Calculation of Anchorage Lengths
Length required to anchor a reinforcement bar can be calculated by using the equations given in the clause 3.12.8.3 of BS 8110 Part 01 1997. However, code also provides simplified values in table 3.27 that can be use to calculate the tension and compression anchorage lengths.
In this post we are concentrating on calculation of anchorage of reinforcements.
Following figure show the equation given in the code for calculating the bond stresses.
Above figure show the equation 48 of the code and if we know the other parameters we can calculate the anchorage lengths. fb which is bond stress is depends on the grade of the concrete and bond coefficient. Method of calculating bond stress is as follows.
Equation 49 of the BS 8110 Part 01 states the equation for calculating the bond stress. We need to find the bond coefficient to calculate the bond stress. Depending on the type of bars used and whether the bare are in tension or compression, is considered to find the bond coefficient. It can be fond in the table 3.26 of the code.
With the values given in the table we can calculate the bond stress.
Consider a example of calculating tension anchorage length
Grade of concrete 25
Deformed type II bars
Bond stress = β√fcu
= 0.5√25
= 2.5
Consider bar diameter of 16mm and bar is stress up to the yielding.
Then stress in bare is 0.95fy
Force in the bar = 0.95fyxAs
Fs = 0.95x460x200
= 87400 N
fb = Fs / πφ el
l = Fs / πφ efb
= 87400 / π x 16 x 2.5
= 695.5 mm
Calculated value of anchorage length is 695.5 mm. So we may provide Anchorage length of 700 mm.
This value can be found from the table 3.27 of the BS 8110. Factor relevant to grade 25 concrete and deformed type 2 bars is 44
Tension anchorage length = 44x16
= 704 mm
Hence, it can be concluded that when a bar is fully stress (yielding) both methods gives similar answers, and we can use the table 3.27 instead of doing lengthy calculations for finding lap and anchorage lengths.
Length required to anchor a reinforcement bar can be calculated by using the equations given in the clause 3.12.8.3 of BS 8110 Part 01 1997. However, code also provides simplified values in table 3.27 that can be use to calculate the tension and compression anchorage lengths.
In this post we are concentrating on calculation of anchorage of reinforcements.
Following figure show the equation given in the code for calculating the bond stresses.
Equation 49 of the BS 8110 Part 01 states the equation for calculating the bond stress. We need to find the bond coefficient to calculate the bond stress. Depending on the type of bars used and whether the bare are in tension or compression, is considered to find the bond coefficient. It can be fond in the table 3.26 of the code.
With the values given in the table we can calculate the bond stress.
Consider a example of calculating tension anchorage length
Grade of concrete 25
Deformed type II bars
Bond stress = β√fcu
= 0.5√25
= 2.5
Consider bar diameter of 16mm and bar is stress up to the yielding.
Then stress in bare is 0.95fy
Force in the bar = 0.95fyxAs
Fs = 0.95x460x200
= 87400 N
fb = Fs / πφ el
l = Fs / πφ efb
= 87400 / π x 16 x 2.5
= 695.5 mm
Calculated value of anchorage length is 695.5 mm. So we may provide Anchorage length of 700 mm.
This value can be found from the table 3.27 of the BS 8110. Factor relevant to grade 25 concrete and deformed type 2 bars is 44
Tension anchorage length = 44x16
= 704 mm
Hence, it can be concluded that when a bar is fully stress (yielding) both methods gives similar answers, and we can use the table 3.27 instead of doing lengthy calculations for finding lap and anchorage lengths.
