i 1 g; a: i i A CHECK OF THE DESIGN OF A “WARD HIGHWAY $106! that for u» on... a I. .5. mm mm coma Ridwd Porter Gillespie 1949 r”‘flll .11 TH E318 st ’9 a? .. 29.11.41“. A; n. .... R 11.x»? .., {An . .. 143...: - . . -..... ....vl. ...4 a. . v, n warning-.... 4 vx .. . . . f . I. u .. | 3.. . ..t l E 4.0 - . . I. ‘E \K‘w . .W In». . . . . . \‘ A... .. .I‘IIFFT ‘ "w . . . ......u M. S . s .. ....f...a\i as“... I} .. 5 ‘ ‘ .. n .‘c . f ‘. ...». .6 Pa? m y N u x). ah.“ " ‘. . (...! a. ’Ffi‘bflflfi K... x w. .... , «m? s W. 3...... .H .13 . : a.“ Q ”3;,“ F ,.L.:..& in... ”A ME. I“. W . .- «711w...» I. « ... no: Lama mm c . g . u... huh 31$. ..Wfflkflw m,_‘ .vt...’ ‘ “a." . ...fig E'mr'i. 1.3m “:1 v.” 0 v .i)'.!..ttm . A CHECK OF THE DESIGN OF A STANDARD HIGHWAY BRIDGE A THESIS SUBMITTED TO THE FACULTY OF MICHIGAN STATE COLLEGE OF AGRICULTURE AND APPLIED SCIENCE BY RICHARD PORTER GILLESPIE CANDIDATE FOR THE DEGREE OF BACHELOR OF SCIENCE MARCH 1949 JfiESIS (3.! ACKNOWLEDGMENT The author wishes to acknowledge his indebted- ness to the personnel of the Bridge Division of the Michigan State Highway for the use of their refer- ence books and their help in obtaining a complete set of Blue prints to use in my thesis. The author also wishes to thank Mr. W. A. Bradley, Department of Civil Engineering, Michigan State College for his help in checking the completed thesis. 216987 I. II. III. IV. V. OUTLINE OF PROCEDURE Introduction 3;: Bridge Railing A. Loading 1. Live load 2. Dead load B. Check Reinforcing Steel and concrete Sidewalk and curb A. Loading 1. Live load 2. Dead load B. Check Reinforcing Steel and concrete FloOr Slab A. Loading 1. Live load 2. Dead load B. Check Reinforcing Steel and concrete Girder Design A. Loading 1. Live load 2. Dead load B. Size of Beams required C. Size of Diaphragms required D. Size of tiéangles required E. Spacing of rivets VI. Abutment Design A. Loading 1. Live load 2. Dead load B. Footing 1. Toe reinforcing steel and concrete 2. Heel reinforcing steel and concrete 0. Wall 1. Stem reénforcing steel and concrete VII. Summary and Conclusion INTRODUCTION The purpose of this thesis is to check the design of a simply supported single span highway bridge. This bridge has been constructed in Sec. 10 and 11 T. 8 S R 5 E Fairfield township, Lenawee County. The bridge crosses the black creek 0.5 miles south of the town of Jasper, Michigan. The existing structure has been removed because of the need for a new and larger bridge. The span length of this bridge is 50' - O" exact and the overall roadway width from curb to curb curb is 38' - 0" exact. Stream Data: Black Creek is a very meandering stream and there is indications of scouring at the bends where there is no willow growth. The water has a very offensive odor due to refuse from a creamery located two miles upstream from the project. The elevation of the water surface at the survey center line is 710.l5 600 ft. upstream measured at right angles to the survey line, it is 710.82 and 500 ft. down- stream it is 709.58. High water elevation was 716.9 and the normal highwater elevation is 715.9'. Soil Conditions: The soil in this vicinity is a heavy clay loam, but there is some indication of sand and gravel in the bed of the stream. -2- The specifications are those of the Michigan State Highway Department published in 1944 and from the specifications for highway design published by the American Association of State Highway Officials in 1944. The maximum allowable unit stresses used are from the Bridge Division, Michigan State Highway Department specifications. fs = 18,000 psi fc I 6,000 psi fc = 1,200 psi 3 3 a .867 k : +AOO n : 10 R : 209 V = 60 psi v : 90 psi U = 150 psi u = 300 psi (special anchorage) Loading H - 20 816 - 44 Shear 15,500 psi power driven rivets Shear 10,000 psi unfinished bolts -5- SYMBOLS A Area Breath or width d Depth of beam to center of steel Eccentricity of application of load f Unit stress I Moment of inertia 3 Ratio of lever arm of resisting couple to depth, d K Ratio of depth of neutral axis to depth, d L Length in feet l Length in inches M Moment n Ratio of modulus of elasticity of steel to modulus of elasticity of concrete R Reaction V Total shear v Unit shear W Load per unit of length C Round U Bond aBBREVIATIONS A. A. S. H. 0. American association State Highway Offflzials a. I. S. C. American Institution of Steel Construction M. S. H. D. Michigan State Highway Department Design of Railing: Railings Substantial railings shall be provided along each side of the bridge for the protection of traffic. The top of railing shall not be less than 5' - 0" above the top of the curb, and when on a sidewalk, not less than 5' - 0" above the top of the sidewalk. Railings shall contain no opening of greater width than (8) inches. Ample provision shall be made for inequality in the rate of movement of the railing and the supporting superstructure due to temperature or erection conditions. (M.S.H.D. Spec. 25, p. 10). Forces on Railings Railings shall be designed to resist a horizontal force of not less than 150 pounds per lineal foot, applied at the top of the railing, and a vertical force of not less than 100 pounds per lineal foot. For railing adjacent to the roadway, the bottom rail shall be designed for a horizontal force of 500# lineal foot of rail, if the rail is properly reinforced the force of 300# lineal foot may be used but if the rail is not properly reinforced use 500# lineal foot. (M.S.H.D. Spec. .55, p. 14)e Design of Railing . Railings: Z ‘2 in single shear Bolts P = S .A P : 10,000 x .4418 = 4,420# Capacity Load 500 x 8.167 : 1225# 2 Strap shear capacity (1 2 - i3 ) 2 x 10,000 = 9.25603”t From the (M.S.H.D) Standard Design of Railing) Use 50# lineal foot for the dead weight of the railing. d 4 309 5 5 0 Load is 504 x 8.167 : 1255 # 2 Bolts will control the design as they have the minimum capacity (1) (max) . 1 g " x g " c 2 i " 1.: me I Where I : 2g: 6 f (Horizontal) Z 1225 x 2.25 x 6 Z 8650 psi .625 x (1:75) f (vertical) 3 1225 x 2.25 x 6 2 4050 psi 57x 1.75 x (6.25) 12,500 psi ok.118,000 psi 5. .____I:] L_____ % 4— 4 r 1,, E' ' .JL Design of Railing (cont.) Rail: Lower rail only considered (max case). For the first computation only, the two side channels are con- sidered to simplify the computations. Horizontal bending 87167 - (2x 1 g ) = 7.90 ft. M .w1 2/8 , ooo x_(7.90)2 x 12 , 28100 in lbs. 8 k A 12 X 1.46: 2.92 sq. in. e 2 2.06 18 8 2x Q 25 :50. 1n. 2 I.:Ae 2 I3 .2.92 x (2.06)2 + 50 - 12.89 in. f 3113 .-. 28100 x 2.5" .. 5450 psi I 12.89 18,000 psi allowable 133280 .5519& over designed we may neglect the design of the top channel of the lower railing in the design because the stresses are low. This top channel would in- crease the strength at the railing which is overdesigned already. Posts -7- l /;+ l +:\§3 4 R0 3 Intermediate Posts standard . 3 M.S.H.D. l \ 4- * . b: 1' - 4" .16" ¥e u :i- ‘3 L qukiL..-Li.'zf._l d : 9%" 1’4" As . 2x .44 a 0.88 sq. in. ‘\ l . ( (2 bars in compression) (2 bars in tension) k s 1 _ l - fs7nfc I ' 18000/10 x 1200o-l ' ' k=,400 J =(1-E ).(1 - .400 ) : .867 .% 5 Bending moments: 150 x 9.5 x 52 x 45,500"# 300 x 9.5 x 5 8 14,200"# 1 Totals 59,500"# I. d ' V M g 59 500 g 4.2 inches required ‘fiE‘ (209 6) fs : u = 59,500 /.88 x .867 x 9.5 s 8250 psi. As 18,000 allowable 18 000 s 219% over designed. 8,250 Posts: The railing and posts are greatly over designed but part of this is due to the fact that large posts and railinggs .produce a more balanced looking bridge in appearance. Design of Sidewalk and Curb: U u I F'T“ “fly—Yj 1 +12? Curbs shall be designed to resist a force of not less than five hundred (500) pounds per lineal foot of curb applied at the top of the curb. (M.S.H.D. Spec. 5b, p. 14) The specified roadway loading shall apply to all sidewalks constructed without guard rails between the sidewalk and roadway to prevent encroachment of roadway loads. As this sidewalk is fully supported the use of this part of the bridge serves only as an additional safety measure for pedes- trians. The only steel required is temperature steel, the rest is pututo bind the structure together. -9- Design of Concrete Slab: 10“ I0 " IO" , ’2" Calculate bending moment by A.A.S.H.0. Art. 5.2.2, p. 158. Main reinforcing perpendicular to center line of roadway. Distribution of wheel loads. For a span of 2 to 7 ft. E c0.65 92.5 Bending moment for continuous span M =0.2 x P/E x S x (100.I *10% for longitudional forces) Bending moment for freely supported span. M: 0.25 x P/E x s x (100+ I +10% for longitudional forces) Where, E , width of slab over which wheel load is distributed. P maximum wheel load in pounds H S 3 distance between flanges plus i width of girder flanges. -10- Design of Concrete Slab: The forces due to traction or sudden braking of ve- hicles shall be considered as longitudinal forces having a magnitude of 10% of the gross live load that can be placed in one traffic line. This load shall be assumed as acting in the direction of traffic movement and applied at the top of pavement. M.S.H.D. Spec. 58, p. 15. I, L +20 3 .22 6Le§6 Design E 30.6 x 5 .14 +2.5 3 5.59 ft. 11.0.25 x 16,000/5.59 x 5.14 x 1.52 .- 4860 ft lbs. d .V M =I2860 x 12/209 x 12 z 4.82 in. R5’ For slabs the distance from the surface of the concrete either top or bottom, to the center of the nearest bar shall be not less than one and one-half times the diameter of the bar nor less than one and one-half inches. Thickness required: 4.82 1.5" : 6.52 in Actual 7.00 in. As; H = (4860 x 12)/18000 x 7 x 5.59 : .675 in req. ‘?33d 8 Actual 1.000 sq. in. Steel at bottom of slab for lateral distribution Percent of main steel required: lOQfg’ 100/ 5.4 = 44.1% (1.2.5.5.0. Art. 5. 2.2 p. 140) AS = .675 x .441 : .298 in/ft. required. -11- Design of Concrete Slab: Slabs designed for bending moment in accordance with the foregoing shall be considered satisfactory in bond and shear. (A.A.S.H.O. Art. 6.2.2 (d) p. 140) -12- Diaphragm Design: The forces due to wind and laterial vibrations shall consist of a horizontal moving load equal to 50 pounds per square foot on 1% times the area of the structure as seen in elevation, including the floor system and railings and on one-half the area of all trusses and girders in excess of two in the span. (M.S.H.D.(Spec. 58, p. 15) (a) Size of Rivets shall be of the size specified but gener- ally shall be 5/4" or 7/8" in diameter. (b) Pitch of Rivets, the minimum distance between centers of rivets shall be three times the diameter of the rivet but preferably shall be not less than the following, For 5/4" diameter rivets - 2%". (M.S.H.D. Spec. 92, p.59-40L The end connections angles of floor beams and stringers shall be not less than 5/8 inch in finished thickness. (H.S.H.D. Spec. 120, p. 47). i (a) Design, Lateral, longitudinal and transverse bracing shall be composed of angles or other shapes and shall have riveted connections. (M.S.H.D. Spec. 126, p. 48) Diaphragms shall be provided at the third points of all I-beams spans of forty feet or more. (M.S.H.D. Spec. 124, p. 48). Area of structure as seen in elevation: 7.89 x 50 400 sq. feet 400 x 1.5 600 sq. feet .5 x 6 x 5 x 47.5 427 sq. feet Total effective area 1027 sq. feet -15- Moving load 30 x 1027 = 50,800# Area required for diaphragm 50 800 a 1.71 sq. inches 151—555 Area furnished 4" x 4" x 5/8" furnished 2.86 sq. inches. The diaphragms placed at 1/5 the width meet all of the necessary M. S. Highway standards they are used principally to keep the beams from turning and also to keep the I beams on the same level. The specifications provided by the M.S.H.D. for depth of web, size of angles, pitch of rivets, depth of tie angles and number of stiffeners place the use of these within the proper limit of design. -14.. Girder Design: For structures with concrete slab floors with out separate wearing surface, a minimum allowance of 20 pounds per square foot of roadway shall be made, in ad- dition to the weight of any monolithically placed con- crete wearing surface, to provide for future wearing sur- face. (M.S.H.D. Spec. 50 p. 12). When provision is made for three or more lanes of traffic, the design shall provide for the following per- centages of the simultaneous maximum loading of all lanes.' For four or more traffic lanes 80%. (M.S.H.D. Spec. 55, p. 15-14). Main trusses and girders shall be spaced a sufficient distance apart center to center to be secure against, overturning by the assumed lateral and other forces. (M.S.H.D. Spec. 76, p. 56). Calculations of stresses, span lengths shall be as- sumed as follows: Beams and girders, distance between centers of bearings. (M.S.H.D. Spec. 77, p. 56). Rolled beams shall be proportioned by the moments of inertia of their net sections. (M.S.H.D. Spec. 80. P. 55) Using H 20516-44 Loading from appendix A. (AoA.S.H.0. p. 229). -15- To fol Span 50' 11 C.G. ESpaceJ C 53-15:" ‘ si‘ 0“ _i¢' 47.5fm Rb Check final design of Beams using H2OSl6-44 loading: Assumptions 68' Rdwy, 2 walksxg l'-6" 7"min slab. One span 50' between R. P. 9001. of crossing Try 55" WF 152# stringers L 800 Take moments about small wheel 8,000# load 52000 x 14 = 448,000 52000 x 28 a: 896,000 8000 x O .: 0 72000 : 1,544,000! # .72 = 18.66 to c. g. from 8,000# load Max moment occurs when 2.0f Span is midway between center of gravity of loads and nearest load. 18.66 - 14.00 = 4.66' c. g. to near load 4.66 g 2.55' distance c.g. placed off centers 2 L. L. moments to determine L. L reactions RA and RB RA 52,000 x 12.12 = 587,840 52,000 x 26.12 -' 855,840 8,000 x 40.12 . 520,960 l,544;640 4 47.58 : 52,460 n.4, -15- RB 8,000 x 7.46 = 59,680 52,000 x 21.46 . 686,720 52,000 x 55.46: 1 154 720 ‘If881f120 4 47.58 = 59,5404 RB 72,000; total 0.x. Check final design L 800 Max moment occurs under middle wheel. RA 52,460 x 21.46 a 696,590'# - 8,000 x 14 ,_ - 112,000 Max mom L.L : 584,590'fi lane Try 56' WF 152# z 8 spaces @ 5' - 1 5/4"==4l'- 2" Distribution L.L. Mom. C.M.+ M = 584,590 x 5.15 10 : 501,060'fi/ beam Dead load Gene. 150 x .651 x 5.15 = 505# Future wearing surface 20 x 5.02 :100 Beam 10% for Diaphs. and = 145 748#/ ft of beam D. L. Mom (under same wheel) 748*!L58' 2.1.46 -17- R _. 748 x47.58 . 17,900.: 2 u,» - 17,900 x 21.46 = 584,000 - 748 x 21.46 x 10.75 . - 175 000 211,000 #1/ beam Impact Factor Lo 20 ‘_ 47.51320 9:67.58 3 0.221 6L+ 20 " 6 x 47.58420 505.48 Total Moment L. L. + Impact : 501,060 x 1.221 = 367,590 “ax. D. Le 3 211 000 0 558.555 5 = 578,590 x 12 , 590" req'd. 18,000 A 55' WE 1524 gives 8 “10498)?5 provided Girder Design -15- Check Deflection .44’ 14' Test Deflection by Lane Loading as per A.A.S.H.O. - 44. By Maxwell's Theorem Ax , WX (012—4 1: 2) m D :.716" allowed L = 0.716" 800 max Axl + A112 +4105 8x1 , 52,000 x 112 - 12) x 12 [(5 x (47.58)2 - 4 48 x 29,000,000 x 6856.8 (12.12)2 x (12)§] 4x1 , 4,157,858,720,000 =.456,e; 48 x 29 x 106*x 8856.8 4x2 , 52,000x21.46x12 [5x(47.58)2x(12)2 - 4(21.46)2x(12)2J 48 Efll 5 875 268 940 800 11x2 1 . . : 0W, .96 .b .666 4x3 3 8,000x'7.§§x12 [5x(47.58)2 x(12)2-4(7.4d)2x(12)f] .615 48 EI : 677 457 944 960 g .071 99 9'6 3b a .466 .615 I..L*20 , 47.58'920 : .221 .071 6E’20" 6 x 47.58"20 , A Totalsl.122/lane D = 1.121 x 1.221 x .515 : .705"/Beam Load Allowable = .715" Use a 63“ WF<@ 152# this is the smallest beam which does not exceed the allowable deflection. -19- Abutment Design: "Rankines" Theory of pressure distribution in non- cohesive granular material, provides that no structure shall be designed for an equivalent fluid pressure of less than 60 pounds per square foot. ’ Retaining walls, abutments and structures built to retain fills shall be designed to resist pressure deter- mined in accordance with the Rankin theory. -20.. Abutment Design 45' - 0" 0-0 sholders @ bridge from prelim. E to sholder 22' - 6" Dist.from bridge seat to top of curb Q" Masonry Plate 2" Bearing Plate 55" Girder 7" Slab 10n Curb 52%" = 4' ~ 4%" seat to top curb. 41 - 4% 6 4' - 10$ (hgt.from top of curb to inter. 0f grd. and back of wing). (4'o10é) x 2 9' - 9" (from sholder to back of wing) 1%} Wing ht. = 15' - 2 5/4" =158 5/4" (prelim plan) Total batter : (2' - 4") -1'-6') = 10" 10" x 5 : 7378" = 3/8" 0 Dist I to out of wing- 22t - 6" 9' - 9" 5/8" 1' - 6' 35’ - 9 5/8" use 55’- 9%" 0 - 0 Wing walls (55' - 9%") x 2 = 67' - 7") -21- Dead Load Superstructure Reaction on Each abutment. Sidewalk . 2.71 x .85 x 50 s 112 cu.ft. Slab 45 x .65 x 46.75 x .5 8 654 cu. ft. Backwall: Length : 21' - 11% x 2.:45' - 11" Av. hgt. .5' - 7 7/8 a 3.66' 1004 cu.ft. 1004 x 150 : 150,600y wgt. conc. Steel Rail 50 x 150 :3 7,500.4; F.W.S. 58 x 20 x 24.5 18,600? Str. Steel and Diaph 48.5 x 9 x 125 x 1.05 x .5 = 28,650# Fillet Walls (1.75 x 10 x 5 x 5) x 2 x 150 : 13,100# Total D. L. 218,450# 67.58 Live Load Superstr. Reaction on Abut. 640 x 47.58 . 40,000) 4 x .8 = 176,000# 2 176,000 x 1 s 2510 #/1 67.58 Abutment Design: —-|I:3|._£La_.uzo -22- f ‘9 d ‘8. k C/LEIAV- L.LIZ6/O z‘\“' O.L.:3230 0 I _' [1-2.1, a) '11— c 9 ‘\ “I b Ew- W) .I ‘Q \ 321/" 2'-4" , an." _JL \e a " N .JL ’— 9!. 9n ‘LTOe -25- ma Area Unit WE. Tatar wt. arm Mon 95;? about toe a 9.75 x 2.5 24.4 150 5670 4.88 17,850 b 2.55 x 15.25 50.8 150 4620 4.67 21,600 c 17 x 5.92 66.6 100 6660 7.79 51,900 Totals Case I W 1 14950 Ml 91,550 Deck D. L. 5250 4.62 14,900 Totals Case IV W IV 18180 MIV 106,250 d 4 x 5.92 15.7 100 1570 7.79 12,200 Totals Case II W II 19750 M II 118,450 Totals Case IV W IV 18180 M IV 106,250 Deck L. L. 2610 4.62 12,100 Totals Case III W III M III 118,550 20790 = -24- Overturning Moments: Case I and III 126 x 15.75 x 7.87 x 15,600# 518 x (15.75 x .5) . 15.75 21 400# __3__ M01 and MOIII Case II 155 x 15.75 x 7.87 . 16,500fi M0 II 55,500# Earth Thrust P 259 777 x 15.755 = 8150# 2 . Case I No superstr. Load or L.L. Surcharge. M I = 91,550 6' 4.87 - 5.65 v 1.24 M I: 57 000 s, P 14 950 .1555 54,550# Arm: 54 550= 5.65 Ea, 6W9 , 6 x 14950 x 1.24 - 1170 IZ,950 I’ 9.75 x 9.75 ’ Min \ ' Armhg 9.75 g 5425 Toe pressure 2700f 5 Heel 565 -25- Case II Superstr. D.L. and L. L. Surch. M II = 118,450 3*4.87 - 5.28: 1.59 M II 8 55 500 2 __19750 : 2120; 64,950 A " 9.75 Arm 3 64 950 x 3.28 9.1-2: 6 X 19750 X 1.59 , 1980? 19,750 I 9.75 x 9.75 Min. Arm:5.25 Toe Pressure = 4100# Heel w : 14% Sliding 8150 19750 .41 Case III Superstr. D. L. and L. L. No surcharge: I 8 III = 118,550 e::4.87 - 592 2 0.95 M III = 57,000 P - 20,790 = 2150# 81,550 A ' 9.75 Arm 81 550 : 5.92 Mo , 6 x 20790 x 0.95.124519: :"20f7§0 I ' ‘9275'i‘9t75"' Min Arm : 5.25 Toe Pressure 5575# Heel 885# 2 4260 2150# ave. ft. -26.. Case IV .Superstr. D. L. (IVO L.L. 0r Horiz. thrust) MsIV 105,250 , 5.85 18,180 Max arm 2/5 x 9.75 = 6.5' e: 5.85 - 4.87: 0.98 P , 18,180 .. 1860# 9.75 A Mo 3 6 x 18 180 x 0.98 g 1,125 I .7 x . Heel pressure 2985;? /D ' Toe pressure 755# /a '. 0888 IV assumes that the earth exerts n0 horizontal force against the abutment wall. -27- ll 6 Moments ,— Earth ups-2650 x 5.5 x 5.5 2 +1420 x 5.5 x 5.5 x.g ‘2‘ 5 = 15,200+5,800 . 22,000'fif _ Conc. down 2.5 x 5.5 x 150 x 5.5: 2,500 2 19,700 '3'" ~@ 12" : .60a"£.= 2.75 Net Up As : 19,700 x 12 :.560n" req'd. 18,000 x.875 x 27 P g As , 0.60 : .00185 Ed 12 x 27 k sV2Pn (Pn)2 - Pn =V1057 (.0185)2 - .0185 k r 0.174 1 = 1 - .174 = 0.942 '77 f8 : I " . 19,700 x 12 Asia . x. x 7 15,500.: /D " Use %" 4} at 12" run bond length beyond face of wall. rs, 2112,19700x12x22 550 /a" j 0 2X. 21 7 v , 26501- 4100 x 5.5 3 11,760 v: 10 450 2 . 54.2.70" 12x.942x27 -5.5 x 2.5 x 150 . 1 510 v = T""5‘0,4 0 ye. v , 10 450 = 150.9%," o.k. (provide use 33 2.75x.942x27 special anchorage) -28- Heel Steel Case IV L 31/1", 224" .1-6 5» .. 7»¢QIZ 709 735 (M about dowel steel Earth up (2018 x 4.17 x 4.17).(962 x 4.17 x 4.17 x 2) “2" "2" 5 = 17,680+ 5570 = 25,250 Earth Down 5.92 x 17.0 x 100 x 2,08 : 15,850fi Conc. Down 4.17 x 2.5 x 150 x 2.08 : 5250# Mom. Down 17100#‘ Net Mon up.= 6,150# As g u s 6150 x 12 : .174 " req'd —fs_jd 18,000 x.875x27 By running every other toe far into heel. .50 " furnished. -29- Heel Steel Top Case II £M about.d0wels Earth down : (17x5.92x100x2.08)l+(9 x 5.92 x 100 x 2.08) = 17,160 Cone“. down 2.5 x 4.17 x 150 x 2.08 = 5 260 Earth up (140x4.17x4.17)+(1690x4.l7x4.17)= 6050 2 2 5 ' Net Mom down. = 14,590 As.- M 1459ng 12 g .41 " req'd I “ fsjd 18000x.875x27 5" 5 e 12" As . .44 to: 2.56 p: .44 -.-.00156 4 12x27 Ks .fzpn (pn)2 - pn 45272 (.000185) -.0156 e .152 J. 1-§.1 - .132 .- .949 5 f3 __, n , 14590 x 12 = 15500#/." Asjd. ' .44 x .949 x27 1'0: 211 - 2 x 14590 x 12 = 274v? 6 " K3532 ‘ ‘1'5""'""‘T'—. 2x.949x 2x2_7x27 -50- V '-' (5.92 x 21 x 100) +(4.17 x 2.5 x 150) = 9815;} -(140 x 4.18) * (1690 x 4.18) : 406§# 2 5750;; v, v , 5750 .. 18.74 / " Bjd ' ‘12 x .9495x 27 a a, V 5750 __ g 95 54/0" (“-4, ' 2.56 x .949 1:27 -51- -Abutment Design (cont.) 0s Design of Wall Steel -—4 234%?" 3; O I u’ ff u 3’24 ' ' A70”« :14 .' .3 N \ 0 {C ..J . . U.\ .9: . 4 2 467 ' :l ‘ I", 5.3:“!!! : ”h. 547_ 5 ' a. f... .513?" Moment 126 x 15.25 x 15.25 + 441 x 15.25 x 15.25 T “2“ “""5 11,000 +12,900 4 25,900 17' 4A8: 23,900 x 12 :0.73 " required 18,000 x .875 x 25 Use 1" ¢ 0 12" area .. 0.78 {a 3 6.14 P g 0078 tr _0 0026 I? x 25 1: 3/752 (.02652 - .025zr.228 - .026 = 0.202 J ‘ 1 " .202 2 0.936 f3 ; 25 900 x.12 €15,7OO#‘[D " o.k. L 0.78 x 0.533x25 -52- Abutment Design (cont.) Design of Wall Steel: to, 25,900 x 12 x 2 2 = 4065/9" O.k. .202 x 0.955 x 12 x25 V : 126i'567 x 15.123 ' 4580# 2 v , 4580 = 16.4 56/5, ' O.k. v ' 5T5 17x2'9-55x25 U, 4580 = 65 M." 0.1!. 5.14 x .0 .955x25 Cut-off of Wall Steel Trial # 1 6' above top of th. P=567 - 6 x 55 1/5-567 M 8126 x 7.23 x 7.234.241 x 7.25 x 7.26 "—2— T T 5500+ 2100 = 5400;; 1 Trial f 2 @ 5' above top of ftg. P:56'7 - 5 x 55 1/5: 467 M = 126 x 10.25 x 10.25 1.541 x 10.25 x 10.25 T T T 6600+6,000 = 12,600# As = 12,600 x 12 : 0.584 a" ' Furnished , x. x 0.390 if every 2nd bar is cut off @ 5' Q bond or @ 4' ~6" above footing- Abutment design: Wing wall. -56- 420”1.L Surabargfl £081"; u’: 4” i a: , 11////// g§:"w5wzf‘6 V.) .1 - ,LZfiE/8’rl’. ‘L‘k /' I. K - - t E of (044", 8 w// °Q qffr.m.gt I d b i 3 z 1 z m «r 9 5° . 2 \ \ f I ‘ g t 64 € 0 3 § L 3.- J" FlLJ+~ 3 -//’ . ‘ ”Indy" 4+ - ‘w s. a ‘ I «a 19" 1“ r r k ’ a; 1; Eh. 7a: .9/ -04- Abutment Design: Stabilization: Load Total Wt. Mom. ent. (a) 2.5 x 9.75 x 150 6670# x 4.88 = 17,850' 5 (b) 1.5 x 15.25 x 150 2980# x 4.25 = 12,680' g (c) 15.25 x .855 x 150 x 5 826# x 5.28 r 4,660' # (d) 14.25 x 5.92 x 100 5590# x 7.85 . 45,500' # (e) 15.25 x .855 x 100 x g 552# x 5.55 == 5,060' # (r) 5.5 x 6.5 x 100 2275» x 1.75 = 5,980' 5 85,450 “1315,2395; “(51,11 ) M = 85,450'# Overturning: 595 x 17 x % 4950f x 5.67' 28,000‘# M(OI) 576# x 6.15' 18,160'# M(OII) NV 122 x 9.44 x Abutment Design: Wing Wall Stability Case I' No live load surcharge or superstr. L. M (81') = 85,400'# M (01') = _ 28,000'# MI' 3 57,430”? R(I') : 57,4501 1; , 6.62' 0.1:. 15,896 # Min arm : 9.75' g 3.25' 3 Case II' Superstructure D. L. L.L. Surcharge. (MS 11) = 85,450' g Mo 11 = 18,150' g M II' : 67,500' # (R 11'): 67,600'fi ._. 4.24' o.k. :8 5 # Min arm = 9.75' .. 5.25! Case IV Superstructure D. L. (No L.L. or Horiz. thrust) 11 :85,450'# W 815,895 i? R IV‘ = 85 460% z 5.38' o.k. 15,895” Min arm : 9.75t g 5.25' 3 Wing Wall Reinforcing Steel: The main wall takes more loads on it than the wing wall does and the loads on the main wall are heavier than the loads on the wing wall. By inspecting the steel erection diagram it shows that the same steel is used for both the main wall and the wing wall, therefore, the stresses in the wing wall are below the allowable. It is therefore, not -55- necessary to check the steel in the wing wall. CONCLUSION Remarks have been placed in their related sections as the checks have been performed on the design of this bridge. The Bridge Division of the Michigan State High- way accounts for the fact that such items as curbs, posts, railings and the concrete slab are overdesigned because it is cheaper to oterdesign such items than it is to draw up plans for each individual bridge. The diaphragms are used to keep the bridge girders level and to keep them from twisting. On the whole the structure is adequately designed and the standard items such as posts, etc., mentioned above are overdesigned. -57- BIBLIOGRAPHY "Reinforced Concrete Design Handbook" American Concrete Institute "Specifications for the Design of Highway Bridges" Michigan State Highway Department "Standard Specifications for Highway Bridges" American Association of State Highway Officials "Steel Construction Manual" American Institute of Steel Construction Sutherland and Reese, "Reinforced Concrete Design" - Second Edition. "Design of Concrete Structures" Urquhart and O'rourke - Fourth Edition .4 i 1.4 Hun-Mwnmgim -41-.1Ni I 1293 03061 < ,. _ - MW“. “...-.m- ..--......- .....- . ,. . '- A ' «haw- .5.