Lightweight Concrete for High Strength - Expanded Shale & Clay

Table A.1 Summary of Development Length Equations
Source / Author of Equation Development Length, l d
AASHTO / ACI
( f
ps
− 2
3
f
se
) db
Barnes, Burns and Kreger
⎛ f
⎞
pt
1.25⎜
+ ( f
ps
− f ⎟
pe
) db
⎜ '
f
⎟
⎝ ci
⎠
Buckner
db
f
si
+ λ ( f
su
− f
se
) db
3
Deatherage et al.
db
f
si
+ 1.5( f
su
− f
se
) db
3
Lane 95%
⎛ 4 f
pt
db
⎞ ⎛ 6.4( f −
⎟ ⎞
su
f
se
) db
⎜ − 5
⎟ +
⎜
+ 15
'
'
⎝ fc
⎠ ⎝ f
c ⎠
Lane 95% ⎛ 4 f
pt
db
⎞ ⎛ 6.4( f −
(10 ksi limit on f c ’) ⎟ ⎞
su
f
se
) db
⎜ − 5
⎟ +
⎜
+ 15
'
'
⎝ fc
⎠ ⎝ f
c ⎠
Lane Mean
⎛ 4 f
pt
db
⎞ ⎛ 6.4( f −
⎟ ⎞
su
f
se
) db
⎜ − 21
⎟ +
⎜
+ 26
'
'
⎝ fc
⎠ ⎝ fc
⎠
Lane Mean ⎛ 4 f
pt
db
⎞ ⎛ 6.4( f −
(10 ksi limit on f c ’) ⎟ ⎞
su
f
se
) db
⎜ − 21
⎟ +
⎜
+ 26
'
'
⎝ fc
⎠ ⎝ fc
⎠
Martin and Scott
135 db
( f
ps
− )
1/ 6
d 0.39
Mitchell et al. 0.33 f
Zia and Mostafa
f
si
d
b
3
f
'
ci
b
+ ( f
su
− f
se
) d
si
( 1.5 db
− 4.6) + 1.25( f
' su
−
f
ci
b
f
se
4.5
f
'
c
) d
b
d b
f pt
f si
f se
f pe
f ps
f su
ES
CR
Prestressing strand diameter
Stress in prestressing strand prior to release
Stress in prestressing strand immediately after release (f pt -ES)
Stress in prestressing strand after all losses (f pt -ES-CR-SH)
Same as f se
Stress in prestressing strand at member nominal strength
Ultimate stress of prestressing strand
Prestress losses due to elastic shortening
Prestress losses due to creep
A-25