Evaluation of test data

Contents
- Developing Fastener Performance Data
- Safety Factor Method
- Statistical Evaluation of Data

Developing Fastener Performance Data
Developing the ultimate or allowable loads for fasteners from theoretical (calculation) methods may not give satisfactory results because of the interrelationships of the many variables involved, which include concrete strength, failure mode, anchor types, friction coefficients, loading direction and type, etc. Thus, all Hilti published data is based on fastener testing.

Fastener testing at Hilti is conducted in accordance with ASTM E 488, Standard Test Methods for Strength of Anchors in Concrete and Masonry Elements, ASTM E 1512 Standard Test Methods for Testing Bond Performance of Adhesive-Bonded Anchors and ASTM E 1190 Standard Test Methods for Strength of Power-Actuated Fasteners Installed in Structural Members. Because of the wide variation in possible concrete reinforcing configurations found in construction, testing is typically performed in unreinforced concrete, which gives conservative results.

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 reliability of the fastening.

Fig. 1 Frequency distribution of fastener loads, demonstrating the significance of the 5% fractile and the allowable load

Safety Factor Method
With this approach, an appropriate safety factor (e.g. 4, 5, etc.) is applied to the mean ultimate load to account for the variations in concrete, steel, fastening reliability, among other influences. It is typified by Eq. 2.2.1.

Statistical Evaluation of Data
The experience from a large number of fastener tests has shown that the load performance approximates a normal Gaussian probability density function as shown in Fig. 1 where the representative test data is arranged in a histogram. This allows the use of statistical evaluation techniques which can relate the allowable load to the reliability of the fastening.

The method used by Hilti for anchors is called the 5% fractile. Using this concept, a characteristic load, Rk, is calculated from test data such that, for a 90% probability (90% confidence interval), 95% of the loads are above that load (the Rk value in Fig. 2.2.1). The characteristic load is determined by Eq. 2.2.2 which relates the number of fasteners in the test to a probability factor, k. A general safety factor, v, which includes concrete and fastening variations is then applied to the characteristic load as shown in Eq. 2.2.2 to arrive at the allowable load. If the individual number of tests is at least 40, k can be approximated by 2 with sufficient accuracy. Fastening systems with low s (and low cv) will have tightly grouped test data signifying a more consistent fastening. Using this equation, tightly grouped data will result in higher allowable loads than widely dispersed data.

Many of the allowable loads in this Technical Guide are based on this statistical calculation method. The allowable loads, unless otherwise stated, are based on static loads and the following safety factors:

• v = 3 for concrete failure and bond failure
• v = 5 for failure of plastic anchors

• differences when setting anchors
• local variations in the strength of the base material
• unforeseen load peaks
• long-time influencing factors
• manufacturing influence

It is the responsibility of the user or design engineer to examine all factors that could influence an anchorage.

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