### Champlain Towers Collapse Structural Analysis in depth

**Champlain Towers Collapse Structural Analysis in depth**

The tragedy of the Champlain Towers collapse took all of us by surprise. Immediately, when I saw the collapse of this building, I dedicated my time to thoroughly understand the origin of such misfortune. The first aspect that intrigued me was that the building was built 40 years ago. It is likely that it has been subjected to much greater loads in the past. Unquestionably loads much greater than those present when the building failed. Additionally, it has withstood hurricanes and strong winds in that timespan. This shows that there were no errors in the structural calculations nor in the construction process.

The second aspect that I reviewed was the way in which the building collapsed. The failure was similar to demolition process in which explosives are placed in the lower columns, in turn causing a vertical collapse. The same thing happened with the building, which makes me believe that the lower columns are the basis of failure.

The third aspect is related to informative reports that there were problems with the concrete slab for 25 years; therefore, cracking and chipping observed in 1996 over the columns originated the structural failure of the slab. As observed in the picture, the columns stayed standing while a hole formed in the slab around the columns and causing the slab to fall to the floor. After considering this information, I focused my attention to find what could have caused the failure of the lower columns of the building.

The following are the results of the study conducted regarding the Champlain Towers Collapse.

### Analysis of the Concrete Slab Failure in the Roof of the Parking Lot

**Punching Shear Failure**

The concrete slab has 9 ½ in thickness with concrete strength of fc = 4000 psi and the N columns are 12 in x 16 in. The most unfavorable condition is found in L/11.1 as shown in Fig. 1. The following will show calculations for the failure due to punching shear, which will include all the loads, including the live load of 60 lb/ft^{2}.

The tributary area:

. *Atrib* := 19.83 • *ft* • 22 • *ft* = 436.26 • *ft*²

Actual service loads:

. *VDL* := *Atrib* • 9.5 • *in* • 150 • (*lb*/*ft*³) = 51.8 • *kip*

. *VLL* := *Atrib* • 60 • (*lb*/*ft*²) = 26.2 • *kip*

**Fig. 1 Punching Shear Failure**

To see Fig. 1 in more detail, please see pdf below.

Champlain Tower In Depth Figure 1.1

Champlain Tower In Depth Figure 1.2

Factored load:

. *Vu* := 1.2 • *VDL* + 1.6 • *VLL* = 104 • *kip*

The effective height:

. *d* := 9.5 • *in* – 0.75 • *in* – (*Φ*/2) = 8.438 • *in*

. *fc* := 4000 • (*lb*)/(*in*²)

Reinforcement:

. *Φ* := (5/8) • *in as* := 40

Critical section perimeter:

. *b* := (12 • *in* + 16 • *in* + 2 • *d*) • 2 = 89.75 • *in*

. *ΦVc* := 0.75 • 4 • (*lb*/*in*²)^0.5 • (√*fc*) • *b* • *d* = 143.7 • *kip*

Since Vu < *ΦVc *and the slab does not fail due to punching shear even if all the live load was acting on it.

The former was confirmed in the photos. If it were this kind of failure, the columns would have a cone shape in the upper part. However, this was not the case.

**Failure due to Bending**

The 9 ½ in concrete slab without beams working in two directions has a positive reinforcement of #4 @ 12” o/c in both directions and a negative reinforcement of 16 #5 in one direction and between 16 #5 and 19 #5 in the perpendicular direction as shown in Fig. 2. This reinforcement corresponds to the zone of level +10’ 10”.

** **

**Fig. ****2**** Negative Reinforcement in the zone of level +10’ 10”**

To see Fig. 2 in more detail, please see pdf below.

Champlain Tower In Depth Figure 2

The negative reinforcement of 16 #5 is distributed in a span of 5’ 6” + 5’ 6” and of those 16 rebars 25% will be placed over the column; therefore, 4 bars #5, the rest are distributed approximately at 9” from each side of the column. In the other direction, the distribution of the reinforcement is approximately the same. This reinforcement has been affected by corrosion due to this zone being the place where radial fissures developed due to the concentration of the bending moments over the columns in both directions. The decrease in area of the rebars overtime has caused the failure due to bending for the loads of the building slab self-weight. With the rebars failing, the cracks of the concrete slab around the column were produced. This can be seen in the photos.

**The Concrete Slab Acting as a Shell**

Once the slab has failed in one column, the one with the worst corrosion, the remaining surrounding columns receive more loads and a generate a progressive collapse. After this moment, is where the big problem begins. Supposedly, the positive reinforcement has not been affected the same way as the negative reinforcement; therefore, the steel begins to behave in a different way than what it was designed for. In order to explain the new function of the slab and its positive reinforcement, we must choose a strip that includes half of the slab from both sides. For example, N gridline can be considered in between the pool and gridline 9.1, as shown in Fig. 3.

** Fig. 3 Strip of the slab acting as a plane in Gridline N**

To see Fig. 3 in more detail, please see pdf below.

Champlain Tower In Depth Figure 3

Due to the cracking of the slab over the column, the slab falls. The increase in loads for the adjacent columns causes the failure. This process is repeated in both directions. If the slab had simple support in the edges, then the slab would have fallen to the floor and the problem would not have continued. Only the slab over the parking lot would have fallen. However, this did not occur. In actuality, the slab is anchored to the pool and the retaining wall on one side and on the lower part of the beam on gridline 9.1, about 2’ 6” under the slab at a level of +13’ 4”. The reinforcement throughout the strip in the study is anchored to the pool, the retaining wall, and the beam in gridline 9.1.

**The slab starts to work like a shell anchored at both of its extremities**

The positive and negative reinforcement throughout the band conforms to a cable with a sum of the areas of the rebars throughout the span of the strip analyzed.

Considering only the positive reinforcement for the total span of B = 19’ 0”:

Area of all the rebars in strip width:

. *As* := ((19 • *ft*)/ (12 • *in*)) • 0.20 • *in² * *As* = 4 • *in*²

All the rebars are equivalent to one cable. This cable is found being supported on both extremities which in turn begins to act as a shell. After being stretched due to the slabs own weight, the slab is subjected to tension and begins to fissure. In this way, the steel has the effect of a cable, similar to a cable used for handrails. The pictures show how the slab stays fixed in the retaining wall and detaches from the pool, causing the reinforcement of anchor to fail. Fig. 4.

**Fig. 4 The effect of the shell (Working as a steel cable)**

To see Fig. 4 in more detail, please see pdf below.

Champlain Tower In Depth Figure 4

**Horizontal Force Created by the Effect of the Cable Supported on the Extremities**

**Case 1 **Effect of the slab failing over a column:

. *L* := 60.33 • *ft l* := 39.67 • *ft yc* := 150 *pcf*

. *B* := 19.0 • *ft kip* := 1000 • *lb*

. *h* := 9.5 • *in *

. *w* := *B* • *h* • *yc *w = 2256.3 • *lb*/*ft *(Only the weight of the slab)

. Steel reinforcement #4 @ 12 in O/C *Spc* := 12 • *in*

. Number of bars *n *:= (B/Spc) +1 *n *= 20

. *As* := 0.2 • *in*² • *n * *As* := 4 • *in*² *Es* := 29000000 • *psi*

. Deformation at the center

. *a* := [((3 • *w* • *l*)/(64 • *Es* • *As*))^(1/3)] • *l *a = 1.509 • *ft*

. Horizontal force at extremities

. *T* := (*w* • *l*²)/(8*a*) *T* = 294 • *kip*

. When the steel cable is subjected to force, the tensions are:

. *Fa* := *T*/*As * *Fa* = 73547 • *psi * <85 • *ksi * strength of steel at failure

. Surpassing the yield strength of reinforcement A615 but under the resistance at failure of steel,

. therefore, it cannot break by itself.

Performing similar calculations for Cases 2 and 3, the values obtained are 300 kip and 447 kip. As we can see in the photos, we can deduct that Case 3 was most likely to cause the failure. We will assume that the horizontal force reaches a value of 350 kip. This corresponds to the failure of the cable at 85 ksi.

### Analysis of a Column “C” of the Structure

We must consider the column located on gridline N and gridline 9.1 in the lower level. This column is 16” x 16” with 8 #11. That is about 4.88% which is high. We must consider that when we splice the bars of the foundation this number is doubled to more than 8% which is the limit to the code specifications. The column has a height of 10’ 9” and is considered as a pin at its extremities. Which results in a conservative estimate. For the following analysis, the effect of the loads of the buildings self-weight components is considered exclusively, with an overload of 20 lb/ft^{2} and the weight of the exterior walls. When the building collapsed, it is assumed that the building has a minimum live load which does not influence the following analysis as shown in Fig. 5.

** Fig. 5 Maximum load on column C of gridline N and 9.1**

To see Fig. 5 in more detail, please see pdf below.

Champlain Tower In Depth Figure 5

. The tributary area:

. *Atrib* := 10.67 • *ft* • 20 • *ft* + 5.67 • *ft* • 6.58 • *ft* = 250.709 • *ft*²

. Number of floors *n* := 12 (11 floors + roof slab)

. Dead Load DL

. *SlabDL* := [9.5 • *in* • 150 • (*lb*/*ft*³) + (*n*+1) • 8 • *in* • 150 • (*lb*/*ft*³)] • *Atrib* = 305.6 • *kip*

. *ColDL* := *n* • 16 • *in* • 16 • *in* • 150 • (*lb*/*ft*³) • 8.83 • *ft* = 28.3 *kip*

. *SlDL* := *n* • *Atrib* • 20 • (*lb*/*ft*²) = 60.2 • *kip*

. *WallDL* := *n* • 8.83 • *ft* • 36 • (*lb*/*ft*²) • 20 • *ft* = 76.3 *kip*

. TotalDL := SlabDL + ColDL + SlDL + WallDL = 470.3 • *kip*

The vertical service load in the moment when the building collapsed was 470 kip.

In the Fig. 6, the column is shown with the horizontal load of 350 kip acting at the level in the middle of the slab. The column now is considered embedded in both extremities. This results to be the real situation and is going to be the condition that creates the least bending moment. Thus, we will be minimizing the effect of said load so that the evaluation is as safe as possible.

** Fig. 6 Column N subjected to the effect of the horizontal load**

To see Fig. 6 in more detail, please see pdf below.

Champlain Tower In Depth Figure 6

. *P* := 350 • *kip a* := 8.65 • *ft b* := 2.10 • *ft l* := 10.75 • *ft*

. The maximum bending moment for the service load:

. *Ma* := (2 • *P* • *a*² • *b*²)/(*l*³) = 186 • *kip* • *ft *at the point of horizontal load

. *M2* := (*P* • *a*² • *b*)/(*l*²) = 476 • *kip* • *ft * at the support closest to horizontal load

. Therefore, column N is subjected to a vertical service load and a bending moment of:

. *P* := 470.3 • *kip * *M2* := 476 • *kip* • *ft*

Now we will obtain a diagram of the interaction for column N with a section of 16” x 16” reinforced with 8 #11 and concrete compressive strength of 6000 psi.

Fig. 7 shows the interaction of Column N in the diagram.

** Fig. 7 Interaction diagram of Column N**

To see Fig. 7 in more detail, please see pdf below.

Champlain Tower In Depth Figure 7

The continuous line represents the capacity of the section for the design after the combinations of the loads factored in the specifications, while the dashed line represents the nominal values, meaning the actual capacity of the section for a combination of axial load and bending moment. In other words, if the section was subjected to a combination of P and M, the point that defines this combination should be located in the interior of the nominal diagram so that it does not fail; however, if it is located on the outside, failure occurs immediately.

In this case the point, which has:

. *P* := 470.31 • *kip M2* := 544 • *kip* • *ft*

falls outside of nominal diagram; thus, this column fails at the instance at which the combination starts to act at the same time. After this instance, the failure of the first column produces the gradual collapse of the remaining columns due to the redistribution of the loads to those adjacent columns, giving way to a type of failure similar to that of demolitions where explosives are placed near the lower columns.

### Conclusion and Observations About Building Design

The fundamental conclusion of this analysis is that the primary cause of the Champlain Towers Collapse is due to the corrosion of the bars at the top of the concrete slab over the parking lot located above the columns. The slab failure created a slab shell effect which originated the horizontal loads that caused the failure of the columns of the building and subsequently causing the progressive collapse and failure of part of the building. All because of poor maintenance.

##### Lastly, I would like to make observations which could help with the future design of buildings located near the ocean, with slabs at different levels in the same floor and the distribution of the shear walls of the structure.

**a)** If we observe the details of the slab reinforcements, we find that the net cover of the negative reinforcement bars in the slab is 3/4”. Even if the codes specify this amount, it is convenient to increase the coverage in situations where there is salt water, balconies, etc.

**b)** The difference in the level of the floor slab within the building and the roof of the parking lot is 2’ 6”. It is evident that the parking lot does not need elevated height, giving way to this difference in elevation. However, it is important to note that the effect of the horizontal slabs can produce horizontal loads due to the retraction of the concrete, the effects of prestressed cables within the slab, the effects of wind loads, or in this case, something unusual, the effect of slab shell. It is suggested that the differences in heights are studied, as shown in continuation.

**c) **In the situation of differential levels, a discontinuity can be achieved if beam is placed with a column separated at 1 or 2 in. from the column of the building or placing a support (ledge) in the beam located at the edge, avoiding the continuation of both parts. Fig. 8

**d)** Finally, another important factor that I noted and would like to expand on is the shear walls. If we look, the progressive collapse finalized at the moment where it met the retaining wall of gridline F.3 but it went over the retaining wall in gridline M, failing there as well. I would like to comment that they designed these walls for wind acting in one direction. But no wall was designed for the wind acting in a perpendicular direction.

**Fig. 8 Different connections**

To see Fig. 8 in more detail, please see pdf below.

Champlain Tower In Depth Figure 8

On behalf of Eastern Engineering Group, we give our sincerest condolences to all affected by the Champlain Towers Collapse. This article reflects the studies of Professor Ernesto F. Valdes regarding the Champlain Towers Collapse and he wrote it specifically for Eastern Engineering Group to publish on his behalf.

Translation By: Ivet Llerena (Eastern Engineering Group).

Structural Drawings By: Eastern Engineering Group.

Photography of Champlain Towers Collapse By: Pablo Lopes.

© 2021 This article was written by Ernesto Valdes and published by Eastern Engineering Group. All rights reserved.

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