RELEASE STRESSES

Prest. (Prestress)

S_t= Section modulus of top of precast alone

= \frac{545894 {i n}^{4}}{(72.00 i n - 36.60 i n)} = 15420.7 {i n}^{3}

S_b = Section modulus of bottom of precast alone

= \frac{545894 {i n}^{4}}{36.60 i n} = 14915.1 {i n}^{3}

Figure 8. Strand Profile (Not to Scale)

Note: All sections at both release and final conditions are measured with respect to the left beam support at final conditions.

Strand eccentricity at beam end:

e = 36.60 i n - 20.29 i n = 16.31 i n

Strand eccentricity at transfer point:

e = 16.31 i n + \frac{(31.57 i n - 16.31 i n) (0.5 f t + 1.56 f t)}{(0.5 f t + 45.90 f t)} = 16.99 i n

Precast-top (Trans) = Stress in top of beam at transfer point due to prestress alone

= P (\frac{1}{A} - \frac{e}{S_{t}})

where:

P = Total net prestress force at release

= (1178.1 k)(1 -0.0865)

= 1076.2 k

Precast-top(Trans)= $1076.2 k (\frac{1}{767.0 {i n}^{2}} - \frac{16.99 i n}{15420.7 {i n}^{3}}) = 0.2171 k s i = 217.1 p s i$

Bottom (Trans) = Stress in bottom of beam at transfer point

= P (\frac{1}{A} + \frac{e}{S_{b}})

Bottom (Trans)= $1076.2 k (\frac{1}{767.0 {i n}^{2}} + \frac{16.99 i n}{14915 {i n}^{3}}) = 2.6294 k s i = 2629.4 p s i$

Precast-top (Midspan)= $1076.2 k (\frac{1}{767.0 {i n}^{2}} - \frac{31.57 i n}{15420.7 {i n}^{3}}) = - 0.8004 k s i = - 800.4 p s i$

Bottom (Midspan)= $1076.2 k (\frac{1}{767.0 {i n}^{2}} + \frac{31.57 i n}{14915.1 {i n}^{3}}) = 3.6814 k s i = 3681.4 p s i$

Self Wt

Precast-top= Stress in top of beam at release at midspan

= \frac{M}{S_{t}}

where: M= Moment at release at midspan.

Note: Span length for computing moments at release is different from span length for computing moments at final conditions.

M = \frac{w l^{2}}{8} = \frac{(799.0 l b / f t) {(116.00 f t)}^{2}}{8} = 1343848 l b - f t

$\frac{(1343848 l b - f t) (12 i n / f t)}{15420.7 {i n}^{3}} = 1045.7 p s i$

$\frac{(1343848 l b - f t) (12 i n / f t)}{14915.1 {i n}^{3}} = 1045.7 p s i$

At midspan, since net stress in top of beam equals 245.4 ps (compression), which is less than -200 psi, no reinforcement is required.

Total

Precast-top(Midspan) = -800.4 psi + 1045.7 psi = 245.4 psi

Bottom(Midspan) = 3681.4 psi - 1081.2 psi = 2600.2 psi

A_s-top

A_s-top = Required amount of bonded reinforcement to resist total tension force in concrete when net top stress exceeds -200 psi or $- 3 \sqrt{f_{c i}}$ Art9.15.2.1