Calculate Probable Moment Strength

[Soicey75]

I am having troubles understanding what the code means exactly by Probable moment strength. Where can I derive this number? what is its relation to Ultimate moment ? I want to grab Mpr for a column. Am I looking for Mpr with a change in Fy to 1.25Fy using the strain stress block equation? am I grabbing the moment load from a structural analysis? There is one article I read which states to analyze it with an axial/moment graph that I can calc for or use programs such as Sp column. The picture I have below says to look at the max moment load but the graph shows capacity with internal points as the "loads". Do I take the max moment capacity or the max moment load the column experiences ?

 

[JoshPlumSE]

First think of it for a beam (i.e. no axial force). Using 1.25*Fy for you steel stress accounts for expected yield (as opposed to minimum yield). There may even be some strain hardening effect in there as well.

Then when it comes to columns, the idea is the same. Except for two things:
1) You don't know what your full strain profile is until you also know the axial stress. Hence, they tell you to calculate it for a range of expected axial forces.
2) It need not exceed the Mpr of the beams that frame into it. Because that limits what moments can be imparted into the column.

 

[Shu Jiang PEng SE]

Probable moment of beam is the possible maximum moment the beam can take. The term is used to design concrete special moment frame. It is kind of detailing design requirements.
For beam, flexural failure is ductile and shear failure is brittle. It is preferred to design the beam to make sure that beam flexural failure occurs before shear failure.

Under seismic lateral load, the maximum possible moment can be reached at two ends of the beam at same time, with opposite signs (Mpr and –Mpr). The shear at end of the beam correspondingly is V=(Mpr-(-Mpr))/l. The total shear of the beam is sum of the shear the load due seismic load and factored gravity. Beam shear capacity should be designed larger than the calculated shear above.

Also the column maximum possible moment should be designed larger than the beam maximum possible moment at same connection joint.

 

[Soicey75]

I understand the concept of increasing the Fy. What I don't understand is where exactly I would take Mpr. It is called strength so I assume it wants ultimate capacity if that's the case why does my axial force cases matter? I as cut and simple. Picture below is my columns capacity depending on the axial loads. Will my Mpr be the highest moment load cause by one of those axial forces ? meaning I'll be grabing Mpr w.r.t to external loads or do i grab my Mpr to be the largest moment capacity/strength my column can take? (the moment located the farthest to the right of the bell curve.

 

[Shu Jiang PEng SE]

here is the definition of Mpr from ACI318r-14

probable flexural strength of members, with or without axial load, determined using the properties of the member at joint faces assuming a tensile stress in the longitudinal bars of at least 1.25fy and
a strength reduction factor ϕ of 1.0, in.-lb
I think you can calculate Mpr either without considering beam axial compression or with axial compression due to seismic load. it is not clear on that from code.

 

[Agent666]

Its often referred to as the 'overstrength capacity' and its used in the application of capacity design which might help find further resources.

As a simplified example of where you might use the property, if you have a weak beam-strong column mechanism in a portal frame lateral load resisting system, your columns are said to be capacity design protected if the overstrength moment capacity (i.e. often determined using the maximum 5% upper characteristic strength of reinforcement and concrete, or simply via application of an 'overstrength factor/multiplier' to increase the capacity to the more realistic upper estimate of strength) of the beams can be resisted by the column and the columns still remain essentially elastic. You need to achieve your dependable beam sway mechanism without further hinges occurring in the columns (which might initiate a soft storey failure). Remember nominal section capacities are based on lower estimates of the material strength, the overstrength capacity is simply an estimate of the likely upper bound of the strength or capacity of a member.