Guide for sizing adhesion stress in anchors
Calculation of anchor lengths
The length required to anchor a reinforcing bar can be calculated using the equations in clause 3.12.8.3 of BS 8110 Part 01 1997. However, simplified values are also given in Table 3.27 which can be used to calculate tensile anchor lengths and compression.
In this article we will focus on calculating reinforcement anchorage.
The following figure shows the equation provided in the code to calculate bond stresses.
The figure above shows Equation 48 of the code. If we know the other parameters we can calculate the anchor lengths. f b The bond strength depends on the quality of the concrete and the bond coefficient. The bond voltage can be calculated as follows.
Equation 49 of BS 8110 Part 01 provides the equation for calculating bond stress. To calculate the bond voltage, we need to find the bond coefficient.
Depending on the type of bars used and whether the bars are subject to tension or compression, the coefficient of adhesion must be determined. It can be found in Table 3.26 of the Code.
Using the values given in the table we can calculate the connection voltage.
Consider an example of calculating the length of the tension anchor
Concrete quality 25
Type II deformed rods
Switching voltage = β√fcu
= 0.5√25
= 2.5
Remember that the rod diameter is 16 mm and the rod is tensioned to the yield point.
So the voltage in the bare state is 0.95fy
Force on the bar = 0.95f j xA S
F = 0.95 x 460 x 200
= 87400N
F b = Fs/πφ t i
l = Fs/πφ t F b
= 87400 / π x 16 x 2.5
= 695.5mm
The calculated value of the anchor length is 695.5 mm. Therefore we can provide an anchor length of 700mm.
This value can be found in Table 3.27 of BS 8110. The relevant factor for Grade 25 concrete and Type 2 deformed bars is 44
Tension anchor length = 44×16
= 704mm
It can be concluded that when a bar is in full tension (yield), both methods lead to similar results and we can use Table 3.27 to determine the overlap and anchorage lengths instead of time-consuming calculations.
