Alternative Support Systems for Cantilever - National Transportation ...

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⎡ ⎢ ⎡ ⎤ 2 2 2 ⎛ dst ⎞ ⎢⎛ ds ⎞ ⎛ dst ⎞ ⎥ ⎛ dst ⎞⎥ ⎢ ⎜ ⎟ + 3.25⋅⎢⎜ ⎟ − ⎜ ⎟ ⎥ − ⎜ ⎟⎥ ⎣ ⎝ 2 ⎠ ⎣⎝ 2 ⎠ ⎝ 2 ⎠ ⎦ ⎝ 2 ⎠⎦ ca1 := c 3.25 a1 = 3.85 in 360deg A := A = 90⋅deg No_Stiff ds chord_group 2⋅ sin 2 A := ⋅ ⎛ ⎞ chord_group = 21.21 in 2 ⎛ ⎜ ⎝ ⎜ ⎝ ⎟ ⎠ ⎞ ⎟ ⎠ 3.0⋅ca1 Amin_group := 2⋅asin A d min_group = 45.24⋅deg s ⎤ Check_Group_Effect := "Group Effect" if A ≤ Amin_group Check_Group_Effect = "No Group Effect" "No Group Effect" otherwise lbreakout := tflex_plate + 2⋅1.5ca1 lbreakout = 12.54 in ( ) 3 AVc := min lbreakout, Ls ⋅ ⋅ca1 AVc 144.67 in 2 = 2 AVco := 4.5⋅ca1 AVco 66.57 in 2 = le := Lflex_plate le = 7 in .2 1.5 ⎛ le ⎞ bflex_plate fc ⎛ ca1⎞ Vb := 13⋅ ⋅ ⋅ ⋅⎜ ⎟ ⋅lbf V tflex_plate in psi ⎝ in b = 10.73 kip ⎠ ⎜ ⎝ ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ ⎟ ⎠ AVc Vcbg := ⋅ψ A ecV⋅ψedV⋅ψcV⋅Vb Vcbg = 32.65 kip Vco Vcbg_parallel := 2⋅Vcbg Vcbg_parallel = 65.31 kip Vc := Vcbg_parallel⋅No_Stiff Vc = 261.23 kip ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ dst Mn_breakout := Vc⋅ M 2 n_breakout = 217.69 ft·kip Flexural Capacity Using Breakout Capacity Mn_bolt = 82.83 ft·kip Mn_pipe = 392 ft·kip Mn_shaft = 296.49 ft·kip Mn_blowout = 337.05 ft·kip Mn_breakout = 217.69 ft·kip 146
FAILURE EQUATIONS Torsion Threshold Torsion 2 ⎛ ds ⎞ Acp π⋅ 706.86 in 2 2 := = ⎜ ⎝ pcp := π⋅ds = 94.25 in Tthreshold := ⎟ ⎠ Cracking Torsion fc Tcr := 4⋅ ⋅psi⋅ psi fc psi psi ⋅ ⋅ ⎛ ⎜ ⎜ ⎝ ⎛ ⎝ A cp 2 p cp A cp 2 ⎞ ⎟⎟⎠ p cp ⎞ ⎠ Nominal Torsional 2 Strength ⎛ dh ⎞ Ao π⋅ 572.56 in 2 2 := = ⎜ ⎝ ⎟ ⎠ 2 ⎛ dhoop⎞ At π⋅ 0.11 in 2 2 := = ⎜ ⎝ ⎟ ⎠ θ := 45deg 2⋅Ao⋅ At⋅fy_hoop Ttorsion := ⋅cot( θ) shoop Tn_shaft := Ttorsion Torsion Tn_breakout_plate = 347.98 ft·kip Tn_blowout = 522.7 ft·kip Tn_shaft = 252.95 ft·kip 147 Tthreshold = 32.76 ft·kip ACI 11.6.1a Tcr = 131.06 ft·kip ACI R11.6.1 θ = 0.79⋅rad Ttorsion = 252.95 ft·kip ACI 318-05 11.6.3.6 (11-21) Tn_shaft = 252.95 ft·kip ACI 318-05 11.6.3.5 (11-20)
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Report No. BDK75 977-04 Date: Augus
Page 3 and 4:
Metric Conversion Table SYMBOL WHEN
Page 5 and 6:
ALTERNATIVE SUPPORT SYSTEMS FOR CAN
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EXECUTIVE SUMMARY During the 2004 h
Page 9 and 10:
CHAPTER TABLE OF CONTENTS 1 INTRODU
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Torsion Test Data .................
Page 13 and 14:
LIST OF FIGURES Figure page Figure
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Figure 4-15. Arrangement of the LVD
Page 17 and 18:
CHAPTER 1 INTRODUCTION This project
Page 19 and 20:
CHAPTER 2 BACKGROUND The following
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information obtained in the late 19
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these problems. The concern with fa
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opposite side, see Figure 2-2 The s
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2.2.4 Helical Pipes This option wou
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2.3 Alternative Foundations from Ot
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Figure 2-10. Drilled concrete piles
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Figure 2-13. Grouted soil anchors G
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The pad and pier foundation, found
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comments and recommendations on pre
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CHAPTER 3 DESIGN IMPLICATIONS Based
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Figure 3-2. Differences between con
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2 [ ] 2 2 ( r ) + 3. 25 ( r ) − (
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eakout surface for a single plate,
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strength of a headed anchor in tens
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Figure 3-9. Schematic of anticipate
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Vbfp l e tfp bfp f’c ca1 = the ba
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3.2.2 Equivalent Side-Face Blowout
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computed. See Equation 3-14 below t
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One method to quantify the failure
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• An additional 12-4.5” long, 1
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Applied load Lever arm Figure 4-4.
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Figure 4-8. Isometric view of embed
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Flexural plate breakout area Torsio
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4.2.4 Annular Base Plate Design The
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torsional strength of the lever arm
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4.4 Concrete Block and Tie-Down Des
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Figure 4-13. Arrangement of the LVD
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4.7 Summary of Torsion and Flexure
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foundation displayed the predicted
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Figure 5-5. Specimen at failure 5.1
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Figure 5-7. Torsional moment and ro
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torsional 45 degree crack formation
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Figure 5-11. Widening of concrete b
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Failure cracks widen Bond loosens F
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Rear of shaft Figure 5-14. Load and
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testing, signifying that the predic
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provided in NCHRP Report 412 were i
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6.2.2 Tapered Embedded Steel Pipe a
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Figure 6-3. FDOT Design Standards I
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This option provides a possible alt
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6.2.5 Cast-in-Place Solid Concrete
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This option does have some disadvan
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Figure 6-9. Embedded steel pipe and
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However, the fillet welds are susce
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APPENDIX A TEST APPARATUS DRAWINGS
Page 111 and 112: Figure A-3. Dimensioned side elevat
Page 113 and 114: Figure A-5. Dimensioned drawings of
Page 115 and 116: Figure A-7. Dimensioned plan drawin
Page 117 and 118: Figure A-9. Dimensioned drawing of
Page 119 and 120: Figure A-11. Dimensioned view of em
Page 121 and 122: STIFFENER DESIGN Calculation of Cap
Page 123 and 124: L breakout Concrete Breakout Equiva
Page 125 and 126: Abrg L⋅b 7 in 2 := = .5 Nsb 200
Page 127 and 128: β 1 f c Calculations Using ACI Str
Page 129 and 130: Determine Flexural Capacity of Roun
Page 131 and 132: DEVELOPMENT LENGTHS OF FLEXURAL REI
Page 133 and 134: Short Pipe Design Flexural Strength
Page 135 and 136: Long Pipe Design Flexural Strength
Page 137 and 138: Superstructure Assembly Strength -
Page 139 and 140: Weld Design Tn_blowout Vweld := Tor
Page 141 and 142: Check_Bolt_Shear := "Sufficient Str
Page 143 and 144: Check Reinforcement No_Bars_Block_R
Page 145 and 146: Tie-Down Design Block Properties Wi
Page 147 and 148: Vmax Total Load that the Tie-down m
Page 149 and 150: λpf := .38⋅ λpw := 3.76⋅ E F
Page 151 and 152: Input and Properties Shaft Torsion
Page 153 and 154: ψcV := 1.4 ψecV := 1.0 ψedV := 1
Page 155 and 156: lbreakout := L + 2⋅1.5ca1 lbreako
Page 157 and 158: Rn_weld := Throat⋅FW Rn_weld 11.1
Page 159 and 160: ⎛ ⎜ ⎜⎜⎜⎜⎜⎜⎜ 9.250
Page 161: Flexural Capacity of T-Plates Using
Page 165 and 166: Required Length of Shaft Based on B
Page 167 and 168: Design Axial Strength ϕcomp := .90
Page 169 and 170: Design Axial Strength ϕcomp := .90
Page 171 and 172: Zp := ⎛ ⎜ ⎝ bp tp⋅ 2 ⎞
Page 173 and 174: Bolt Properties - D1" ASTM A325 Cen
Page 175 and 176: CONCRETE BLOCK Concrete Block Desig
Page 177 and 178: Check Shear Check_Shear_B := "Suffi
Page 179 and 180: 7'-4" 8" 5'-4" 8" 1'-3" Calculate s
Page 181 and 182: Required Capacity of the Channel As
Page 183 and 184: Check_Flange_Compact_Unit := "Compa
Page 185 and 186: Rear of Shaft Face of Shaft Figure
Page 187 and 188: Bolt slippage ends Predicted failur
Page 189 and 190: APPENDIX D DESIGN GUIDELINES For th
Page 191 and 192: The designer should then use this i
Page 193 and 194: • Determine the angle required fo
Page 195 and 196: Superstructure Base Connection Foun
Page 197 and 198: 1.5ca1 1.5ca1 Length of bearing are
Page 199 and 200: Vu = 9.04 kip T .u = 198.88 ft·kip
Page 201 and 202: Increase threaded rod diameter to 2
Page 203 and 204: Embedded Pipe and Torsion Plates De
Page 205 and 206: ⎝ ⎠ Check_Breakout_Torsion := "
Page 207 and 208: Lbreakout := tflex.plate + 2⋅1.5c
Page 209 and 210: ( ) .85 if fc < 4000psi β 1 f c .6
Page 211 and 212: REFERENCES 1. Cook, R.A., and Halco
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