Structural Analysis Results

The structural model for the Norick Arena was used to study the structural behavior of the structure under various load combinations and conditions. The implications of these results in the context of selected field measurements are presented. The theoretical sag at the middle is taken as 17 ft. 3 in. as determined from the original structural drawings. All deflection results are presented from this benchmark sag. Table 2 summarizes the results from the various analyses.

Case 1

This base model was considered in order to understand the expected behavior of the roof structure from the original design. This model considered a dead load of 56 psf, live load of 12 psf and the post-tensioning as fully effective. Gross section properties were considered for the column sections.

The analysis shows that the maximum downward deflection at the middle of the roof is about 2.1 in. below the benchmark sag. It was found that the columns developed bending moments in excess of the cracking moment.

Table 2. Summary of Analysis Results.

Case

No.

Column

Inertia

Long­

term

Modulus

DL

(psf)

LL

(psf)

Additional PT Losses from

fps = 0.6 fpu

(%)

Center Deflection from Theoretical Sag (17 ft. 3 in.), Positive Downward (in)

1

Ig

No

56

12

0

2.1

2

0.5 Ig

No

59

0

0

1.3

3

0.5 Ig

Yes

59

0

0

3.2

4

0.5 Ig

Yes

59

Varies 0 to 19

0

Varies 3.2 to 7.5

5

0.5 Ig

Yes

59

0

10

4.2

6

0.5 Ig

Yes

59

0

25

5.6

7

0.5 Ig

Yes

59

0

50

8.1

Case 2

This case closely reflects Case 1, except that the column stiffness was reduced to 50% of that based on gross section properties to account for cracking. The field observations presented previously confirmed the presence of flexural cracks. Also, the dead load was increased to reflect the weight of the foam roof. The live load was removed to reflect conditions when field measurements were taken.

The field measurements indicate that the present roof sag is in the range of about 17 ft. 4 in. to 17 ft. 8 in. This is an increase in sag of 1 in. to 5 in. The computed value of Case 2 is in between these values.

Case 3

As part of the various analyses of the structure, this model considered long-term effects. This model is based on Case 2 with the addition of long-term effects. These effects are modeled by reducing the elastic modulus of the structural members by a factor corresponding to the long-term conditions expected on the structure. In this case, a factor of 0.4 was computed, indicating that for long-term conditions, the effective elastic modulus is about 40% of its original value. The structural analysis yields an increase in downward deflection of 3.2 in. The sag in the center of the roof increases by only about 2 in. considering time-dependent effects. The computed deflection is virtually in between the range of measured values. This strongly suggests that there has been no measurable loss in prestressing of the post-tensioning tendons.

Case 4

The ACI 318 Building Code (ACI 318, 2005) requires that a post-tensioned structure limit tension

stress to under full service loads. Case 4 was conducted to determine the level of live load

acting on the structure needed to exceed the limiting tension stress. This value would be one possible index in determining the current load rating of the roof. Analyses showed this value to be about 19 psf. Under this loading and under similar conditions as in Case 3, the maximum downward deflection increases by 7.5 in. from the benchmark sag.

Cases 5 to 7

These analyses consider additional losses in the post-tensioning tendons due to some form of deterioration such as corrosion or other factors that might result in a partial loss of prestressing. These additional losses considered were 10%, 25% and 50%, respectively. These losses were applied to the same analysis model and loads of Case 3. The results are summarized in Figure 10. This graph shows that considering 0% losses in the post-tensioning, the deflection in the middle of the roof is about 3.2 in., whereas, 50% losses in the effective post-tensioning stress results in a deflection of 8.1 in. The analysis indicates that the center deflection of the roof is not overly sensitive to assumed losses in the post-tensioning from some form of deterioration. The increase in roof deflection is linear with the percentage of prestressing losses.

60

0123456789 Roof Center Deflection, inches

Figure 10. Deflection at middle of roof compared to assumed additional losses in post-tensioning.

Collapse Conditions

As a perspective of the conditions that would result in the “collapse” of the roof under its existing weight, a collapse analysis indicates that, on average, 65% of the post-tensioning would have to be lost from the effects of corrosion or as a result of some type of catastrophic event. The resulting increase in sag would be about 10 in.

Conclusions

A field evaluation and structural assessment was conducted for the post-tensioned concrete roof of the Norick Arena, which was designed by T. Y. Lin in l965. There were no signs of significant deterioration that would indicate that the structural roof system has been compromised in its 40-year life thus far. It was determined that the roof will continue to safely carry the intended code-required loads as long as the roofing material is adequately maintained to mitigate ingress of water and as long as the roof drains are maintained.

The analysis indicates that the post-tensioning system was designed to balance a total load of about 68 psf. The present dead load of the roof is approximately 59 psf. Thus, the allowable additional live load from purely a load-balancing perspective is 9 psf. This exceeds the current snow load of 7 psf.

References

ACI Committee 209 (1997), “ACI 209R-92: Prediction of Creep, Shrinkage and Temperature Effects in Concrete”, American Concrete Institute, Detroit, MI, 47 pp.

ACI Committee 318 (2005), “ACI 318-05: Building Code Requirements for Structural Concrete and ACI 318R-05: Commentary”, American Concrete Institute, Detroit, MI, 430 pp.

ASCE (2002), “Minimum Design Loads for Buildings and Other Structures”, American Society of Civil Engineers, Reston, VA, 376 pp.

Lin, T. Y. and Burns, N. H. (1981), “Design of Prestressed Concrete Structures”, Third Edition, John Wiley & Sons, New York, NY, 646 pp.