APPENDIX B-Continued 



\ \42a p,f 



to Adiv* Earth Pi 



FI9. 7: Pr*»«ur« Diagram For Bulkhaad. 



rod level -are computed as shown in the following 



julation: 







Force 



Arm 



Moment 



540 pounds 



-1.0 Ft 



-540 Pound Ft 



220 



1.52 



340 



1,190 



4.08 



4,850 



340 



6.69 



2,280 



2,290 





6,930 



The location of the zero value (point "0" in Fig. 7) for 

 the combined pressure diagram is found to be at a 

 dista.ice below the outsidt bottom of: 



334/162 = 2 06 ft. 

 The required penetration below point "0" is designated 

 by the letter "d". Then the equilibrium of moments 

 condition is expressed by the equation: 



(162d2/2)(8.06 + 2d/3) = 6,930 

 This equation is best solved by trial, whence d = 2.92 

 ft. The total depth of penetration below outside bottom 

 is then 2.06 + 2.92 = 4.98 ft. The residual passive 

 pressure intensity at the bottom of the sheet piles is 

 computed as: 



162 X 2.92 = 470 psf 

 The area of the residual passive pressure triangle is: 



470 X 2.92 X 1/2 = 690 pounds per lineal foot of 

 wall. 



TIE ROD REACTION (Design Step 4) 



The tie reaction then becomes: 

 2.290 - 690 = 1,600 pounds per ft of wall 



BENDING MOMENT IN SHEET PILING (Design Step 5) 



Bending moment in sheet piling: Maximum moment 



occurs at elevation of zero shear 



Let "Z" - distance below MLW to plane of zero shear 



Then in the case of Fig. 3 (Part 1, 32) Z is found as 



follows: 



Shear at MLW = 1.600 -540 -220 = 840 lbs. 



2622 + 18Z'/2 = 840 lbs 



Z " 2.92 ft 

 Moments of forces above plane of zero shear taken 



with respect to plane of zero shear are shown in the 

 following tabulation: 



Force Arm Moment 







Clockwise 



Counter- 

 clockwise 





■4.92 



7,870 





540 



5.92 





3,200 



220 



3.39 





750 



763 



1.46 





1.110 



77 



097 





75 



600 







5,135 



Bending moment in sheet piling per foot of wall length 



= 7870 - 5135 = 2735 ft-lbs. This is conventionally 



called the "free earth support" moment. 



The "free earth support" moment may be reduced by 



a factor of 30% to allow for beneficial effects related 



to flexibility of sheet piling, (see Ref. 1 , p. 1261 .) Hence, 



Design Bending Moment = 0.7 X 2,735 = 1,910 lbs. 



per foot. 



SHEET PILING THICKNESS (Design Step 6) 



Required thickness of sheet piling: 



Try 4X12 sheeting, actual thickness = 3Vi inch 

 Section modulus = 12 x 3.6252/6 = 26.3 inch' 

 Bending stress = 1,910X12/26.3 = 870 psi 



Try 3X12 sheeting, actual thickness = 2H inch 

 Section modulus = 12 x 2.625'/6 = 13.8 inch' 

 Bending stress = (1910 X 12)/13.8 = 1,660 psi 



For sheet piling of common commercial grade, the 4- 



inch thickness should be used. 



TIE ROD SIZE AND SPACING (Design Step 7) 



The size and spacing of lie rods must be compatible 



with the design of the wales and anchorage. A spacing 



of eight feet will be selected. 

 Tie Rod Pull - 8 X 1,600 - 12,800 lbs 



For 1%-inch diameter tie rod, area at root of thread " 



0.89 square inches. 

 Tensile stress ■= 12.900/0.89 = 14,400 psi. 



This conservative unit stress is desirable to allow for 



effects of corrosion, surcharges, unequal yield of 



anchorages, and other variables 



317 



