Steel Flashcards
What is FLS?
Fatigue Limit State.
How is Miner’s Law Applied?
Fill the resevoir. Drain from the deepest point. Repeat, draining from the next deepest point. The height drained each time is the cyclic stress.
How would:
….. ….
…… …… ………..
….. …. ……..
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be filled according to Miner’s rule?
Drain from the lowest point (lowering level by 3 layers. Then drain from next lowest point (lowering level by 1 layer).
What is the Perry Robertson Formula?
(sigma - sigma_y) (sigma - sigma_E) = \eta sigma sigma_E
sigma_E is the euler buckling load
sigma_y is the yield stress
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?
MUST check c/t ratios and ensure it is Class 1/2/3. UBs may be class 3 - which would massively change my calculations.
What does a ‘plastic’ section mean?
Class 1
What is a ‘compact’ section?
Typically Class 2 (or more generally class 1 & 2)
A beam is class 4. How should I start to consider it’s BM capacity?
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.
How are xi - lambda curves used for LTB?
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.
A beam carries lots of shear. What needs to be done?
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()
What safety factors are needed for connections?
gamma_M2 = 1.1 is used for fracture failure (bolts failing and weld failure)
What is fu for S355 steel?
470
How would one derive Perry-Robertson?
Consider a beam with an imperfection
v0 = e0 sin(pi x / L)
What is the residual stress profile for a rolled section?
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.
What is the residual stress profile for a welded section?
At the flange/web join - where welding has happened - the material tries to shrink post-welding and so is forced into tension.
For LTB, at what point is
xi = fn ( sqrt( Mpl / Mel)
calculated?
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
The shear load V is equal to the shear capacity Vc. What effect does this have on the moment capacity?
rho = (2 * V/Vc - 1)^2 = 1
Therefore, WEB PLASTIC moment capacity is reduced by (1 - rho) = 0.
Hence, Zpl = Zy - Zpl (web)
What is the interaction diagram between shear and Mpl?
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.
What is the M - N interaction diagram for a very short column?
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.
A section is class 4. How would you calculate its plastic axial capacity?
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.
A section is class 4. How would you calculate its bending capacity?
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
What is psi for a flange in bending?
In bending, the flange stress is constant so psi = 1
What is psi for a flange in compression?
In compression, all stress is constant so psi = 1
What is psi for a web in bending
-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.
How would you START to analyse a stiffened beam?
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.
I am analysing a stiffened beam and have found that part of the web is class 4 in bending. What do I do now?
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.
How would I check a stiffener?
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
How would I check a stiffener?
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.
What is M(LT1)?
pi / L * Sqrt( G J E I_yy )
What musn’t you forget for M(LT1)?
pi / L * Sqrt( G J E I_yy )
where pi / L is super important!!
What is the capacity of an 8.8 bolt?
fu = 800MPa fy = 640MPa
A beam has its web connected to a column. How should the resulting connection be modelled?
Only shear is carried in the web, so model as pin-ended.
Why is welding on site bad?
Weld areas may be wet, can’t be pre-heated, and quality control is harder.
Sketch a load-elongation graph for a shear connection.
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.
Compare tear out and net section failure.
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
Under what scenario is a block torn-out in shear?
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.
Where should a shear plane go through a bolt?
The shank (NOT the threads)
What is the throat of a weld?
The throat is the smallest width of the weld (typically 0.7 * fillet.
What is the leg of a weld?
The fillet. The throat thickness, t (used for design), is t = 0.7 * leg.
How are shear studs tested in composite sections?
Wack them with a hammer. They need to yield - NOT the weld fracturing.
What is the effective width of a composite section?
b = L / 4
It is best to neglect b0 UNLESS we KNOW that there will be two rows of studs.
How would we handle an insufficiently shear connected composite slab?
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.
How would you check the shear capcity of a composite section?
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
What is the shear modulus of steel?
G = 81 GPa
I have found a beam to be class 4 in bending. What is the plastic bending moment?
Zel,eff * fy
Note that Zel,eff = I_eff / y_max
Zpl is a whole other thing!
When does one use Zpl? Zel?
Zpl for class 1 & 2 Zel for class 3 & 4 (use Zel,eff)
What is the concrete stress block?
0.85 f_cd for the full depth to the neutral axis.
Hence, C = 0.85fcdB*H is the maximum
What is the r.h.s. of the Perry-Robertson formula?
eta * sigma_E * sigma
Note the r.h.s. does NOT depend on sigma_y
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?
\eta is defined in the UK N.A. to be 1. This table is full of ‘\eta’ - they’re all 1.
What are the axes for a m-n interaction diagram?
m is HORIZONTAL
In an m-n interaction diagram, what value goes up the y-axis?
n goes up the y-axis.
I am analysing the flexural stiffness (ie deflections) of a composite beam. How many different cases for the neutral axis are there?
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.
I am analysing the flexural strength (ie moment capacity) of a composite beam. How many different cases for the neutral axis are there.
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.
In a LTB question, what is the first thing that I should do?
Go to DB, write down all the required parameters, and calculate c/t ratios.
Perry-Robertson for axial buckling is derived analytically. Can the same be done for LTB?
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.
Does \rho for shear-moment interaction affect the elastic, plastic, or ultimate moment capacity?
Plastic capacity. Hence, it must be calculated BEFORE doing lambda = sqrt()
