Beams Flashcards
What is fcd, the concrete design stress given by?
fcd = acc * fck / Yc
where acc = 0.85
yc = the partial safety factor for concrete
What is epsilon,cu?
The ultimate strain in concrete = 0.0035
What is the value of the partial factor in concrete?
1.5
What is the value of the partial safety factor in steel?
1.15
Describe the stress-strain graph of steel?
Hits a yield point, then yield plateau, the srain hardening where it increases in stress then decreases, then failure.
What does f,yd equal?
f,yd is the design yield strength of steel = f,yk / Ys
What does the moment equal in relation to flexural stiffness and phi?
M = EI*phi (phi is the curvature)
Describe the moment-curvature realtionship of concrete and steel in a graph:
1 - Uncracked, concrete and steel are both linear elastic
2 - Concrete cracks in tension, the tensile in the concrete is transferred to the steel.
3 - Inelastic, both steel and concrete are ineastic, concrete reaches the ultimate strain
4 - Failure
What is the modular ratio, a,e?
Modular ratio = E of steel / E of concrete
What is the 3 step method to find the second moment of area of an uncracked section?
1 - Find the modular ratio
2 - Find x,u using the formula table
3 - Find I,u using the formula table
What is the moment at first crack, Mc equal to?
Mc = (fcttm*Iu) / (h-xu)
If concrete fails in tension, what happens to the neutral axis?
It moves up
Before first crack, what does Fc equal?
Fc = Force steel + force of concrete in tension
If steel (tension steel) yields before concrete crushes, what type of failure is this?
Under-reinforced failure.
If concrete crushes before steel in tension yields, what type of failure is this?
Over-reinforced failure
In under-reinforced failure, what yields first, what happens to the neutral axis, and describe 3 features of the failure?
Steel yields first, neutral axis moves up. The failure is ductile, gradual and predictable,.
What is shear failure, and how does it appear?
Diagonal fractures or slips along a shear plane.
Often at a 45° angle to the applied load.
Brittle materials show jagged, irregular fractures.
Ductile materials may twist or stretch before failure.
In over-reinforced failure, what yields first, what happens to the neutral axis, and describe 3 features of the failure?
Concrete fails first, neutral axis moves down the cross-section. The failure is sudden, brittle and unpredictable.
What is the desired failure mechanism?
Under-reinforced failure.
What is tension failure, and how does it appear?
Brittle materials have straight, clean fractures perpendicular to the load.
Ductile materials show necking and stretching before fracturing, with a fibrous or jagged fracture surface.
Fibrous materials may tear along thread-like structures.
What is compression failure, and how does it appear?
Brittle materials crush or shatter, with cracks radiating from the compression point.
Ductile materials experience plastic deformation, often bulging or buckling.
Compression can lead to crushing zones or indentations.
Columns may exhibit buckling or bending before failure.
What does a balanced section mean?
Steel yields at the same time as concrete crushes, which can be used in design.
In the balanced section, what does the angle phi equal?
Ecu / x = esyd / (d-x)
What does epsilon,syd equal?
0.00217