hand rule. All side ones come from the centre. Middle ones are distances that connect the relevant ends.

How to find displacements for shear slip soil stuff

With a little vector diagram (1 rel 2 and 2 rel 0 crossover etc)

Explain upper bound and lower bound theorems

UB is forces that definitely cause collapse. LB is forces that cannot cause collapse anywhere. For determinate, UB = LB

How do you do lower bound theorem questions

Add pins to make determinate, put in moments equal to Mp. Plot BMD and see what bounds it fits within

How do you find I of an odd shape

Split into rectangles, find local I’s from bd³/12, sum all local I plus Ay² where y is distance to the neutral axis

What area Ae do you use for torsion

Area enclosed by the cross section

Is shear stress from torsion uniform around a cross section

Yes

What stresses do you use for von mises/ tresca

The principal stresses, which must be found with Mohrs circle

How do you find the number of redundancies

Redundancies- mechanisms = bars + restraints - (dimensions x joints)

How do you use databook cases to get deflections from moments

Split into sum of symmetric and antisymmetric cases. Antisymmetric have zero central deflection, symmetric you can chop it in half and use the cantilever case

How do you do the projection method for collapsed slabs

Look from an edge towards the bend- use the rotation of that edge and the length of bend seen from that direction. Add together two perspectives onto the bend.

Can a self stress state require reaction forces

Yes

How do you find Ae, ds/t bits when you are doing torsion tube things

It’s the area enclosed by (and length of) a line in the middle of the wall

How to find the neutral axis (distance Y above base where y = 0)

Y x (total area) = sum of all small areas x distance from centre of area to y = 0

How do you find y for q = SAcY/I

It is the distance from the neutral axis to the centroid of the cut area