Calculating Crack Widths

[GalileoG]

I realize that any calculation to determine crack characteristics is highly approximate, but I would like to calculale the crack widths on my 2 meter deep beams (and to verify the crack width output that the software that I am using is outputting.) I was not able to find any guidance on crack widths on the Code (CSA A23.3-04 - Canadian.) Thanks!

Clansman

 

[EdR]

Haven't really thought this through but how about something like: Compute the slope of the beam for an uncracked section...then compute the slope of the beam for a cracked section (at the same point)....use the difference in slopes times depth from neutral axis to outside edge as the crack width. This would at best be approximate since the location of the neutral axis is different for the two cases but if it is not too different it might give a good approximation......

Ed.R.

 

[GalileoG]

Update: I was able to find an equation "Gergely & Lutz" and "Suri & Dilger" on the PCI manual which I have used to calculate an approximate crack width.

Clansman

 

[WpgKarl]

Clansman - your beams are 2 meters deep - that's getting up there.....What's your span to depth ratio on the beam. Be careful that you do not have a deep beam in checking the design.

PS - I believe that A23.3-04 code has a limit for "z" which is another form of the eqn. for calculating the crack widths. The limiting values for z are equivalent to the limiting values for crack widths.

 

[GalileoG]

Thanks WpgKarl. I was never able to understand the concept of "z" though. Crack width is something I can visualize but what exactly is the theory behind "z"?

My span to depth ratio is 5. My beams are spandrels that will have double-tees spanning into them. According to the Canadian Code, I do not have to use strut and tie as long as my span to depth ratio is greater than 2.

Clansman

 

[cooperDBM]

I have no specific knowledge of the decision to go with z though I believe it's to avoid comparison between a code calculated crack width and an actual measured width, which will never agree. The z value represents a potential degree of cracking instead of an actual crack width which is dependent on the virtually unknowable crack spacing. Crack spacing isn't account for in the Gergely & Lutz equation, which is the basis for z, and this spacing very dependent on how well distributed the crack control steel is.

 

[WpgKarl]

Clansman - see commentary to the Cdn code on 10.6.1, which explains where the theory for that code check comes from. The eqn for "z" is buried in the eqn for "w".

I think the newer versions of ACI specify an actual bar spacing rather than calc. a crack width, or value for "z". Note that the crack width is proportional to the strain in the reinf. rather than the stress, as the strain in rebar at the permitted crack widths is assumed to be limited to fs/Es = 0.0012, which is why you can assume fs = 0.60 fy = 0.0012.

 

[Gumpmaster]

Acutal crack width is very hard to calculate. The "z" calculations are approximate at best. Crack widths in the field will probably vary a large amount from anything ACI will give you.

The free program Response 2000 has a crack width function. Evan Bentz wrote it. I think it's a great program. You get a fairly accurate idea of what the actual beam response will be.

Mr. Bentz works with Michael Collins and Frank Vecchio so you know he's a pretty smart guy.

 

[GalileoG]

Thanks all for the great responses!

Clansman

"If a builder has built a house for a man and has not made his work sound, and the house which he has built has fallen down and so caused the death of the householder, that builder shall be put to death." Code of Hammurabi, c.2040 B.C.

 

[BAretired]

But let us look at the rest of the Hammurabi code.


History of Building Codes
HISTORIC CODES

The Code of Hammurabi (circa 3000 B.C.)

One of the oldest known writings of early civilization is the Code of Hammurabi. Hammurabi was the founder of the Babylonian Empire over 5,000 years ago. The portion of the Code of Hammurabi which related to buildings read:

228: If a builder build a house for a man and complete it, that man shall pay him two shekels of silver per sar (approx. 12 sq. ft.) of house as his wage.

229: If a builder has built a house for a man and his work is not strong, and if the house he has built falls in and kills the householder, that builder shall be slain.

230: If the child of the householder be killed, the child of that builder shall be slain.

231: If the slave of the householder be killed, he shall give slave for slave to the householder.

232: If goods have been destroyed, he shall replace all that has been destroyed; and because the house was not made strong, and it has fallen in, he shall restore the fallen house of his own material.

233: If a builder has built a house for a man, and his work is not done properly and a wall shifts, then that builder shall make that wall good with his own silver.

The Code of Hammurabi though quite harsh by today's standards, shows that civilization has tried to bring about some control over building safety.


Best regards,

BA

 

[WpgKarl]

Today's version of that code.....

If a builder builds a house and anything goes wrong, sue everybody who has money...oh ya, and blame the engineer!