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C & PC > Steel > Flashcards

Steel Flashcards

1
Q

What is FLS?

A

Fatigue Limit State.

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2
Q

How is Miner’s Law Applied?

A

Fill the resevoir. Drain from the deepest point. Repeat, draining from the next deepest point. The height drained each time is the cyclic stress.

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3
Q

How would:
….. ….
…… …… ………..
….. …. ……..
……

be filled according to Miner’s rule?

A

Drain from the lowest point (lowering level by 3 layers. Then drain from next lowest point (lowering level by 1 layer).

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4
Q

What is the Perry Robertson Formula?

A

(sigma - sigma_y) (sigma - sigma_E) = \eta sigma sigma_E

sigma_E is the euler buckling load
sigma_y is the yield stress

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5
Q

I am evaluating the bending stiffness of a UB. What is the FIRST thing that I should do? Why is it extremely important to do it FIRST?

A

MUST check c/t ratios and ensure it is Class 1/2/3. UBs may be class 3 - which would massively change my calculations.

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6
Q

What does a ‘plastic’ section mean?

A

Class 1

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7
Q

What is a ‘compact’ section?

A

Typically Class 2 (or more generally class 1 & 2)

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8
Q

A beam is class 4. How should I start to consider it’s BM capacity?

A

Will need to find effective areas of class 4 elements. For flanges this is easy, \psi = 1. For a web, it is necessary to assume a N-A so that \psi may be calculated.

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9
Q

How are xi - lambda curves used for LTB?

A

Need to establish which curve to use using h/b ratios. Then lambda = \sqrt{ Mpl / M(LT, after everything incl c_unequal) }

Mcr = xi * Mpl

Note that ‘Mpl’ doesn’t necessarily mean Zpl * fy. It might be Zel * fy if class 3 or Zel,eff * fy if class 4.

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10
Q

A beam carries lots of shear. What needs to be done?

A

The plastic moment resistance needs to be reduced by rho * Mw, where Mw is the moment resistance of the web, and rho is:

rho = (2* V/Vc - 1)^2

So Mpl = Mpl,0 - rho * Mw

only then can we do lambda = sqrt()

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11
Q

What safety factors are needed for connections?

A

gamma_M2 = 1.1 is used for fracture failure (bolts failing and weld failure)

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12
Q

What is fu for S355 steel?

A

470

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13
Q

How would one derive Perry-Robertson?

A

Consider a beam with an imperfection

v0 = e0 sin(pi x / L)

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14
Q

What is the residual stress profile for a rolled section?

A

The tips of the flanges and the middle of the web cool first, so when the rest of the section cools, they are forced into compression.

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15
Q

What is the residual stress profile for a welded section?

A

At the flange/web join - where welding has happened - the material tries to shrink post-welding and so is forced into tension.

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16
Q

For LTB, at what point is

xi = fn ( sqrt( Mpl / Mel)

calculated?

A

Mpl is found from Zpl fy or Zel fy or Zeff fy

Mel is RIGHT AT THE END - after M(LT1) ; M(LT2) ; M(cr)

Mpl is RIGHT AT THE END of any effective area reductions

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17
Q

The shear load V is equal to the shear capacity Vc. What effect does this have on the moment capacity?

A

rho = (2 * V/Vc - 1)^2 = 1

Therefore, WEB PLASTIC moment capacity is reduced by (1 - rho) = 0.

Hence, Zpl = Zy - Zpl (web)

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18
Q

What is the interaction diagram between shear and Mpl?

A

Mpl = Zy * fy

for V < 0.5 * Vc

Above this value, Mpl falls parabolically to

(Zy - Zpl(web)) * fy

This coincides with rho rising from 0 to 1.

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19
Q

What is the M - N interaction diagram for a very short column?

A

We neglect elastic capacities, so just plot Mpl and Npl.

The web fraction is a = A(web)/A(tot)

Then draw straight lines through (m,n) = (1, a/2). m is on the x-axis ; n is on the y-axis.

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20
Q

A section is class 4. How would you calculate its plastic axial capacity?

A

psi = 1 for all plates in compression. Then find k_sigma Then, find lambda from

b/t * 1/(28.4 epsilon sqrt(k_sigma))

Then find rho.

Then apply b_eff. This gives Npl.

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21
Q

A section is class 4. How would you calculate its bending capacity?

A

Assume a N-A to find psi for all elements.

Note that you can’t check web slenderness without assuming a N-A and therefore psi = -1

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22
Q

What is psi for a flange in bending?

A

In bending, the flange stress is constant so psi = 1

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23
Q

What is psi for a flange in compression?

A

In compression, all stress is constant so psi = 1

24
Q

What is psi for a web in bending

A

-1 is a good guess

In bending, we need to assume a N-A to find psi for a web. The effective areas will move the N-A but these effects are secondary.

25
Q

How would you START to analyse a stiffened beam?

A

Assume a N-A to get a stress profile in each plate. Can then check the class of all plates - See if any are class 4.

26
Q

I am analysing a stiffened beam and have found that part of the web is class 4 in bending. What do I do now?

A

Using the assumed N-A, psi gives k_sigma. This gives lamda, and hence b_eff. The class 4 part of the web will have some loss of effective area.

27
Q

How would I check a stiffener?

A

Model as a T column with 15 epsilon t either side (OR LESS). Find centroid and buckling stiffness out of plane. Now, get lambda and xi.

Finally, check xi * fy > sigma_design_load

28
Q

How would I check a stiffener?

A

Model as a T column with 15 epsilon t either side (OR LESS). Find centroid and buckling stiffness out of plane. Now, get lambda and xi. Check

xi * fy > sigma,

where sigma is the stress at that part of the section due to applied moments.

29
Q

What is M(LT1)?

A

pi / L * Sqrt( G J E I_yy )

30
Q

What musn’t you forget for M(LT1)?

A

pi / L * Sqrt( G J E I_yy )

where pi / L is super important!!

31
Q

What is the capacity of an 8.8 bolt?

A 
fu = 800MPa
fy = 640MPa
32
Q

A beam has its web connected to a column. How should the resulting connection be modelled?

A

Only shear is carried in the web, so model as pin-ended.

33
Q

Why is welding on site bad?

A

Weld areas may be wet, can’t be pre-heated, and quality control is harder.

34
Q

Sketch a load-elongation graph for a shear connection.

A

Without pre-loading, the bolt will slip at a certain load (much less than the design load). Thus, we have linear behaviour, followed by a sudden jump in elongation, followed by more linear behaviour that plateaus as the connection yields.

35
Q

Compare tear out and net section failure.

A

They are basically the same equation, except that net section failure ONLY applies to a fault line across the bolt lines, and is reduced by a factor of 0.9

36
Q

Under what scenario is a block torn-out in shear?

A

Think of a beam - column web connection. The beam’s web is connected by a plate to the column. This plate is experiencing pure shear. Bolt tear out would occur along a fault line around the bolts : the shear area is a verical plane, and the tensile area is a horiontal plane.

37
Q

Where should a shear plane go through a bolt?

A

The shank (NOT the threads)

38
Q

What is the throat of a weld?

A

The throat is the smallest width of the weld (typically 0.7 * fillet.

39
Q

What is the leg of a weld?

A

The fillet. The throat thickness, t (used for design), is t = 0.7 * leg.

40
Q

How are shear studs tested in composite sections?

A

Wack them with a hammer. They need to yield - NOT the weld fracturing.

41
Q

What is the effective width of a composite section?

A

b = L / 4

It is best to neglect b0 UNLESS we KNOW that there will be two rows of studs.

42
Q

How would we handle an insufficiently shear connected composite slab?

A

Let the degree of shear connection be \eta = N (provided) / N(required)

For \eta =0 , M = Mpl (steel)
For \eta =1, M = M(fully composite)

Between these, linearly interpolate.

43
Q

How would you check the shear capcity of a composite section?

A

All shear is carried in the beam. The shear capacity of a beam is

Aw * fy / sqrt(3)

where Aw is the area of the web

44
Q

What is the shear modulus of steel?

A

G = 81 GPa

45
Q

I have found a beam to be class 4 in bending. What is the plastic bending moment?

A

Zel,eff * fy

Note that Zel,eff = I_eff / y_max

Zpl is a whole other thing!

46
Q

When does one use Zpl? Zel?

A 
Zpl for class 1 & 2
Zel for class 3 & 4 (use Zel,eff)
47
Q

What is the concrete stress block?

A

0.85 f_cd for the full depth to the neutral axis.

Hence, C = 0.85fcdB*H is the maximum

48
Q

What is the r.h.s. of the Perry-Robertson formula?

A

eta * sigma_E * sigma

Note the r.h.s. does NOT depend on sigma_y

49
Q

In calculating the shear capacity of a beam with buckling, we need to know chi_w. This is given in a table and is equal to \eta for non-slender webs. What is \eta?

A

\eta is defined in the UK N.A. to be 1. This table is full of ‘\eta’ - they’re all 1.

50
Q

What are the axes for a m-n interaction diagram?

A

m is HORIZONTAL

51
Q

In an m-n interaction diagram, what value goes up the y-axis?

A

n goes up the y-axis.

52
Q

I am analysing the flexural stiffness (ie deflections) of a composite beam. How many different cases for the neutral axis are there?

A

Only 2. Either the N-A is in the concrete, in which case neglect tension concrete, or it is below the concrete, in which case all concrete works.

53
Q

I am analysing the flexural strength (ie moment capacity) of a composite beam. How many different cases for the neutral axis are there.

A

3: The N-A in the concrete, in the steel flange, and in the steel web. Note that it CANNOT be in the gap because moving the N-A in the gap for a plastic section doesn’t change the axial load.

54
Q

In a LTB question, what is the first thing that I should do?

A

Go to DB, write down all the required parameters, and calculate c/t ratios.

55
Q

Perry-Robertson for axial buckling is derived analytically. Can the same be done for LTB?

A

In order to derive Perry-Robertson, a form for the imperfection eo/L is assumed. For LTB, there are two imperfections to characterise. This makes the maths much harder. The curves for LTB are a curve fit - nothing more.

56
Q

Does \rho for shear-moment interaction affect the elastic, plastic, or ultimate moment capacity?

A

Plastic capacity. Hence, it must be calculated BEFORE doing lambda = sqrt()

C & PC (5 decks)

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