through steel truss highway bridge

AL-NAHRAIN UNIVERSITY COLLEGE OF ENGINEERING CIVIL DEPARTMENT

THROUGH STEEL TRUSS HIGHWAY BRIDGE FINAL YEAR PROJECT SUBMITTED TO AL-NAHRAIN UNIVERSITY, COLLEGE OF ENGINEERING, CIVIL DEPARTMENT, IN PARTIAL FULFILLMENT FOR THE REQUIREMENTS OF THE DEGREE OF B.SC IN CIVIL ENGINEERING By

OLA ADEL QASIM Supervised by

ASS. PROF. MOWAFFAQ T. AL-SAMAANI JUNE 2004

Date of Oral Examination:

Examiner:

Examiner:

Supervisor:

Head of department:

Date of the examination:

/

/ 2004

Acknowledgment I would like to thank God who helped me to overcome all the difficulties to reach the goal of my work. I am deeply grateful to my supervisors Mr. Mowaffaq T. Al-

Samaani for his encouragement and assistance during the period of accomplished this research providing to me the guidance and information on this subject. And I would like to express my deep thanks and to all of my teachers for their support. Also I like to thank my dear parents and my sisters for their love and assistant. In the end I thank my friends, and all that helped me to complete this project.

Ola Adel Qasim 2004

Abstract

ABSTRACT This research specifies the design of through steel truss bridge using AASHTO specifications. This project has four lanes through truss bridge and designed of span 210 ft, 62 ft, width and 40 ft truss high. This study is divided into four chapters: - The first chapter presents the introduction of steel truss bridge. - The second chapter contains and discusses the loads and its distribution on bridge according to AASHTO specifications. - The third chapter presents and contains the design calculations of slab, floor beam, and truss girder. - The forth chapters present recommendations of this study.

Through Steel Truss Highway Bridge

the

conclusions

and

1

.

SUBJECT

PAGE NO.

List of Contents……………………………………...

I-II

Symbols & Abbreviations…………………………...

III

List of Tables………………………………………...

IV

List of Figures……………………………………….

V

Abstract……………………………………………...

1

Chapter one:- Introduction 1-1 Introduction……………………………………..

2

Chapter two:- Loads on bridges LOADS ON BRIDGES……………………………...

4

(2-1) AASHTO specifications……………………….

5

(2-2) Dead loads……………………………………..

7

(2-3) Live loads……………………………………...

8

(2-4) Lane load……………………………………...

10

(2-5) Impact load……………………………………

11

(2-6) Longitudinal forces…………………………...

12

(2-7) Wind loads…………………………………….

13

I

(2-8)Miscellaneous condition……………………….

13

Chapter three:- Design (3-1) Design of concrete slab……………………….

14

(3-2) Design of stringer……………………………..

17

(3-3) Design of floor beam………………………….

20

(3-4) Design of truss………………………………...

22

(3-4-1) Dead load on truss……………………….

22

(3-4-2) Live load distribution on truss…………..

22

(3-4-3) Influence line of members………………

24

(3-4-4) Forces in truss due to lane loading……..

26

(3-4-5) Forces in truss due to dead load………...

27

(3-5) Wind load on truss…………………………….

32

(3-5-1) Design of bracing………………………..

33

(3-5-2) Design of portal………………………….

41

Chapter four:- Conclusions and recommendation (4-1) Conclusions……………………………………

44

(4-2) Recommendation……………………………...

44

References

45

II

A E L Fb Fy fc’ fs Fv I S I R S Fa fc

Cross Section area (in) Modulus of elasticity of steel (psi) Span length (ft) Allowable bending stress (psi) Specified minimum yield point of steel (psi) Ultimate compressive strength of concrete as Determined by cylinder rat age of 28 days (psi) Tensile stress in reinforcement of service loads (psi) Actual shear stress (psi) Moment of inertia (in) Section modulus (in3) Impact factor Concentrated force or reaction Distance in feet between stringers, (ft) Allowable axial stress (psi) Actual compressive strength (Psi)

III

TABLE NO. (3-1) (3-2) (3-3) (3-4)

SUBJECT Force in truss due to lane load Force in truss due to dead load Design of tension member design of truss Design of compression member design of truss

PAGE NO. 28 28 30 31

(3-5)

Design of tension member design of portal

43

(3-6)

Design of compression member design of portal

43

IV

FIGURE NO.

SUBJECT

PAGE NO.

(2-1) (2-2) (2-3) (2-4) (2-5) (2-6)

Girder Bridge cross section Through truss bridge. Top view Through truss bridge. Side view Through truss bridge. Top plan view Distribution of truck loads lane loading typical member of a simple single span through truss Bridge cross section Design of stringer Design of floor beam distribution of wheel lands component of a through – truss bridge Live load distribution on truss Influence line of members final stress for live & dead load combination Wind load on truss wind brace and portal action Design of lower bracing final results of Design of lower bracing Design of upper bracing

4 6 6 6 9 10

(3-1) (3-2) (3-3) (3-4) (3-5) (3-6) (3-7) (3-8) (3-9) (3-10) (3-11) (3-12) (3-13) (3-14) (3-15)

Final result bracing

of

(3-16)

Design of portal

design

of upper

14 15 17

20 20 22 23 24

29 32 33 33 37 37 40 41

V

Chapter One

Introduction

Chapter One INTRODUCTION Steel truss bridges are modern Design Bridge. The primary forces in its members are axial forces.  There are many types of steel truss bridges such as sub divided truss, cantilever truss bridge, continuos bridge truss, arch bridge, etc…  Trusses are further classified as deck, through or half through trusses where:  Deck trusses: locate the deck near the top chord so those vehicles are carried above the chord.  Through trusses, place the deck near the bottom chord so that vehicle passes between the trusses.  Half through trusses carry the deck so high above the bottom chord that lateral and sway bracing cannot be placed between the bottom chord.  Various types of trusses are used in bridge building. Most of these trusses are either Pratt or Warren trusses with some modifications.  Although trusses are usually used in highway bridges only for long span and (in the case of through bridges) safety with high- speed traffic and not critical.  Generally, truss bridges is economical for spans greater than 100 ft and are suitable for the span range of 130 to 1230 ft.  The depth of a simple- span bridge trusses usually ranges from about one fifth to one eighth the span, shorter spans being relatively deeper (AASHTO


2

Chapter One

Introduction

specifications set a minimum of one tenths for this ratio).  The depth span ratio is also somewhat dependent upon the life loads.  Trusses of economical proportion usually result if the angle between diagonals and vertical ranges from 45o to 60o.


3

Chapter Two

Loads on Bridges

Chapter Two LOADS ON BRIDGES The design of bridge is very important to civil engineer. Such structures are composed of interconnected members and are supported is such a manner that they are capable of holding applied external force in static equilibrium. Through truss highway bridge is structure of three dimensional but it can be divided into six component structure the two main vertical truss the top chord lateral system the bottom chord lateral system and the two end portals. Stringer

Floor beam

Girder

Fig. (2-1): Girder Bridge cross section The through truss is a simple truss and easy in the calculations of the design. The design of such bridge requires the design of concrete slab, stringers, floor beam and the truss girder. Different kinds of loads have to be considered in the design such as dead loads, live loads, wind loading, impact loading, lane loading and other kinds of loading.


4

Chapter Two

Loads on Bridges

(2-1) AASHTO specifications: Some code and design specifications encountered by civil engineers are: -

commonly

AASHTO: standard specifications for highway bridge American Association of State Highway and Transportation Officials, Washington, D.C, 1989 . Steel bridge may be classified in a number of ways. The more important of these are: 1- Span type: -simple span truss. 2- Cross section: -through type. 3- Functional: -vehicle, pedestrian. 4- Span length: -intermediate. 5- Degree of redundancy: -indeterminate. Influence line shows the influence on a certain function as a unit load crossing the structure.

Uses of influence line: 1-

To determine the position of the live load that will give the maximum value of sum particular function for which the influence lines have been constructed.

2-

To obtain the maximum values of that particular functions with the live load or determine the value of the section for any one. According to these specifications live loading consist of standard trucks loading, or of the corresponding lane loads (which are equivalent to truck trains).


5

Chapter Two

Loads on Bridges

AASHTO design vehicle loading are two classes of trucks:  H – truck: - consist of two-axle truck, or of the corresponding lane loading H20, H15, and H10.  HS – truck: - consist of a two-axle truck, or of the corresponding lane loading HS20, HS15.

The loading consist of five weight classes:  H10, H15 they are the lighter loads and they used for the design of lightly traveled state roads.  H20, HS15 they are used for national highway.  HS20 used for the design of bridge on the.

The most important system of a typical through truss bridge. Stringer Diagonal of bottom chord lateral system Floor beam

Fig. (2-2): - Top view A

A

Fig. (2-3): - Side view

Diagonal of top chord lateral system

Portal

Fig. (2-4): - Top plan view


6

Chapter Two

Loads on Bridges

2.2 Dead loads: The dead load represents the weight of structure itself and any other immovable loads (equipment) that are constant in magnitude and permanently attached to the structure. Thus The dead loads acting on a structure consists of the weight of the main supporting trusses or girder the floor beams and stringer of the floor system. Structural design is that the true dead load of the structure that cannot be determined until the bridge is designed and a final design cannot be accomplished unless the true dead load is known. The dead load acting on a member must be assumed before the member is designed, one should design the member of a structure in such a sequence that to as great an extent as practicable the weight of each member being designed is a portion of the dead load carried by the next member to be designed. Thus for a highway bridge, on would first design the road slab, then the stringer that carry the slab loads to the floor beams, the floor beams that carry the stringer loads to the main girders or trusses and finally main girder or truss. It is therefore necessary to make preliminary estimate of the structure and then can be calculated and compared with the previously estimated weight. The dead load assumed to be uniformly distributed along the length of the structure elements, such as slab beam or truss.


7

Chapter Two

Loads on Bridges

2.3 Live load: The live load for highway bridges consists of weight of the applied moving load of vehicles and pedestrians. Highway bridges should be designed to safely support all vehicles that might pass over them during the life of the structure actually, the traffic over highway bridge will consist of multitude of different types of vehicle. It’s not possible for the designer to know what vehicles will be use the structure or what the required life of the bridge will be to ensure the safety of the structure. Some form of the control must be maintained so that the designer has to provide sufficient strength in the structure to carry present and future predicated loads. The regulation of vehicle using the bridge has to be such that excessive weight vehicle are prohibited from crossing the structure. Design control is provided in the United States by (AASHTO). State laws regulating the weight of motor vehicles provide which specifies the design live load and traffic regulation.


8

Chapter Two

Loads on Bridges

W = combined weight on the first two axle which is the same as for the corresponding H truck. V = variable spacing – 14 feet to 30 feet inclusive spacing to be used is that which produces maximum stresses.

W = total weight of truck and load.

Fig. (2-5) Through Steel Truss Highway Bridge

9

Chapter Two

Loads on Bridges

2.4 Lane lading: Nearly all highway bridges are design for one of the four classes of the load recommended by the (AASHTO spec. 89). These are consist of a system of concentrated loads represent a truck or of loading distributed uniformly along the traffic lane, together with a concentrated load to represent a long line of a medium weight traffic with heavy vehicle somewhere in the line. The two systems are necessary because of the difference in length of traffic responsible for maximum forces in the various parts of a bridge.

The lane loading may be used with two reasons: 1. Stringers will usually be of such length that it can support only one or two axles of a truck, and since the effect of one or two concentrated loads on a beam is quit different from the effect of an equal amount of load distributed uniformly. 2. On the other hand, the force on chord member of simple truss span will be largest when the full length of the bridge is loaded. A Relatively small error results from the substitution of a uniform load for a large member of concentrated loads. Concentrated load

18,000 formoment 26,000 forshear Uniform load 640 lbs. per liner foot of load lane

H20-44 loading HS20-44 loading

13,500 formoment Concentrated load 19,500 forshear Uniform load 480 lbs. per liner foot of load lane

H15–44 loading HS15-44 loading

Fig. (2-6) lane loading


10

Chapter Two

Loads on Bridges

2.5 Impact loading (dynamic effect of vehicle): The live load applied gradually by vehicle moving across the bridge at normal rate of speed produced the deformation of the structure. The live load produces greater stresses than if they were considered as a static position on the structure. Since the deformation is greater the stress in the structure is higher this increment in stress can be called the (dynamic effect). The terminology for dynamic effect among bridge designers and bridge design specifications is impact. In addition to the true impact effect and the sudden loading effect there is also third effect, which is caused by the vehicle, vibrating on its springs. Uneven roadway surfaces contribute to this effect. The vibrating of the vehicle on its springs induces vibration of structure. The magnitude of stresses is dependent on the relative masses of the vehicle and the bridge, the natural frequency of the structure and the damping characteristic of the bridge. Impact stresses are usually obtaining by multiplying the live load stresses by fraction called the (impact fraction) and depend on:  Time function, which the live load, is applied.  The portion of the structure over which the live load is applied.  Elastic and inertia properties of the structure itself. For highway bridge, the impact fraction (I) is given in specifications of (AASHTO) by this equation: 50 I  125  L Where: I = impact stresses. L = loaded length of the structure and the value of this equation not exceed the maximum value of impact factor suggest by (AASHTO) specification is equal (0.300).


11

Chapter Two

Loads on Bridges

2.6 Longitudinal force: When the vehicle crossing the structure increase or decreases (accelerate) their speed a longitudinal force (F) are transmitted from the wheels of the vehicle to the deck (Horizontal force acting in the direction of the longitudinal axis of the structure). Since they are inertia forces resulting from the acceleration on deceleration of vehicle, they act through the centers of gravity of the vehicles.

The magnitude of longitudinal force is depending on the:  Amount of acceleration or deceleration.  Frictional forces that can be developed between the contacts surfaces of the wheels of the vehicle applying these force to the roadway or track and the surface of truck or roadway.  Weight of the vehicle.  The velocity of the vehicle at the instant of braking.  Time interval to come to complete stop

F 

w v ( ) g t

Where: W = weight of vehicle (k). g = acceleration of gravity = 32.2 ft / sec. ∆V = change in velocity (ft /sec) in the time interval (∆ t) (sec). The (AASHTO) specification provides for a longitudinal force of (5 %) of the live load in all lanes carrying traffic headed in the same direction.


12

Chapter Two

Loads on Bridges

2.7 Wind loads: Wind loads have been the concern of the bridge design engineers for many years, but the determination of the effect on a bridge is very complex. Studies on wind loads on bridge have yielded same information on this subject. The wind load may be defined as a dynamic force. (AASHTO) specifies that the wind load shall consist of moving uniformly distributed loads applied to the exposed area of the structures. The exposed area shall be the sum of the areas of all members, including floor system and railing as seen in elevation by (90o) to the longitudinal axis of the structure. The bridge designer should be aware of the vertex-shedding phenomenon, even though it is unlikely to occur in most bridges, several members of truss bridges have vibrating in the wind as result of a vertex shading effect and repairs have been necessary.

2.8 Miscellaneous condition: After these types of loads that applied to the structures of the through steel Highway Bridge there are additional forces that may be applied to same type of structure under particular condition. Temperature changes, Shrinkage, elastic shortening, and earth pressure cause such forces. These can be estimated either by making a judgement based on study of the particular conditions.


13

Chapter Three

Design

Chapter Three

3-Design The typical member of a simple single span through truss is identified in figure (3-1).

Fig. (3-1)

3.1 Design of concrete slab: Given: -

      

Span center two center of bearing = 35 ft Load center two lanes of HS 20 f c`= 3000 Psi f c = 1200 Psi n = 10 f S = 20 000 Psi Bridge cross section as shown in figure (3-2).


14

Chapter Three

Design

Fig. (3 –2) Bridge cross section Width of flange = 0.8’ 0.8 Slab span ( Seff )  7.25   6.85' 2 Case (A) [AASHTO specification]

Live load-bending moment MLL  0.8( S  2) P 20 32 0.8(6.85  2)  * 16  3.54k . ft 32

Dead load bending moment

7 150 [ *1 *1 * ] * (6.85) 2 W *L 1000  D. L  12 16 16 2

MD.L

= 0.2566 k. ft

Impact 50 L  125 50  6.85  125

I 

Then Use (30 %)

= 37.92 % > 30 % [AASHTO specification].


15

Chapter Three

Design

Impact bending moment MI = I * ML.L = 0.3 * 3.54 = 1.062 k. ft

Total bending moment M total = MD.L + ML.L + MI = 0.2566 + 3.54 + 1.062 =  4.9 k. ft

For reinforcement d 7 fC

k

fC 

j 1

fc n

1 1  6 ( 2 2 

1 Cover 2

,

1 2

wearing)

1200  0.375 1200  2000

k 0.375 1  0.875 3 3

2m 2 * 4.9 *12 *1000   5.01' '  6' ' (o.k) fC * b * j* k 1200 *12 * 0.875 * 0.375

d

Total depth = d + cover + wearing = 5.01 + 0.5 + 0.5 = 6.01’’

Area of steel As 

M 4.9 *12000   0.56 in 2 / ft fS * j * d 20000 * 0.875 * 6

The longitudinal or distribution reinforcing steels p

220 220   84.05% S 6.85

Max 67 % (Then Use 67 %)

AS = 0.67 * 0.56 = 0.375 in2 /ft


16

Chapter Three

Design

3.2 Design of stringer: 8k

32 k

32 k

CL

Stringer

Floor beam 35’ 8k

32 k

14’

14’

8k

32 k

14’

Axle load

32 k

14’

32 k Max reac. = 32+ (32 (21) /35)+ (8(7)/35) = 52.8 k

72 k 2.33

8k

32 k

32 k Abs. Max. Moment = 31.2 (17.5 -2.33) – 8*14 =361.304 k. ft

31.2

40.8

k

k

361.3 k/ft 36.5 k/ft

238.3 k/ft

B.M.D Abs. Max. M (k/ft)

Fig. (3-3) From AASHTO specification for 35 ft span: Lane moment = 361.3 k. ft Lane shear = 52.8 k Through Steel Truss Highway Bridge

17

Chapter Three

Design

Fraction of wheel loads to stringer S (S < 14) 4.5 6.85   1.522 4.5

Wheel loads / stringer 

1.522Wheels = 0.761 lane / stringer 2Wheels / axle Impact 

50 50   31.25 % > 30 % I  125 35  125

D.L (slab level) =

7 * 7.25 * 1’ * 150 = 634.37 ib/ ft length 12

Assume stringer weight = 145 Ib/ ft Total D. L = stringer weight + D.L = 145 + 634.37 = 779.4 Ib/ ft

W *l2 D.L moment  8 0.7794(35) 2   119.34k . ft 8 L.L moment = 0761 (361.3) = 275 k. ft Impact moment = 0.3 (275) = 82.5 k. ft Total moment = D.L moment +impact moment + L.L moment = 119.34 + 82.5 + 275 = 476.84 k. ft

S required 

467.78(12000)  286.104in 3 20000

Choose W 30*124 ,

S x = 355 in3 > 286.104 in3


18

Chapter Three

Design

Check deflection Δmax

5 * W * L4  384 EI

but ML.L

W * L2  8

5M L. L * 8 L2 *12 2 15M L. L L2   max   384 EI EI L EI    800  15 L * M L. L L 30000 (5360)   856.7  800  15(357.5)(35)

Check shear VD.L  0.7794 * (35)  13.65k 2 VL.L = 0.761 * (52.8) = 40.2 k V impact = 0.3 (40.2) = 12.06 k V total = VD.L + V L.L + V impact =13.65 + 40.2 + 12.06 = 65.91 k

fv 

65.91 < Fv = (0.33) Fy d * tW



65.91  3.73ksi  12ksi(o.k ) 30.17 * 0.585


19

Chapter Three

Design

3.3 Design of floor beam 4k

16 k

16 k

14’

14 ‘

35‘

35’

Floor beam Fig. (3-4)

16 (16  4)  25.14 K 35 Assume floor beam weight W F.B = 0.85 k/ ft Reaction FB  16 

WD.L  779.4  35  3.76 k / ft 1000 7.25 W total = 0.85 + 3.76 = 4.61 k/ ft 2 M D.L  4.61* (62)  2215.105 k. ft

8

The following distribution of wheel lands gives maximum moment figure (3-5). 13’

25.1 4k

6’

25.1 k

4’

25.1 k

6’

25.1 4 k 2’

31 96k

Fig. (3-5) Distribution of wheel lands


20

Chapter Three

Design

ML.L = 100.56 (31) – 2514 (2 + 8 + 12 + 18) = 2112 k. ft Impact 

50  0.267 < 0.3 62  125

M impact = 0.267 * 2112 = 564 k. ft M total = 564 + 2112 + 2215.105 = 4891.105 k. ft

S required 

4891.105 *12000  2934.66in 3 20000

Use W 36 * 848 Use plate 1* 4 on the flange of W shape S = 3170 in3

I = 67400 + 4*1* (21.72)2 = 69288 in4

d = 42.45 in

, t w = 2.52 in

L EI 30000 * 69288    15M L. L * L 15 (2676) (62) = 835.23 > 800

Check shear VD.L 

4.61* 62  142.92k 2

VL.L = 0.761 (100.56) = 76.52 k V impact = 0.267 (76.52) = 20.4 k V total = 142.92 + 76.52 +20.4 = 239.86 k 239.86 FV   2.24ksi < 12 ksi 42.45 * 2.52


21

Chapter Three

Design

3.4 Design of truss

Fig. (3-6) Component of a through – truss bridge

3.4.1 Dead load on truss Slab D.L = Curb 

7 150 * * 31  2.71 k / ft 12 1000

7 150 *6*  0.525 k / ft 12 1000

Railing estimate = 0.01 k /ft

Stringer * 0.145  0.652 k / ft truss Floor beam  3.76 k / ft *12  1.289 k / ft 35' Super imposed dead load = 5.2 k / ft Stringer  4.5

3.4.2 Live load distribution on truss The maximum reaction on truss may be obtained according to (figure 3-7) as follows: L.L truss



Lane (14  26  39  51) Lanes  2.1 62 truss


22

Chapter Three

6’

Design

10'

2’

10

3’

2’

10

10

3’

6

14 26 39 51

Fig. (3-7) Live load distribution on truss

Lane in truss: Uniform lane load = 2.1 * 0.64 = 1.344 k/ft Concentrated lane load = 2.1 (18) = 37.8 k

50  0.145  0.3 210  125 37.8 37.8 Super imposed live load  1.344   0.149 [1.344  ] 35' 35 = 2.785 k/ft Impact for 210 ft 

Total superimposed load = 2.785 + 5.2 = 7.985 k / ft

Estimate truss weight W L

W 7.985  210  * 1000 d 9

=1097.2 k/ft Bottom panel  5.2  Top panel 

1.0972  5.75 k / ft 2

1.0972  0.548k / ft 2


23

Chapter Three

Design

3.4.3 Influence line of members The following I.L of the selected truss is of (Pratt type). U1

(-) Comp. (+) Tens.

U2

U3

U4

U5

40 ft

L0

L1

L2

L3

L4

L5

L6

6 @ 35 ft = 210 ft I.L for U1U2

A=-122.43

A=-137.76

1.166

I.L for U2U3 U3U4 1.312

A=-122.43

I.L for U4U5 1.166

I.L for U1L0

A=-116.6

1.11

I.L for U5L6

A=-116.6 0.73 1.11

I.L for L0L1 L1L2

A=76.7 1.166

I.L for L2L3

A=122.43 1.166

I.L for L3L4

A=122.43 0.73

I.L for L4L5 L5L6

A= 76.7


24

Chapter Three

Design

1.0

I.L for U1L1

A= 35 1/3 A= 14 A=-31.5 14’

I.L for U2L2 -1/2

ZERO

I.L for U3L3 1/3

I.L for U4L3

A= 14 A=-31.5 -1/2

14’ 1.0

A= 35

6.89

I.L for U5L5

0.876

I.L for U1L2

A= 73.6 A=-4.61 0.66

-0.22

I.L for U2L3

A= 40.0 A=-19.7 -0.44

15.7’ 0.66

I.L for U4L3

A= 40.0 A=-19.7 15.7’

-0.44 0.876

6.89

I.L for U5L4

A= 73.6 A=-4.61 -0.22

Fig. (3-8)


25

Chapter Three

Design

3.4.4 Forces in truss due to lane loading Uniform lane load = 1.344 k / ft Concentrated lane load = 37.8 k Impact load percentage = 0.149

U1U2 LL = -[1.344 (122.43) + 1.166 (37.8)] = -208.6 k I = -[0.149 (208.6)] = - 31.1 k

U2U3 LL = -[1.344 (137.76) + 1.312 (37.8)] = -234.7 k I = -[0.149 (234.7)] = - 34.97 k

U1L0 LL = -[1.344 (116.6) + 1.11 (37.8)] = -198.67 k I = -[0.149 (198.67)] = - 29.6 k

L0L1, L1L2 LL = [1.344 (76.7) + 0.73 (37.8)] = 130.7 k I = [0.149 (130.7)] = 19.47 k

L2L3 LL = [1.344 (122.43) + 1.166 (37.8)] = 208.6 k I = [0.149 (208.6)] = 31.1 k

U1L1 LL = [1.344 (35) + 1.0 (37.8)] = 84.24 k I = [0.149 (84.24)] = 12.64 k

U2L2 (+) LL = [1.344 (14) + 37.8 (1/3)] = 31.4 k Through Steel Truss Highway Bridge

26

Chapter Three

Design

I = [0.149 (31.4)] = 4.68 k (-) LL = [1.344 (31.5) + 37.8 (1/2)] = - 61.23 k I = [0.149 (- 61.23)] = - 9.12 k

U2L3 (+) LL = [1.344 (40.07) + 37.8 (0.664) = 78.95 k I = [0.149 (78.95)] = 11.76 k (-) LL = [1.344 (19.74) + 37.8 (0.442)] = - 43.18 k I = [0.149 (43.18)] = - 6.43 k

U1L2 (+) LL = [1.344 (73.6) + 37.8 (0.876)] = 132.03 k I = [0.149 (132.03)] = 19.67 k (-) LL = [1.344 (4.617) + 37.8 (0.22)] = - 14.52 k I = [0.149 (14.52)] = - 2.16 k

3.4.5 Force in truss due to dead load WD.L = 5.75 k/ ft

U1U2: DL = 5.75 (122.43) = -704 k U2U3: DL = 5.75 (137.76) = -792.12 k U1L0: DL = 5.75 (116.6) = -670.45 k L0L1, L1L2: DL = 5.75 (76.7) = 441.025 k L2L3: DL = 5.75 (122.4) = 704 k U1L1: DL = 5.75 (35) = 201.25 k U2L2: DL = 5.75 (14) = 80.5 k

= - 100.62 k

= 5.75 (31.5) = -181.12 k


27

Chapter Three

Design

U1L1: DL = 5.75 (40.07) = 230.4 k

= 116.9 k

= 5.75 (19.74) = - 113.5 k

U1L1: DL = 5.75 (73.6) = 423.2 k

= 396.66 k

= 5.75 (4.617) = -26.54 k

Table (3-1) Force in truss due to lane load Force in truss U1U2 U2U3 U1L0 L0L1 , L1L2 L2L3 U1L1 U2L2 U2L3 U1L2

Lane load -208.6 -234.7 -198.67 130.7 208.6 84.24 31.4 -61.25 78.95 -43.18 132.03 -14.52

Impact load -31.1 -34.97 -29.6 19.47 31.1 12.64 4.68 -9.12 11.76 -6.43 19.67 -2.16

Table (3-2) Force in truss due to dead load Force in truss U1U2:D.L U2U3:D.L U1L0:D.L L0L1, L1L2:D.L L2L3:D.L U1L1:D.L U2L2:D.L U2L3:D.L U1L2:D.L

Dead load -704 -792.12 -670.45 441.025 704 201.25 -100.62 116.9 396.66


28

Chapter Three

Design

When the combination process has made between forces resulting from the live and dead load, then the member subjected to reversal stresses must be designed according to final stress for combination or both of them. The following figure shows the final forces. U1

L =-198.67 I =-29.6 D =-670.45 T =-898.72

L0

L =130.7 I =19.47 D =441.025 T =591.2

L =84.24 I =12.64 D =201.25 T =298.13

L1

L =-208.6 I =-31.1 D =-704 T =-943.7

L =132.03 I =19.67 D =396.6 T =548.3

L =130.7 I =19.47 D =441.025 T =591.2

U2

L =61.23 I =-9.12 D =-100.6 T =-170.95

L2

L =-234.7 I =-34.97 D =-792.12 T =-1061.7

L =78.95 I =11.76 D =116.9 T =207.61

L =208.6 I =31.1 D =704 T =943.7

U3

0

L3

Fig. (3-9): Final stresses for live & dead load combination


29

Chapter Three

Design

Selection of truss member 1)

Design of tension member Allowable tension = 20.000 Psi Max KL = 200

,

K=1

(AASHTO specification)

r Member L0L1 591.2 Design 35 Length 2.1 rmin. 27.37 A g (in2) 2 23.26 A eff (in ) W24*104 Section Asec >Aeff 30.6>23.2 144.2 L/rsec.23.4 144.2

L2L3 U1L1 943.7 298.13 35 40 2.1 2.4 43.69 13.802 37.136 11.73 W24*131 W24*104 38.5>37.1 30.6>11.7 141.41 144.2

U1L2 548.3 53.15 3.19 25.4 21.59 W24*492 144>21.59 187

Table (3-3)

Example for calculation of the table above (3-3) L0L1 = 591.2 k Length = 35 ft Ag

591.2  27.37 0.6 * 36 A eff = 0.85 * 27.37 = 23.26 

rmin 

35 *12  2.1 200

Try section W 24*104

, A=30.6 > A efff = 23.26 , r = 2.91

L 35 *12   144.32 < 200 (ok) r 2.91


30

U2L3 207.61 53.15 3.19 9.61 8.2 W24*492 144>8.2 198.8

Chapter Three

Design

Design of compression member member L0L1 U1U2 U2U3 U2L2

Design Force (k) 898.72 943.7 1061.7 170.95

Length (ft)

A trial

section

KL/r

Fa

A