Re-entrant corners will usually cause cracking. Proper planning of the joint pattern to eliminate re-entrant corners will correct this problem. Even though you isolate the column box as shown here the slab will still develop uncontrolled cracks. In most cases, as shown here, the simplest way to avoid the re-entrant corner may be to rearrange. Re-entrant corners are corners that point into a slab. For example, if one were to pour concrete around a square column, you would create four re-entrant corners. Because the concrete cannot shrink around a corner, the stress will cause the concrete to crack from the point of that corner (See Figure 1).
This paper examines cracks which occurred at the re-entrant corners at the dapped ends of bulb tee girders used on the MIA Mover APM System at Miami International Airport. Cracks were initially identified during load testing at the precast yard, although typically they did not occur until the beams were erected. The load test and crack mechanism is described herein. Post-erection cracking is compared with that observed under load test conditions and differences are discussed. FDOT criteria were applied in determining the appropriate protection strategy. Gears of war pc mods.
Re-entrant Corner Reinforcing - Code Reference
Re-entrant Corner Reinforcing - Code Reference
Re Entrant Corner Cracked
I am aware from experience to always add diagonal reinforcing in a re-entrant corner in a slab on grade. I normally require (2)-#5 x 4', with 1' clear from the top of the slab.
However, I am now in the position where I have a slab with a textbook 45 degree crack from multiple re-entrant corners within 20 (+/-) days of placement. The situation is though that as an owner's representative, I need to provide proof to the owner that these bars were 'required by code.' I have looked in ACI 315 (Detailing of Reinforcing), ACI 224.3R (control of Cracking), ACI 224.1R (Causes, evaluation, and repair of cracks) and none of these 'require' diagonal reinforcing at re-entrant corners. ACI 360R (Design of Slabs on Ground) has Figure A7.3.3 which shows the diagonal bars, but it is considered 'typical conceptual details that have been used sucessfully on projects.'
Has anyone ever seen a reference that states these bars are 'required?' Thanks in advance.
Re-entrant corners will usually cause cracking. Proper planning of the joint pattern to eliminate re-entrant corners will correct this problem. Even though you isolate the column box as shown here the slab will still develop uncontrolled cracks. In most cases, as shown here, the simplest way to avoid the re-entrant corner may be to rearrange. Re-entrant corners are corners that point into a slab. For example, if one were to pour concrete around a square column, you would create four re-entrant corners. Because the concrete cannot shrink around a corner, the stress will cause the concrete to crack from the point of that corner (See Figure 1).
This paper examines cracks which occurred at the re-entrant corners at the dapped ends of bulb tee girders used on the MIA Mover APM System at Miami International Airport. Cracks were initially identified during load testing at the precast yard, although typically they did not occur until the beams were erected. The load test and crack mechanism is described herein. Post-erection cracking is compared with that observed under load test conditions and differences are discussed. FDOT criteria were applied in determining the appropriate protection strategy. Gears of war pc mods.
Re-entrant Corner Reinforcing - Code Reference
Re-entrant Corner Reinforcing - Code Reference
Re Entrant Corner Cracked
I am aware from experience to always add diagonal reinforcing in a re-entrant corner in a slab on grade. I normally require (2)-#5 x 4', with 1' clear from the top of the slab.
However, I am now in the position where I have a slab with a textbook 45 degree crack from multiple re-entrant corners within 20 (+/-) days of placement. The situation is though that as an owner's representative, I need to provide proof to the owner that these bars were 'required by code.' I have looked in ACI 315 (Detailing of Reinforcing), ACI 224.3R (control of Cracking), ACI 224.1R (Causes, evaluation, and repair of cracks) and none of these 'require' diagonal reinforcing at re-entrant corners. ACI 360R (Design of Slabs on Ground) has Figure A7.3.3 which shows the diagonal bars, but it is considered 'typical conceptual details that have been used sucessfully on projects.'
Has anyone ever seen a reference that states these bars are 'required?' Thanks in advance.
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