Diaphragm Design

[civg]

As a young engineer, I am having difficulty trying to fully grasp the design concepts required for lateral loads. It seems an entire college course could be devoted to this area of structural design, and the courses I have taken did not cover much of this material.

My questions are regarding the diaphragm design of a one-story building constructed with open web steel joists, joist girders bearing on steel columns, and perimeter CMU walls. Let’s say the building is rectangular with no re-entrant corners or jogs for now. I think I understand the load paths and the function of the boundary elements (chords, collectors). What I’m trying to understand is the elements that comprise the chords and collectors and the proper calculations of the forces acting on these elements.

The perimeter CMU walls have a bond beam at the roof level. The roof deck is welded to the horizontal leg of a continuous angle that bears on the joist top chords, and the angle is welded to steel embed plates (let’s say spaced every 48” o.c. for the sake of discussion) that are attached to the masonry wall at the elevation of the bond beam.

Depending on the direction of loading, a boundary element can act either as a collector or a chord, correct? So basically these elements have to be designed for the controlling force? For this type of construction I have described, would you consider the bond beam the boundary element and the continuous angle to be the connector that transfers the lateral forces from the roof deck? That’s what I am thinking...

 

[JAE]

It sounds like you have a pretty competent understanding of it. Nothing you stated sounds incorrect.

One thing to consider too is the second order effects of the building's, and specifically the diaphragm's, lateral movement.

With masonry shearwalls, the walls themselves probably won't deflect laterally too much to create any PDelta effects but the diaphragm itself, for larger roof/diaphragm buildings, does deflect and this creates second order forces that ADD to the collector & drag strut loads.

Say you have a building and the wind load is perpendicular to a wide diaphragm. The diaphragm will deflect sideways - maximimum in the center and zero at the shearwalls.

The dead load on the columns will then be applied to columns that lean in varying amounts across the building width.

What you can do is do a one-step estimation of the second order effects - take the maximum diaphragm deflection at its midspan. The diaprhagm deflects mostly in shear and you need to calculate the AVERAGE lateral deflection across the width of the building.

This then is also the average column deflection across the entire diaphragm. Then calculate the additional lateral force on the diaphragm by multiplying the total roof dead load x average deflection / roof height.

This gives you the total, first iteration lateral load on the diaphragm. You can then split this into two and send half to each shearwall as additional PDelta load.

In reality, the lateral sway will produce yet more deflection in the diaphragm which in turn produces more lateral load, then more deflection, etc. You can manually iterate if you wish.

 

[slickdeals]

One of the things that you have to worry about in roof joist construction (again depending on the joist seat dimensions) is rollover. Typically, the lateral forces are being transferred to the top of the joist and the joist bears on the support. This lateral force has to then be transferred from the top of the joist to the bottom.

I have seen people using HSS members or other members whose depth is equal to that of the joist seat to transfer the lateral shear from the deck to the element that is supporting the joist.

We are Virginia Tech
Go HOKIES

 

[JAE]

slickdeals - yes - good point.

 

[civg]

Thank you both for the information. Now in trying to understand the basics for the bond beam and continuous angle design, consider the following simple example: Building is 100'x100', with uniform lateral load of 100 lb/ft. This gives a shear reaction of 5 k and a chord force of 1.25 k. So for the bond beam, am I checking the failure mode in compression as crushing of the grouted CMU, and tensile failure of the reinforcing steel, both for 5 k?

For the angle, with embeds spaced at 48", I would have a force of 5,000lb/100ft x 4 ft = 200 lb? Is that correct? Then the chord force of 1.25 k would control for the angle and I would design it for tension, or compression with a 4' unbraced length? Any more feedback would be much appreciated.

 

[JAE]

Sounds like you have it right.

 

[civg]

Awesome, thanks. NOW, let's say we have a realistic building that is not a perfect rectangle. I attached a crude sketch that shows some re-entrant corners and jogs. How do I calulate the shear reactions/deck shears and chord forces for a case like this? Is it necessary to have shear collectors at every geometric irregularity?

 

[Prestressed Guy]

Civg, on a CMU building, I would not design the angle as the chord. The CMU is much stiffer and with attachments CMU/angle attachments at 48” o.c., the CMU will be the chord. This is why the top bond beam reinforcement is usually continuous across the control joints. With a CMU bond beam chord, you will not need the angle to be continuous which eliminates the need for coping at each joist. A discontinuous collector angle between the joists is much cheaper to fab and erect. You will need to design it for the appropriate over-strength factor however.

With a collector angle between the joists and welded to embed plates in the CMU you will not have any rollover load in the joist seat. SJI does not recommend lateral force transfer through the bearing.

 

[JAE]

Only thing with that, Haydenwse, is that longer CMU walls have control joints in them and you then have to consider the relationship between a continuous chord and a discontinuous wall with joints. What do you typically do for that?

 

[jike]

cvig:

Chords need to be continuous! When considering an angle or a bond beam as a chord, you need to detail and note it as continuous, otherwise, it will be fabricated/built in segments.

Just remember, it is all in the details!

 

[msquared48]

civg:

You appear to be a competent, bright young engineer who can express his thoughts well in writing. Keep asking your questions here, and we will all be glad to help.

Also...please pay it forward.

Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask

 

[ToadJones]

I'll say that this is a good discussion. As a engineer mostly involved in industrial facilities and steel this is an area I always wished to further my knowledge.
I have learned the basics only through studying for licensing tests.