LIBRARY Mics? :: State University MSU RETURNING MATERIALS: Place in book drop to LIBRARIES remove this checkout from a a your record. FINES will be charged if book is returned after the date stamped below. Analysis of Beal Road Bridge A Thesiaz Submitted to Zhe Faculty of the Michigan Agricultural College by F. b. Hendriok pre Candidate for tne Degree of Bachelor of Soience dane 1921 THESIS te aman INDEX Dis cussion Introduction General conolusions Plate girder design Design of a 60' plate Girder, @10 86G@11 Conclusions for the deck girder spans Design oP 35° through plate girder G 8 Summary of amalysis of girder G 8 Complete design of 86' through plate girder G 2 Summary of analysis of girder G2 Complete design of 83' through plate girder G 3 Sammary of analysis of girder G@ 3 Annlysis of cross beams B1& B 2 Analysis of concrete footing under Colum CL l Analysis of gusset Analysis of columns and sway bracing Miscellaneous data Final sonclusions Bibld ography. Drawings Location plans Marking diagram Typical stress diagram Stress sheet for Girder G 10 Stress sheet for Girder G 8 Stress sheet for Girder @ 2 Strese sheet for Girder @ 3 101169 Page , o a - 14 “15 21 22 25 25 29 30 52 S2 a 4s oOo oo *» GS &W Stress sheet for cross bears B1l&B 2 Section through columns Half section of bridge Girder Bridges All bridge structures may be divided into three groups, Beam Bridges, Suspension Bridges, and Aroh Bridges. Beam bridges exert only a vertical pressure upon the bearings or supports. Beam bridges include, simple bridges, draw- bridges, continuous bridges, and cantilever bridges. A simple bridge is one resting on two supports. Simple bridges are of two Kinds, truse bridges and girder bridges. A girder bridge has its floor supported by solid or built up beams. A wooden beam, a rolled I bean, and a plate girder formed by riveting angles and plates together are examples of girders. Girder bridges are used for short spans, usually less than 100 feet. Other kinds, however, such as the 140 feet built up plate girders are not uncommon. About 1860, built up plate girders, formed by riveting angles to a solid web plate, were used in Europe. Plate girder bridges were not used extensively in this country until 1895. Today, the plate girder is the first choice for spans from 30 to 100 feet in length. The advantages of a girder bridge are greater stiff- ness, advantage in erection, a solid floor may be used vith the regular ballast and very shallow floors. The through plate girder hes the added advantage of requiring very little headroom. —_@ Teal LOBG Bric,.c,j[es.ing South. ‘ nese iaiina Bie ge PBR ae ee - NP Siew GPoinon). ra we vViCwW ar! vss. Orve..@5t we LCw s2lr U aah Cuve Introdustion The Beal Road Bridge was built in the late summer of 1913. The structure was built by the Michigan Railway Ing. Co. for the Michigan & Chicago Railway Co. The actusl con- struction and erection was done by the Toledo Bridge and Crane Co. Mr, Wm. Fargo was the consulting engineer. Beal Road is a highway one mile south of Grand Rapids. At the location of the bridge, the G, R. & I. R.R. orosses the highway at grade. The Michigan and Chicago Railway was forced to cross the G. R. & L. roadbed overhead. The G. R. & I. rails at the crossing has a curve of 2° without a spiral easement. The two railways cross at an angle of 31° 3'. This fact arbitrarily fixed the location of the supporting members. (See drawing 1) The bridge is plate girder type throughout carried on conorete end piers and ten columns composed of buil up sections. The bridge consists of two deck spans, each sixty feet long, and three skew through spans, in addition to two short through spans which connect the skew spans and the deck spans. Due to an arbitrary placing of the colwms no two girders in the through span are of the same length. The arrangment of girders is shown in Drawing 2. The bridge is an extremely long one for an overhead crossing. This is due to the fact that the earth f111 at the north end of the bridge has a depth of 28° under the pier. The approach from the south is also an earth fill and is 12' deep under the south pier. The greatest clearance over natural earth is 30'. The olearance over the G@. R. & KE rails is 22%, The bridge is in strict keeping with the rest of the roadbed of this division, The maximum grede on the Kalamazoo- Grand Rapids division 1s 1% and the greatest curve outside of the cities is 2°, The Michigan Railway Company operates its Kalamazoo- Grand Rapids division oars over this bridge. The weight of their orrs are as follows: Limited cars ------------- 76 tons. Local cara ---<---------- -60 tons. Freight motors «<«--<-+--+--73 tons. The bridge is designed for E 40 loading with a liberal ellowance for dead load. The floor of the structure consists of 3/6" steel plates supported on 10" - S0# I beams resting directly on the flanges of the girders. Te inoh ceder ties are used on the bridge and the ballast is crushed rook. The analysis of the structure will fall under three heads, First, the computation of the stresses in one of the deck girders, two thourgh girders, one pair of columns, the sway bracing between them, and one pair of solumn footinga. The second step will be the actual design of the members noted above. This design will be base on A. R. E. A. specifications of 1910. The third step will be the comparison of the authors design with the design actually found in the structure, An attempt will be made to account for differences found and justify them if possible. %. General Conclusions A close examination of the bridge in April 1921 showed the structure to be in very excellent condition. There were absolutely no signs of rust on any of the girders, I beans, or lateral breeing. There was a tendenoy exhibited for the paint to peel from four of the columns exposing the shop paint. The most serious signs of depreciation were at the bases of the columns where the concrete was beginning to weather eway. The conorete was poured about the colwnn to a distance about six feet above the column footing. The conorete had failed to form ea close seal to the column and water wag working down between the steel and the concrete, encasing it, and upon freezing, was causing the steel to rust and the concrete to fall away from the steel. There is no reason to fear that the columns will fail before any of the rest of the structure. The concrete in the piers scemed to have been of poor quality «8 large pit-noles are forming in the sloping top of the bases. Local aggregates were used in the concrete and organic matter is quite liable to have cotten into the concrete. Design of a Plate Girder Bridge The specifications used in this design are those prepared by the American Railway Engineering Association in 1910. The loads that will be considered in this design are the dead load, live load, impact, and wind loads, The live load will consist of Cooper's E40 loading. The dead load will consist of the weight of the metal in the structure, the floor, traek and fastenings, ballast and all loads that are constantly aprlied. Rapidly moving trains produce greater stresses in a bridge than would the same load simply standing on the structure. For this reason allowance is made in the live load stresses for the additional stress, The allowance is a certain per cent of the live load stress and varies according to the length of the bridge. This ration is found from the formla = | wee OQ T= 5 ( L * 300 The horizontal pressure exerted on bridges by the wind is called "Wind Pressure", Thirty pounds per aquare foot on the horizontal projection is usually allowed. Wind pressures will be found included in the lateral forces described in the specifications. i oe be ere i | a PS rs cee aed ee eee ¢ ”* 8 rr U Fe 3 re ac = 3E STRESS Complete Design of 60' Single Track Deck Plate Girder Span, @ 10 - ll Data: Length 59' c-o of bearings. Dead load as computed. width 7* a-0 of girders. Live load Cooper's E 40. Calculations for main girder. Dead load. Metal only. (12.5 L - 100) .9 = 765# Tie 1507 Rails and fastenings 15 Ballast 6 ou. ft. 80 I beam 280; Plates 12' long 184 Third reil and Tw b nee 2 1/2" oF o curb Ls 6 =z x | 3/8" 247 - Lé638F — Total dead load 24007 per ft, of track. M due to dead load = 1/8 x 1200 x 59° x 12 = 504,600 in # From table in Eetcham's Handbook Max. VW. due to E40 Loading on a 58' span = 1223,400 in # For maximum impact 500 = 83.6% S300 + 60 83.6% of 1223,400 in # = __1025,200 in # fotal moment at the center 2753,200 in # The next thing to do is to determine the economic depth. Mo web should be less than 8/8" thick. Ye will assume 3/8" as thickness of this web and substitute in the formula 1.1 = *“/ 16000 x 348" So we will use a web plate 75" x 3/8". fhe flange area will next be determined. It is readily seen that the effective depth will be slightly less than the total depth, so assume 74" as the effective depth. 2763,200 + 74 = 372000# For the glange stress 372000 ¢ 16000 = 24.2 sq. in. recuired in each flange. Use in each flange; 218 6x6x 6/8 - 1/2" 11.72 sq. in. net 9.5 sq. in. net lL pl. 16 x1/2 x 42° 7.00 7.0 1 pl. 16 x 1/2 x 31 7.00 7.0 20.72 Sq. in. 23.6 aq. in. 1/8 web 3.37 5.37 69.09. “E6.87 The thickest cover plate should be placed next to the angles, but in this cage both cover plates are the same thickness. For the length of the longer plate we have: 60 / 7,00 = 30.6! 26.87 end for the length of the longer plate 60 / 24:20 14.00 - 41,2! 26.87 According to the specifications one cover plate must cover the entire flange. The other plate will be made the same length as the longer under plate. The next thing to determine is the stiffening angles and web. The masimum end shear is: Dead Load 34800F Live Load 95900 Impact — 80800 BILOOOF 10,000#/aq. in. is allowed Por shearing stress. Therefore, £1. aq. in. is required in the web. A web plate 72" x 3/8" gives an area of 24 sq. in. According to the specifications, the outstanding leg of the stiffeners must not be less then 1/30 of the depth of the girder plus 2". ee = 4.5" The angle nearest this is 6" x 31/2" which will be used throughout for the intermidiate stiffeners. The end stiffeners must be designed to carry the entire end shear “nd aot as columns, Then assuming 5” x $ 1/2" x 1/2" used, we have for each solum used: L. r= f ~ + 19.98 - 2.88 8 Then substituting this value of r and the column length: 16000 = 70 Se - 15, 0784 and for the allowable compressive stress on the end stiffeners: £11,000 - 14.85 sq. in. req'd. 15, O75 So we will use 4 + 5" x 31/2" x 1/2" Le area 16.00 aq. in. We will use the minimum size intermidiate stiffeners and make the spacing accordingly. Using the assumed web 75" x 3/8", we have: Bt — FAL 000 - 7,018¢ for the maximum unit shearing stress in the web. From which ad = 218 (12,000 - 7,015) = 47" for the required spacing near the end of the girder. Since this is less than 1/2 the depth of the girder, we vill use e spacing of 45" or Bt cg ¥ For the bearing on the masonry, ee = 352 sq. in. Use bearing plates 18" x 20", Each bearing must be designed so that there will be at least this much bearing on the masonry. This compleses the necessary saloulations for the main girders, and the next thing is the lateral bracing. The latersl bracing should be symmetrical about the center of the span, The laterals should have a slope as near 45° as practicable. The distance betveen cross frames should never exceed 15°. In accordance with this there will be six inter- mediate cross frames in a 60° span. The lateral bracing will be as shown: ll 10 9 8 7 6 5 4 5 8 1 66 65 45 36 28 21 #15 10 66 6S Acoording to the specifications the laterals must resist @ uniform lateral force of 200 + .10( 5850 ) = 775#. Suppose this load moves on from the right as a ui form live load. The load at each panel point will be 4.6 x 776 = 37580; (about). Then for the maximum shears in each panel, we have: Shear in panel 320 x1 = S20# nm 320 x 3 = 9607 ml 320 x 6 = 19207 1k 320 x 10 = 22007 Eh 320 x 15 = 48007 hg 320 x 21 = 6620¢ ef 320 x 28 = 89407 fe 320 x 36 = 11,3007 ed $20 x 45 = 14,200# do 320 x 55 = 17,6004 ob 320 x 66 = 20,6007 ba Tangent of the angle —#- es .686 geo 9 = 1.213 $ #¢ Then for the maximum stresses in the diagonals,we have: rf = 6620 £1,212 = 7500 minus qf = 8940 x 1.213 = 10,800 plus dq = 11,300 x 1.213 = 13,620 minus pad = 14,200 x 1.2135 ® 17,200 plus pb = 17,600 x 1,213 = £1,400 minus bo = 20,800 x 1.213 = 25,200 plus It will be seen that the diagonals have to resist both compression end tension, but compression will probably gove . Let us try @ single angle sey 1-L 31/2" x 3 1/2" x 3/8", fhe radius of gyration of this angle is 1.07 ' L =» 106”. en substituting {n the compression formula, 16,000 =- 70 2 . Yr 16,000 - 70(-20-) = 9,000 for the allowable stress, Dividing the greatest compressive stress, which ocours in bO 20,800 ¢ 9,000 = 2.31 for the req'd cross section of the lateral and the assumed ZL has an area of 2.48 sq. in. For the area required in tension, 20,800: # 16,000 s 1.30 Bq. in., 80 the angle is quite sufficient for the end lateral. The angle selected is the smallest allowed by the specifications so it will be used throughout in the lateral brecing. il The cross frames oan be fairly well anelysed. The stress in the top angle of the frame oan be taker equal to one-half of the lateral force per foot of span multiplied by one-hald the length of the span, and this force multiplied by the secant of the angle of sippe of the diagonals. The bottom angle of | the frame has no stress( theoretically). Then according to the e@bove we have: for the stress in the top angle of the frame and as the dia- gonels have a slope of about 45° with the horizontal the stress in the diagonals will be: 11,500 x 1.4 = 15,8007 A3i1/2" x 21/2" x 3/8" 1s plenty large for thia position, so ea $1/2" x 3" x 3/8" sngles will be used in the cross frames. This concludes the preliminary computations for the design of the girder, wt, per 60" Girder No. |ft. (Total Web 60" x 72" x 3/8" 1 =|91.8 |5508# |11,016; Flange Angles 160' x 6 x 6 x 5/8 4 (24.2 |5808# |11, Plate 60" x 16" x 1/2" 1 |27.2 |1632$ Plate 32" x 16" x 1/2" 2 27.2 1741# Plate 42" x 16" x 1/2" 1 27.2 1138# Rivets 7/8" x 4 800 675¢ |21,988¢ Stiffeners 6" x 31/2" x1/2" x51 8 |13.6 652i 6" x 3" x 5" x 2/8" 12 9.8 704i Fillers 3 1/ 2" x 5" x 6/8" 8 4.46) 778% Rivets "fe" D 110 14¢ | 3,216# Cross Frames |3" x 3" x 3/8"x 7'=-5" 7.2 2167 Angles (endj3 1/2" x 3" x 3/8" 7.2 | 144¢ Plates 12 1/2" x 17" x 1/2" 4 |e1.26 126# 14 1/2" x 16" x 3/8" 24.65) 121# 8" x 8" x 3/8" 2 (13.60) 18# Rivets 7/8" D 104 567 e71# Tintermediate — Angles 3° x 3" x 3/8" x 7"'6" | 12 7.2 | 648% 3" x 3" x 3/8" x 5'11"| 12 7.2 | 519¢ 12 1/2" x17" x 1/2" 12 |21.25| 378¢ 14 1/2" x 16" x 3/8" | 12 |24.65) 4997 8" x 8" x 1/2" 6 |13.60| 554 Rivets 7/8" D 104 55 | 2,513¢ Lateral Bracing Plates 117" x 29" x 3/8" 6 [21.04 840F 17" x11" x 3/8" 6 116# on 608 1 ! | ' Angles 3" x 3" x 3/8" x 8°68" 12 | 7,2 | 750# Rivets 7/8" D 260 141# | 1,807# Web Splice 9" x 30" x 3/8" 2 | 9361, 48f Plates 13" x 42" x 3/8" 2 /16.58| 1167 Rivets 7/8" D 42 457 418¢ roth 41 ,469# 14 Conclusions for the Deck Girder Span Considerable difficulty was encountered at first in discovering the dead load allowed which would produce the etress which the web plate would sustain. The span is designed for a dead load of 24007/ft. of track which makes a liberal estimate of the weight of ballast. Using the E 40 live load and the dead load as stated, the total shear is found to require a web area of 21.18 sq. in. Aweb 75" x 3/8" gives an area of 28 gq. in. The economic depth is 75.7 sq. in., but a depth of 75" was found in the girder. The flanges as designed were found to be exactly the same as those found on the girder. The flange areas are 2.5 sq. in. in excess of the required areas. The cover plates as designed were elso the same length as found in the flange. The end stiffeners as designed were the same L om, —s 4 4 ys acre 1 - : § ee FrOAD GRIPGE ve ae eaadadod Ore oe Aloe ‘ie ae Bee any es aad (at tas ge eps ra ey ES Uae Ne Lubes ee te: - 15 Complete Design of a 35' Through slate Girder, @ 8.---(Johnson, Bryan, and Turneau) Length 35' o-c of bearings. Width 16' o-«o of girders. Dead Load (metal only) 0.9(12.5 L + 100) = 4857. Total dead weight 20008/ ft. of track. Maximum moments occur at the center of the span Dead Load 153,125 Live Load 523,000 Impact 468 , 300 “1,144,400 in # Maximum shear occurs at end Dead Load 17,500 Live Load 69,200 Impact 62,000 1800 F For the depth(economical ) h= V 2 “t / as +h, ( Q a a a w = 6 aps 36) 1/2 he 49 42 —S2222 os psp ain, 160 3/8" is the minimum thickness used so a web plate 3/8" will be used. , For the economical depth h = 1.1/1,144,425 = 51.6" 14,000 x 3/8 ° Reducing this by 20%, h = 40.5". Ye will use a web 42" x 3/8", area 15.75 aq. in. The Glange area will next be determined. The effective depth will be slightly less than the total depth, so an effective depth of 41" will be essumed. 1,144,425 in.# » 41 = 280,000} for the flange stress, 280,000 # 16,000 8 17.5 Sa. in. in lower flange. For the upper flange P 16,000 = 70 ¢ ~ 280,000 16,000 . 70 x 35 x 12 | 14 = £0.2 Sq. in. Use in the lower flange 21s 8 x 8 x 5/8" 19.22 16.72 1 pl 6" x 5/8" 3.76 2.60 1134" x 3* x 3/8" 2.48 1.78 1/8" web 1.97 1.97 Babe —SE.0E aq. in. Use in the upper flange 2le 6" x 6" x 5/ 8" 11.72 1 pl. 14" x 7/16" 6.25 1 pl. 14” x 2/8" 4.50 1/8" web 1.97 “£3.44 gq. in. The thicker cover plate should be placed next to the angles and in the upper flange one cover plate must cover the entire length of the cover plates. The length of the shorter plate is given by the formila: » [mares A 4.54 5.2 : / oe = 22.6! end for the length of the cover plates on the lower flange no cover plates are used, frem which 17 The next thing to calculate are the stiffeners. End etiffeners must be carried on fillers and carry the entire load at the end of the girder, The maximum end shear was 148,¥00#. According to the specifications the outstanding leg of the angle must equal 2" + 1/30 of the depth of the girder. 2" 4+ 3 = 3.4". We will try Ls 31/2" x 31/2" x 3/8" for the end stiffeners, Then assuming each two of these angles to act as a colum we have: 5, = £296 x 1.88: 2 @e rs / Ash e188" + Peo = 2.18 , using this valle of "r" and the colum length of 21" 16,000 = 70 fli: 15,320# for the allowable compressive stress in the stiffeners, 148.700 - 9.62 mq. in. for the required area in 15,320 the end stiffeners. We will use 4 ls, 31/2" x 31/2" x 5/8". Area 9,62 Bae in. Using the angles as calculated, we will have to find the required spacing of the intermediate stiffeners. a = 148,700 ¢ 15.75 = 9,4507 maximum unit shearing stress in the web from which | “as —86_ (18,000 ~ 9,450) = 23.5" since this is less than the tepth of the web, the spacing will be considered satisfactory. —___ -— — —.0.w cv ————————— 18 55' Girder &ssumed dead load 20007. Effective span 35'. Maximum end shear Dead Load 17, 5008 Live Load 69,2008 Impact 62 , O00F "148, 00 Use in bottom flange 1/8 web area 1.97 1.97 2le8x8 x 6/8 F.L. 19.22 16.72 1 pl. 6 x 5/8 8.75 2.50 1L4x3x 3/8 2.48 1.73 Required web area 14,87 sq. in. Use 42" x 2/8" , 15.75. Use in top flange 21s 6x 6x 5/8 14.22 11.72 1 pl 14 x 7/16" 6.12 5.25 1 pl 14 x 3/8 x 18" 5.25 4.50 1/8 web 1.97 1.97 Maximam momentum at center Live load 153,125 in? Dead load 523,000 in# Impact 468,300 inf 1,144,485 inf Stiffeners Veight of 35° Girder Web Flange Angles Angles Plate Angle Plate Plate Rivets Stiffeners Angles Angles Pillers Angle Filler Fillers Angles Angles Angles Angles Angles Pillers Fillers Rivets Gussets 51z6 38' x 42" x 3/8" 6x 6 x 5/8" x 35! @ x 8 x 5/8" x 35° 6" x 6/8" x 35! 4" x 3" x 3/8" x 35! 14 x 7/16" x 35' 14 x 3/8" x 18° 7/8" D 6" x 6" x 5/8" x 36" 5" x 3" x 3/8" =x 3'6" 3" x 5/8" x 2'4" 4" x 3" x 3/8' x 4! 6" x 5/8" x 3° 3" x 5/8" x 4° 5" x 3" x 3/8" x 3'6" 5" x 3" x 3/8" x 2'4" 6" x 4" x 3/8" x 214" 5" x 31/2" x 3/8" xo'e 8" x 31/2" x 1/2" x35" 31/2" x 5/8" x 2'4" 31/2" x 5/8" x 9' 1/4" bo. ~é FY YF YF Ww WwW 720 a *® PF oO A sz wT a YH HF &w& Ww BW a: "wt. a per _ ft. Total 53.55| 1880f | 1,880# 24.2#| 17004 32.77 | 2280F 12.75| 445% 8.5%| 2974 £0.83 728i 17.85| S227 | 420# | 6,192¢ 24.2 | 169.4 9.8 68.6 1.87} 88.0 8.6 | 34.0 8.75| 11.25 1.87| 652.2 9.8 | 241.0 9.8 | 178.0 11.0 77.0 10.4 | 110.0 18.6 | 191.0 8.18| 205.0 2.18; 61.8 55.8 1,362 .4# 150.0 300.0 fotal 9,738 44 Summary of Analysis of 35' Through Girder Length 35° | Depth 16' cc of girders. The weight of the metal in this girder by empirical formala is 485#. The other dead load sonsisting of track, ties, eto., was 1638#. The total dead load ia 21237/ft. of track, but Mr, Fergo's figures allowed 29007/ft. of track. The maximum shear was 148,7007 and required @ web plate area of 14.87 Bq. in. The wed plate used was 42" x 3/8" - 15.765 8a. in. The maximum moment was 1,144,425 in # and with an effective depth of 41", a flange area of 17.5 sa. in. was required. Due to the construction of the larger girders, the same size angles were used in the 35' girder as in the larger girders, The lower flange used had an area of 22.92 aq. in and the upper flange en area of 23.44 8a. in. The shorter cover plate as determined from the empirical formula was 15.2", The cover plate used on the girder was 18' long. No cover plates were used. The spacing of the intermediate stiffeners was found to be quite s&tisfactory as all spacings were very conservative. The weight of 9,7387 is in excess of that given by the formula 9(100 + 12.5 x 35). Since 20007 ft. of track was Gllowed for the deadt-load weight, the increase in weight is taken care of. ee Ob Completed Vesizn of an 86' Through Plate Girder Data: length 8640" o-c. of bearings Dead Load 3000#/ft. of track Width 16'-0" o-c. of eirders Live load Cooper's class E 40 Caloulations: Veight of track, ballast and etc. 1636} Weight of metel in girder .9(12.5 L + 100) = .9(1075 + 100) LOGO# 2696# Total weight M due to dead load 2 1/8 x 1500 x 86° x12 1,354,600 in # From table in Ketcham's Jandbook Max. M due to E40 loading on 86' span 2,407,000 in F Impact = 83.6% of live load moment 1.875.600 in # Total moment at the center span B,6o7,,00 in ¢ The first thing to do is to find the economics depth. The specifications require a web thickness of at least 3/8" so that thickness of web will be assumed in these calculations. This thickness is at once used in the formula: af # 2% /_5,637,100 = 107" 16,000 x 3/8 h Led A web platell4" x 3/8" was necessary in the 101' span and for the sake of appearance, all of the longer through spans will use the same size web plate, 114" x 3/8". Since the flange takes all the moment, the flange area will next be determined. The effective depth will be slightly less than the depth of the web plate so we will assume an effeotive depth of 112", 65,637,100 ¢ 112 = 50,300 in # for the flange stress. 50,300 in 7 # 16,000 © 32.6 sq. in recuire: flange area. ob Use in the lower flangs Gross Net 2 Ls 8" z 8" x 5/8" 19.22 15.47 l pl 6" =x 5/8" 3.75 2.25 1 pl 18" x 7/16" 7.88 7.00 1 pl 18" x 2/8" 6.75 6.00 1L 4" x 3" x 3/8" 2.48 1.73 1/8" web 5.34 5,34 total 45.45 “38.04 Use in upper flange 2 Ls 8" x 8" x 5/8" 19.22 1 pl. 18" x 5/8" 11.25 1/8 web 5.34 1 pl 18" x 9/16" 3 Total 9 Required area in upper flange is found from the formla As P — 16,000 = 70 4. b - 50,300 in 7 z 42.6 aq. in. from which A * T6.000 _ 90 x 66 x iB a 18 The thickest cover plate should be pleced next to the engles. For the lower flenge and the longer plate, we have: 38 .04 and for the shorter plate: 96 #8200 + 8.00 - 50.2" 58.04 According to the specifications one of the upper cover plates must extend the full length of the girder. The next thing to determine is the shear in the web and the necessary stiffeners. The masimum shear is at the end of the span and is maze up as follows: Dead load 63,750 Live load 130,700 Impact 3.6% of live load 101,900 Total 96,050 + The allowable unit shearing stress is 10,0007 per sq. in. 80 29.6 sy. in. of web area ig required. Ane Clad a TB) Lea a Vall TAA Bo) (toate tT aad 4 ar J SLALS FPOAOD PIE FS MICHIGAN RAILWAY ENG €Q AMiCH. & CHICAGO RY late alin] ENGINEERING CO OL dnalysis of the Concrete Footing under Colum. Chl. the total dead load from the girders to the golwm is 269 ,OOO0F + 210,0007 = 480,000#. The weicht of the colum is approximately 27,000. The pier ig 10' square and 3* 6" deep. At 150#/ou. ft., the peer weichs 60,0007, making the total weight on the soil underneath the pier 567,000% spread over an area of 100 aq. ft. The unit beering stress resulting is 5.67 tons per Bq. ft. or 2.83 tons. The allowable pressure on the foundation is from 2 to 3 tons for ordinary cley and dry sand. The founda- tion here rests on a gravell,y soil underlaid by a layer of hard hlue clay over s deep bed of nuek. Hence the footing will be considered safe for bearings pressure. Piers commonly fail from pinching shear, that is the section directly underneatch the column bearing plate being forced dorm through the footing. The colwm rests on a plate 24" x 36" having © perimeter of 10 ft. The conorete in the piers was made of local ungraded aggregate in a ration of 1: 2: 6. The concrete was carelessly mixed and placed so the allowable compressive atress will be teken as 1500#/sq. in. The pier has both vertical end horizontal reinforcement 80 6% of the compressive stress will be allowed for shear. The load producing punching shear is: 400 = = 6 x 507,000# = 475, 000# The minimum depth then for punching shear is 47 000 ~ ep £x10x12 x 90 10! Since @ = 36” es | | E . #§ the totai shear on EFGH - 200 ~ 8= 9 y 507,000 = 100 ‘lo! 142, 0004 bjd 388 x 875 x 32 - Keen eo lel 12 4; SO no 24" | 36" | | | are needed, bending moment on each set of rods is M > Cpdp 6, = .615 615 x 507,000 x 120 = 3,160,000 in # AS © we 22t60,000 =- 6.4 in of steel. 16,000 x 356 x 0,875 Fourteen <- 3/4" round bars. Area 6.21 Ba. in. Hence from this analysis it will be seen that the pier has sufficient area for bearing and are deep to prevent punching by the colwnmn. The fourteen round bers give ample reinforcement in the bottom of the pier, In addition there are ring bars and angles attached to the column itself which increases the allowable utress allewable in the concrete. The piers will probably carry fully 50% more load then will ever come upon then. Analysis of One Gusset Consisting of 2 ls 3 1/28" x 3" x 3/8" x 5° 3" and 1 plate 16" x 3/8" x 6’ 3", The radiue of gyration of these angles is 0.91 and the length 98". Substituting in the compression formula: 167000 = 70 _ = 15,250# The area ef these two angles is 4.22 aq. in. or the total com- pressive stress that these angles will take is 4.22 x 16,250# = 64,100#. Bg The flango stress due to overturning is 1016200) + 200 = 720F applied 7* above the reil. 4s the rail is about 2’ above the lower engles and the girders are 16' apart, the overturning moment ia; | 720 x + = 406# The bending moment at the center of the span is: 2 406 : 100" — = 457,000 ft.# and the rewalting flange stress 1s ee x 12 = 48,100/. It is hard to determine the exact stress passing from the yirder to the gusset plate, but standard practice requires 2 Le Ss" x 3" x 3/8" and a 3/8" web plate between them. This is the arrengment used in the gussets on this bridge. Veight of Gussets Sle 3" x 8" x 3/8" x 6" 3" 76.17 1 pl. 16" x 3/6" x 6° 2" 192.42 BO 03/4" Rivets 14.14 Rae OF Official ChearLline Rivets § WenHoles £ ieee | ; ee 2 iS <9 sey : i es iin holes /2’ceas betweenls } fe OF O™ 2 beams ?*tt« 2/0206 ar braces /6-O' Co <. HALF SECTION OF SARIDGE CROSSING OVER GRSIAY AT SEALS AQAD Yd PMLA ball Lac Farka eld Jel 4 4 AT/CP4E& CHICAGORY TRACED APRIL ef S92 / ‘@) SovleZ yO aNnaLySis O41 Colwanig ana Sway Breuoine aL ONO Final Conclusions The Beal Road Bridge is a very good example of the best practice in recent bridge building. Bridge designing like all other forms of structural designing is an ert. f design a bridge, one must do more than to compute the various stresses in the bridge and to make all members amply strong. He must so proportion all the parts as to make an economical design to build, but also a structure easily erected and when once erected, capable of resiating not only the loads it carries, but the elemcnts as well untii a time until newer structural prastice makes if advisable to repiace the structure. This bridge ia designed to carry what is known as Cooper's Class E 40 Loading. This loading consists of a standard Locomotive eof a certain weight followed by loaded oars also of definite weight, Since no standarfised loading has been provided for electric railway stractures, steam road loadings have to be used. A cereful analysis of the forces caused by om electric ear passing over a bridge shows that those forses are from 50 to 75% of those caused by # 40 Loading. Hence Beal Road Bridge will be able to carry interurban cars from 33 1/3 to 50% larger than ere being now used. Although it is hard to prophesy the future erowth and @cvelopment of electrical railways, it is safe to assume that the Bridge will not require replacement for 50 years. A comparison of the results obtained from my scomputa- tions of the design of several members of the structure with the actual conditions found in the bridge show the bridge to be en- tirely safe. Extreme conditions were watched out for and these conditions ampiy provided for, The greatest stresses in the bridge ocourr in the girders. Every girder shows excess material. If a bridge was not stiffened and braced throughout, there would be excessive vibration when the cars passed across the bridge. Due to the rock ballast used and the thorough bracing of the entire strueture, a car passing over the bridge will not jar a coin placed on a horisontal surfeee on the bridge. Lack of vibration makes riding on the Kalamasoo Interurban oars much more pleagant than is sonmonly attributed to eleetris railway cars. Ho structure can stand for long unless it has secure foundations. All piers are of heavily reinforced concrete with broad vases. The piers rest directly on gravelly soil mized with clay which forms the best bracing support offered by any sells, The steel colums supvorting the girders appear to be manmeths to the layman. These solume are filled with soncrete te prevent rusting of the metal on the inside of the columns and to give added stiffness to the structure. The iaynan mey fail to see the economy of an overhead crossing at this point. The struoture cost very nearly $50,000 and the approaches several thousand dollars more, But the state Rellroad Commiagsion ruled there must be e separation of railroad grates. The reason for this is quite apparent when one considers the amount of traffic on each, The Michigan Railway Company operates 56 passenger trains a day end the G, R. & I. operates about 20 trains a day on this line. The roads cross at very acute angles which forma the same conditions eas was prcsent at the recent wreck at La Porte, Indiana. A grade separation 36 prevents the greater number of accidents and has a value which cannot be measured in dollars and cents. fhe Beal Road Bridge is by all means a monument to modern engineering foresight and skill. A bare plate Girder bridge is never a thing of beauty, but it serves its purpose well. The designers of this bridge have made the best of the comiitions present and have produced a strueture which is stable and thoroughly suited to its Location, Miscellaneous Data Rivet spacing in flange angles at end of girder Girder G10 ¢S8 @2 G8 Qs Spacing 2.5" 8.0" 2.5" 2.5" 2.5" Maximum moments for remaining girders not analyzed: Girder 45° 101° 96° Moment 1,805,000 in # 7,610,000 in # 6,989,000 in # Shear 180,150# 337 , 5S0F 326, 500# Greatest web area recuired 55.76 Bq. in, Boonomical denth 114" BIBLIOGRAVHY The following books were used throughout the preparation of this thesis: Ketcham's "Structural Engineer's Handbook". Kirkham's "Structural Engineering”. Johnson's, Bryen, and Turneau's "Modern Framed Structures". Hool and Johnson's "Concrete Engineer's Handbook". The author is greatly indebted to Mr. Wm. G. Fargo of the Fargo Engineering Company end the Ingineering Department of the Michigan Railway Company for the ready and willing assistance they have given him in the preparation of this thesis. wih ai ina