Unbonded Prestressed Reinforcement Behavior
For service conditions, RAM Concept assumes that unbonded tendon stresses are not affected by cross section strains.
For "accident" strength conditions, RAM Concept assumes that unbonded tendons have no stress.
For ultimate resistance moment calculations, RAM Concept 's general approach to unbonded tendon stress-strain curves is detailed in Chapter 51, "Section Design Notes". For BS 8110-1997, the maximum unbonded tendon stress (fpb, called flimit in Chapter 51, "Section Design Notes") is defined by equation 52 and 0.7fpu.
When equation 52 is used in a cross section that contains multiple tendons, the following terms are used in the calculation:
l / d = length of an individual tendon divided by its depth
fpu Aps = sum of all the individual tendons' fpu multiplied by the vector component of their Aps.
fcu bd = minimum concrete cube strength multiplied by the compression face width and the depth to the centroid of the vector component tendon area
For BS 8110: 1997, the value used as a strain reduction factor for unbonded tendons is: k = 5d / L
where
L = length of the unbonded tendon.
d = depth of the post-tensioning tendon (measured from furthest concrete face)
This is equivalent to assuming a neutral axis depth of 0.5 d and "zone of inelasticity" of ten times this length [see BS 8110 code text that accompanies equation 52].
In equation 52, RAM Concept needs to determine "d" and "b". RAM Concept assumes that each tendon is placed on the more beneficial side of the cross section centroid (the same limiting stress value is used for both positive and negative moment capacity calculations at each cross section). This assumption typically has no impact on the ultimate stress in the tendon as when the tendon is on the "wrong" side of the cross section centroid, the stress in the tendon is less than fpb, due to the small tension strains (possibly compression strains) in the cross section at the tendon elevation.
The tendon length " l " in equation 52 is (conservatively) not modified to assume multiple simultaneous inelastic zones.