Centroid to bridge deck 1

[bigjeremy]

This should be simple, but I'm having some troubles. Looking through the FHWA LRFD Steel Bridge Design Example

http://www.fhwa.dot.gov/bridge/lrfd/fhwanhi04041_steel.pdf

On page 3-13 (page 124 of 648), they go through and calculate the section properties for the girder only, 3n, and n. I cannot figure out how they got the "Centroid, d" for the slab in either of the 3n or n.

The bottom flange thickness in the positive moment region is 0.875", web height is 54", top flange thickness is 0.75", haunch is 3.5", and effective slab thickness is 8.0"(according to page 3-7). I pretty sure the centroid to the deck should be all of those added together using half effective slab thickness. Doing this, d = 0.875 + 54 + 0.75 + 3.5 + 8.0/2 = 63.125" In the table, they show 62.375". Any idea what they are doing differently, or what I may be doing wrong? I thought maybe they assumed the top of the deck was cracked and used the depth to the top bars, which I isn't common practice according to my knowledge. The clear distance from the top of the deck is 2.5". Using that clear distance, the slab thickness is 5.5" and I get a d = 61.875. In order to get the 62.375" from their table, their effective slab depth has to be 6.5".

To further confuse me, at the bottom of the same section properties table they calculate the Ytopslab. They show it to be 24.992 for the Composite 3n. Subtracting the Ytopgdr from the Ytopslab, you get 10.75". This includes the haunch, so subtracting the 3.5" haunch gives the distance of 7.25" for the slab thickness. As you can see, this slab thickness doesn't match what was used in the centroid calcs. The actual depth of the slab is 8.5" but 0.5" is the wearing surface and should be neglected in the calcs.

Sorry if this seems so basic to most of you, but its been driving me nuts. I'm studying for the SE exam, which is why I'm going through this design example. Errors are possible in a lengthy design example like this, but I also have the latest example that was updated to the 4th edition of LRFD and it still shows the same values....but I guess this error could have gone unnoticed?

 

[cooperDBM]

I only took a quick look at the example so I can't be positive with my response. The centroid of the deck would include the concrete haunch and the slab. This combination would have a lower centroid than the slab alone (which is what you're calculating).

They may also have included the transformed area of the longitudinal rebar in with the deck. The centroid of this steel is a bit lower that the centroid of the concrete slab. If this is the case then it would also show up in the area (I didn't check).

Good luck with the exam.

 

[cooperDBM]

Sorry, since the properties are in steel units the rebar area wouldn't be transformed.

 

[bigjeremy]

They do consider the steel in the negative moment region, but it it separated from the deck in the table. I wondered about the haunch too, until I read this excerpt before the section properties table:

"For this design example, the slab haunch is 3.5 inches throughout the length of the bridge. That is, the bottom of the slab is located 3.5 inches above the top of the web. For this design example, this distance is used in computing the location of the centroid of the slab. However, the area of the haunch is not considered in the section properties.

Some states and agencies assume that the slab haunch is zero when computing the section properties."

 

[cooperDBM]

I had a closer look and noted that the haunch thickness is measured from the top of the web (see Tip - Slab Haunch) on the previous page. You had measured the haunch from the top of the top flange. That would give you the d of 62.375, ignoring the rebar and haunch area.

 

[bigjeremy]

Doh! Thanks for the heads up. I knew it was something simple!!