Ultimate load of steel beam

[davidovitsh]

In four point bending test, when loading a simply supported A36 steel beam to failure, where shear is very low and buckling is prevented, how much the ultimate bending moment is expected to diverge from the theoretical value: M=Fy.Z ?

Please, if any references for more readings are available then please include the links.

More info: I know the actual Fy and Fu of the steel section. And let's suppose that the failure is due to bending moment only, all other failures are prevented, how accurate M=Fy. Z will be? and does Fu contributes to the ultimate load?

 

[Shu Jiang PEng SE]

The possible failure modes include yield, lateral torsional buckling, flange local buckling and web local buckling. The ration of web/flange height to thickness control local buckling failure, the lateral unsupported length controls the lateral torsional buckling. You can expect beam fails form theoretical value M=Fy*Z if all the three scenarios are excluded.
You can refer ACI360 for more details.

 

[jayrod12]

It also depends on what you're considering failure. If yielding is your criteria then are you using the proposed Fy of 36 ksi, or the true Fy of the material? many times material is classified lower than it's true yield. It would be prudent to take a coupon of the material and test it to determine the true yield stress of the material being tested. You may be able to get this information from mill test reports for that specific beam, most suppliers are able to track down the MTR for material they are supplying.

 

[WARose]

You (theoretically) don't have much left once that hinge forms (if the load is constant and increasing beyond the plastic strength). You might have some extra because the specimen has strength a bit beyond what ASTM requires. (I.e. normal statistical deviation.)

 

[KootK]

Consistent with seismic design provisions, I would suggest 1.25 x Fy x Zx as a reasonable first approximation.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[BridgeSmith]

KootK, the 1.25 overstrength factor for seismic is the theoretically the upper bound for expected strength, reaching into the strain hardening region of the stress-strain curve. That being the case, jayrod's point about needing to define what constitutes failure is a key distinction. Without a mill cert. or coupon test, expected full plastification should occur well below the 1.25 Fy * Zx. Based on the few mill certs I've reviewed, I would expect it closer to 1.1 Fy * Zx. If the section is compact enough and pushed far enough to reach strain hardening, it could approach 1.25 Fy * Zx, more likely it would fracture by the time it reaches 1.2 Fy * Zx.

 

[KootK]

I realize that it's intended to be an upper bound HotRod, that's why I mentioned it. I thought that was what you were going for. It would be helpful if you told us just what it is that you are shooting for here. Upper bound? Lower bound? Accurate as possible? What's the application that we're working with here?

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[davidovitsh]

Let's use numbers for the question.
In a real four point experimental work, an IPE 160 steel beam has resulted in ultimate moment 53 kN.m. Fy and Fu from tensile test in the laboratory is 305 MPa and 382 MPa respectively. The plastic modulus section from charts is 124,000 mm3.
Fy.Z= 37.82 kN.m
Hence, the ultimate from the experimental work is about 1.4 of the Fy.Z, can this be theoretically justified? Do you think that I have to redo my experimental work because of this "large" divergence?

 

[rb1957]

Fy*Z is a conservative ultimate allowable. Fu*Z = 47.4 kN.m ... much closer to your test result. If you want to really "flog" this, redo the test with some strain gauges ... how does the extreme fiber stress compare with predictions ? I'd look at both tension and compression sides.

another day in paradise, or is paradise one day closer ?

 

[BridgeSmith]

Sorry, KootK. I read it that the goal was predicting expected failure. I would have anticipated full plastification well below the 1.25, given that it's supposedly the upper bound. Perhaps it's not an ultimate upper bound as much as it is the maximum anticipated difference between the ultimate strengths of components of the same structure.

"...the ultimate from the experimental work is about 1.4 of the Fy.Z, can this be theoretically justified?"

Again, it depends on what constitutes failure (full plastification vs. fracture). Was the beam deflected to the point of strain hardening of a substantial portion of the section, or to fracture? If so, as rb1957 pointed out, using Fu*Z is about what you would expect. It would likely be even somewhat lower than the peak applied moment, since stress drops off from its peak value before fracture.