Example 9.1 PCI Bridge Design Manual

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Example 9.1 PCI Bridge Design Manual

• Noncomposite Adjacent Box Girder
• Simple Span
• Standard Specifications

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Connection of Beams
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Shear Key
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9.1.2 Material Properties (1) Concrete f'ci
4,000 psi 4.0 ksi f'c 5,000 psi 5.0 ksi
wc 150 pcf 0.150 kcf
The AASHTO Standard Specifications require a
pretensioned member to be designed at 5000 psi
(6000 psi at the discretion of the engineer).
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9.1.2 Material Properties (2) Strand 0.5-in.,
seven wire low relaxation fpu 270 ksi fpi
0.75fpu 202.5 ksi Es 28,500
ksi Nonprestressed Steel fsy 60 ksi Es
29,000 ksi
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9.1.3 Cross-Section Properties (1)
A 813 in.2 I 168,367 in.4 yb 19.29
in. Sb 8,728 in.3 yt 19.71 in. St
8,542 in.3
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9.1.3 Cross-Section Properties (2) At
release Eci 33,000 (0.150)1.5 (4.0)1/2
3,834 ksi At 28 days Ec 33,000
(0.150)1.5 (5.0)1/2 4,287 ksi
Modulus of elasticity is needed for various
calculations
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9.1.4.1.1 Dead Loads per Girder Beam self weight
0.847 kip/ft Diaphragm weight 0.73
kip/diaphragm at ¼ pts) Barrier weight 0.086
kip/ft Wearing surface 0.134 kip/ft
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Shear and Moment at h/2 Compute Vci
Vci0.6(fc)1/2bdVd(ViMcr)/Mmax Vd 50.0
kips shear due to dead loads VLLI 32.7 kips
shear due to live loads Md 82.8 ft-kips
moment due to dead loads MLLI 53.2 ft-kips
moment due to live load Vu 136.0 kips
factored shear force
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Strand Pattern-Midspan (Fig 9.1.5.4-1)
Whats with the 2 at the top?? Discussed
later! Pattern is symmetrical must be or beam
bends sideways!
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Strand Pattern-Beam End (Fig. 9.1.8.2-1) Debond 7
strands in bottom row for 5 ft.
PATTERN STAYS SYMMETRICAL
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Strand is covered with teflon to prevent
bonding.
DEBONDED STRAND
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9.1.11 Shear Design Members should be designed
such that Vu lt f(Vc Vs) Critical section is
h/2 from face of support Shear forces at this
section are given in Table 9.1.4.2.4-1 In
reinforced concrete, ACI and AASHTO use d from
face of support, but in prestressed concrete, d
often varies due to debonding and/or harping.
Thus, h/2 is used.
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9.1.11 Shear Design Compute Vci
Vci0.6(fc)1/2bdVd(ViMcr)/Mmax
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9.1.11 Shear Design Mu 223.1 ft-kips
factored moment Vmu 136.0 kips factored
shear force occurring with the factored moment
Mmax 140.3 ft-kips Mu - Md Vi 86.0 kips
Vmu - Vd fpe Pse/A (Pseec)/Sb e
eccentricity at h/2 13.96 in. Pse
24(0.153)(171.6) 630.1 kips fpe
1.783 ksi
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9.1.11 Shear Design
fd Md/Sb (82.8(12))/8,728 0.114 ksi Mcr
(6(fc)1/2fpe-fd)Sb (((6(5000)1/2)/1000)1.783-
0.114) (8,728/12) 1,522.5 ft-kips
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9.1.11 Shear Design (4) d 39.0-5.33 33.67
in. gt 0.8(h) 31.20 in., therefore d 33.67
in. Vci 0.6(5000)1/2(10)(33.67)50.0((86.0(1,
522.5)) 1000 140.3 997.5 kips Is
Vci gt minimum Vci ? minimum Vci 1.7(fc)1/2
bd (1.7(5000)1/2)/1000)(10)(33.67) 40.5
kips lt Vci 997.5 kips OK
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9.1.11 Shear Design Compute Vcw Vcw
(3.5(fc)1/20.3fpc)bdVp fpc Pse/A
630.1/813 0.775 ksi Vp 0 for straight
strands Vcw (((3.5(5000)1/2)/1000)0.3(0.775))(1
0)(33.67) 0 161.6 kips
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9.1.11 Shear Design (5) Vc 161.6 kips (lesser
of Vci and Vcw) Vu 136.0 lt fVc 0.9(161.6)
145.4 kips Since VcgtVu the concrete resists the
total shear and shear steel is not required to
assist in resisting Vu. Therefore provide min.
reinforcement.
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Graph of Vu and concrete shear strengths
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9.1.11 Shear Design (6) Minimum shear
reinforcement Av-min (50bs)/fy minimum area
of web reinforcement Set s 12 in. Av-min
50(10)(12) 60,000 0.10 in.2 (per
foot) Maximum spacing 0.75h 0.75(39) 29.25
in. use 24.0 in. Use 4 at 24 in. spacing in
each web (Av 0.20 in.2/ft)