2.2 EVALUATION OF TEST DATA
2.2.1 Developing fastener performance data
State-of-the-art anchor design uses what is known as the Strength Design Method . By using the Strength Design Method , nominal strengths are first calculated for all the possible anchor failure modes . Subsequently , strength reduction factors are applied to each nominal strength to obtain a design strength . The controlling design strength is finally compared to a factored load . The provisions of ACI 318 Chapter 17 are the basis used for Strength Design .
Strength Design data for Hilti mechanical anchors in concrete is derived from testing as per the provisions of ACI 355.2 and ICC-ES AC193 . Strength Design data for Hilti adhesive anchors in concrete is derived from testing as per the provisions of ACI 355.4 and ICC-ES AC308 .
Beginning with IBC 2003 , the IBC Building Codes have adopted the Strength Design Method for anchorage into concrete of both cast-in-place and post-installed anchors .
Another anchor design method known as " Allowable Stress Design " is still used as an alternative to the Strength Design provisions especially when used for anchoring into masonry base materials . Section 2.2.2 provides detailed explanations of the Allowable Stress Design provisions used by Hilti . Allowable Stress Design data for Hilti mechanical anchors is derived from testing based on ASTM E488 , ICC-ES AC01 and AC106 . Allowable Stress Design data for Hilti adhesive anchors is derived from testing based on ASTM E1512 , ASTM E488 , ICC-ES AC58 and AC60 .
There are two methods of developing allowable loads ; ( 1 ) apply an appropriate safety factor to the mean ultimate load as determined from a given number of individual tests , or ( 2 ) apply a statistical method to the test data which relates the allowable working load to the performance variability of the fastening .
2.2.2 ALLOWABLE LOADS
Historically , allowable loads for anchors have been derived by applying a global safety factor to the average ultimate value of test results as shown in Eq . ( 2.2.1 ).
F all =
F v ( 2.2.1 )
Where :
F = mean ultimate value of test data ( population sample ) v = global safety factor
Global safety factors of 4 to 8 for post-installed anchors have been industry practice for nearly three decades . The global safety factor is assumed to cover expected variations in field installation conditions and in anchor performance from laboratory tests .
Note that global safety factors applied to the mean do not explicitly account for the coefficient of variation , i . e ., all anchors are considered equal with respect to variability in the test data .
2.2.3 STATISTICAL EVALUATION OF DATA
Experience from a large number of tests on anchors has shown that ultimate loads generally approximate a normal Gaussian probability density function as shown in Fig . 2.2.1 . This allows for the use of statistical evaluation techniques that relate the resistance to the system performance variability associated with a particular anchor .
The 5 % fractile characteristic value has been adopted by the IBC as the basis for determining published design loads based on anchor testing results for Strength Design . There is a 90 % probability that 95 % of the test loads will exceed a 5 % fractile value . The 5 % fractile value is calculated by subtracting a certain number of standard deviations of the test results from the mean based on the number of trials . See Eq . ( 2.2.2 ) and the referenced statistical table by D . B . Owen . For a series of 5 trials , the 5 % fractile value is calculated by multiplying the standard deviations by k = 3.401 and subtracting from the mean .
Owen , D . B ., ( 1962 ) Handbook of Statistical Tables , Section 5.3 . Reading : Addison-Wesley Publishing .
Fig . 2.2.1 Frequency distribution of anchor ultimate loads , demonstrating the significance of the 5 % fractile
R k
= F - k · s = F ( 1 - k · cv ) ( 2.2.2 ) Where :
R k
|
= |
characteristic resistance of the tested |
|
|
anchor system |
F |
= |
mean ultimate resistance of the tested |
|
|
anchor system |
k = distribution value for test sample size n s = standard deviation of the test data cv = coefficient of variation = s F
Thus , test series with low standard deviations are rewarded with higher 5 % fractile characteristic design values . This is typical of ductile steel failure modes .
Characteristic Strength Design loads may be converted to allowable loads . See Section 3.1.6 .
12 Anchor Fastening Technical Guide Edition 22 | 2.0 ANCHORING FASTENING TECHNOLOGY | 2.2 EVALUATION OF TEST DATA Hilti , Inc . 1-800-879-8000 | en español 1-800-879-5000 | www . hilti . com | Hilti ( Canada ) Corporation | www . hilti . ca | 1-800-363-4458