DEFLECTION AND CAMBER

Deflections are calculated at the midspan based on the gross moment of inertia [LRFD Art. 5.7.3.6.2].

Deflection Due To Prestressing Force at Transfer

Δ_{p} = \frac{p_{i} e L^{2}}{8 E_{c i} I}

Where:

P_i = total prestressing force at transfer = 804.456 kips

e = eccentricity of prestressing force = 18.48 in.

L = overall span length = 101 ft

E_ci = modulus of elasticity at transfer = 4066.84 ksi

Δ_{p} = \frac{804.456 \times 18.48 \times {(101 \times 12)}^{2}}{8 \times 4066.84 \times 203086} = 3.303 i n

Δ_{b e a m} = \frac{5 w L^{4}}{384 E_{c i} I}

Where:

w = beam self-weight = 0.878 kip/ft

Deflection due to beam self-weight at transfer

L = overall beam length = 101 ft

Δ_{b e a m} = \frac{5 \times (\frac{0.878}{12}) {(101 \times 12)}^{2}}{12 \times 4066.84 \times 203086} = 2.489 ↓

Δ_{D} = \frac{19 P L^{3}}{384 E_{c i} I}

Where:

P = Diaphragm self-weight concentrated at quarter points = 0.81 kip

Deflection due to diaphragm self-weight used to compute deflection at erection:

L = span length = 100 ft

Δ_{D} = \frac{19 \times 0.81 \times {(100 \times 12)}^{3}}{384 (4066.84) (203086)} = 0.076 ↓

Deflection Due To Barrier and Wearing Surface Weights

Δ = \frac{5 w L^{4}}{384 E_{c} I}

Where:

w = barrier weight, DC = 0.075 kip/ft

= wearing surface weight, DW = 0.127 kip/ft

E_c = modulus of elasticity of precast girder at 28 days = 4496.06 ksi

L =span length = 100 ft (because these loads are applied to the structure in its final location)

Δ = \frac{5 (\frac{0.075}{12}) {(100 \times 12)}^{4}}{384 \times 4496.06 \times 203086} = 0.185 i n ↓

Δ = \frac{5 (\frac{0.127}{12}) {(100 \times 12)}^{4}}{384 \times 4496.06 \times 203086} = 0.313 i n ↓

At transfer=(Δ_p+Δ_beam)=3.303-2.489=0.814 ↑

Total deflection at erection using PCI multipliers (see PCI Design Handbook):

= 1.8(3.303) + 1.85(-2.489) - (0.076 + 0.185 + 0.313)=0.767in↑

Total deflection at final using PCI multipliers (does not include live load deflection):

= 2.45(3.303) + 2.70(-2.489) - 3.00(0.076 + 0.185 + 0.313)=-0.349in↓