Lightweight Concrete for High Strength - Expanded Shale & Clay

including strand diameter, embedment length, concrete strength, percentage of reinforcement,
and strand surface condition. All beams were loaded until failure. Hanson and Kaar reported
observations similar to those of Janney. The results of Hanson and Kaar’s research were the basis
for the current AASHTO development length expression shown in Equation A.16 and developed
by Mattock. Equation A.15 simplifies to Equation A.16.
l
d
= l
t
+ l
fb
=
f
se
3
d
b
+ ( f
*
su
−
f
se
) d
b
( A.15)
l
d
= ( f
*
su
−
2
3
f
se
) d
b
( A.16)
where
l d =
development length of prestressing strand (in.)
l fb =
flexural bond length (in.)
l t =
transfer length of prestressing strand (in.)
d b =
diameter of prestressing strand (in.)
f se =
effective prestressing stress after losses (psi)
f su *=
stress in prestressed reinforcement at nominal strength of member (psi)
Shortly after the development of Equation A.16 concerns developed based on the introduction
and common use of Grade 270 prestressing strand.
A.11.3 Martin and Scott, 1976
Martin and Scott re-evaluated the currently suggested equation (Equation A.16) and
determined that inconsistencies may have been responsible for the collapse of a 20-ft span slab
under construction loads. They suggested two new equations that did not determine
development length, but specified a maximum strand stress based on a given embedment length.
The two equations are shown below for the given location l x .
For l x less than 80d b :
A-19