Plastic Modules Z with two different Fy 1

[struc100]

For a given build up section with different Fy for each plate , I have the following questions:

1- To calc. PNA , The area * Fy above PNA = area * Fy below PNA.

2- To Calc Z ,sum off all (individual area* (distance form CG of each elemant to PNA))above and below the the PNA.


3- Mp = Z * Fy ( Fy= 50 ksi or 36 ksi based on the element location in the build up section)

Is this correct?

 

[strucguy]

What are you trying to do here? Mp is the property of the whole section. It can be calculated directly without having to calculate Z. Just sum all the moments( of forces) about neutral axis.

 

[strucguy]

Correction to my post above
"sum of all the moments (of forces) about PNA"

 

[struc100]

I have wide flange beam Fy=50 ksi reinforced in the bottom flang with a WT Fy=36 ksi, I am trying to find Mp, Z etc.
to check the size

 

[ToadJones]

Huh?
Mp=Z*Fy , no?

 

[paddingtongreen]

Interesting, there is a tee in 50ksi compression above the neutral axis, a tee in 50ksi tension below the NA and a reinforcing tee below that in 36ksi tension.

Simplify, multiply the area of the tee by 36/50 to transform it to 50ksi steel.

Can you place a neutral axis so that the compressive force equals the tensile force, and, the moment above the neutral axis equals the moment below? do you have to?

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[vandede427]

applied stress doesn't know what the allowable stress is for the material it has loaded. check each extremity.

 

[dcarr82775]

You are basically correct. Solve for where C=T to get the PNA, then sum moments about the PNA. You really do not calculate a Zx because summing the moments about the PNA gives you Mp. given the two different yields it is best to ignore thinking of Zx and just go with Mp

 

[struc100]

To all
I have found PNA and the C=T (area * FY 50 or Area*36) based on the material.

Mn= C * d1 + T1 * d2 + T2 * d2

The PNA is in the web of the wide flange beam

C= 50 * A (the tee above the PNA part of upper W shape)
T1= 50 * A ( the tee below the PNA- part of the lower W shape)
T2= 36 * A ( the WT reinforcing with FY = 36 KSI)

d1= distance from CG to PNA of the element(upper portion of W shape0
d2= distance from CG to PNA of the elemant (lower portion of PNA)
d3 = distance from CG ot the WT reinforcing to PNA

Is this correct

Thanks to all

 

[rb1957]

am i missing something ... you guys are talking about shapes but no pix ?

i'd start with an elastic (linear) bending stress and see which yield is reached first. i think you can continue the analysis assuming a perfectly elastic plastic material (stress doesn't exceed yield) and you have to recalc the NA position (to maintain zero net force).

 

[dcarr82775]

That looks good

 

[struc100]

Thank you, dcarr82775