DESIGN LOADS (2012)

a. General.

E_b = ratio of area of bars cut off to total area of bars at the section. See Article 2.13.1

E_c = ratio of long side to short side of concentrated load or reaction area. See Article 2.29.6andArticle 2.35.6

E_d = ratio of maximum factored axial dead load to maximum total factored axial load, where the load is due to gravity effects only in the calculation of P_c in EQ 2-43, or ratio of the maximum factored sustained lateral load to the maximum total factored lateral load in that level in the calculation of P_c in EQ 2-43. See Article 2.34.2

E₁ = a factor defined in Article 2.31.1

G_b = Moment magnification factor for members braced against sidesway to reflect effects of member curvature between ends of compression member.

G_s = Moment magnification factor for members not braced against sidesway to reflect lateral drift resulting from lateral and gravity loads.

O = correction factor related to unit weight of concrete. See Article 2.29.4 and Article 2.35.4

P = coefficient of friction. See Article 2.29.4 and Article 2.35.4

U = tension reinforcement ratio = A_s/bd Uc = compression reinforcement ratio = Ac_s/bd

U_b = reinforcement ratio producing balanced strain conditions. See Article 2.32.1

U_s = ratio of volume of spiral reinforcement to total volume of core (out-to-out of spirals) of a spirally reinforced compression member. See Article 2.11.2

U_v = ratio of tie reinforcement area to area of contact surface

U_w = reinforcement ratio (As/bwd) used in EQ 2-15 and EQ 2-46. See Article 2.29.2 and Article 2.35.2

) = strength reduction factor. See Article 2.30.2

Compressive Strength of Concrete (fc_c) Nominal Strength

Deformed Reinforcement Plain Reinforcement

Design Load Required Strength

Design Strength Service Load

Development Length Spiral

Embedment Length Stirrups or Ties

Embedment Length, Equivalent (l_e) Yield Strength or Yield Point (f_y)

End Anchorage Concrete, Structural Lightweight

(1) The following loads and forces shall be considered in the design of railway concrete structures supporting tracks:

(2) Each member of the structure shall be designed for that combination of such loads and forces that can occur simultaneously to produce the most critical design condition as specified in Article 2.2.4.

b. Dead Load.

(1) The dead load shall consist of the estimated weight of the structural member, plus that of the track, ballast, fill, and other portions of the structure supported thereby.

(2) The unit weight of materials comprising the dead load, except in special cases involving unusual conditions or materials, shall be assumed as follows:

• Track rails, inside guardrails and fastenings – 200 lb per linear foot of track. (3kN/m) • Ballast, including track ties – 120 lb per cubic foot. (1900 kg/m3)

• Reinforced concrete – 150 lb per cubic foot. (2400 kg/m3) • Earthfilling materials – 120 lb per cubic foot. (1900 kg/m3) • Waterproofing and protective covering – estimated weight. c. Live Load.

(1) The recommended live load for each track of main line structure is Cooper E 80 (EM 360) loading with axle loads and axle spacing as shown in Figure 8-2-1. On branch lines and in other locations where the loading is limited to the use of light equipment, or cars only, the live load may be reduced, as directed by the engineer. For structures wherein the material in the primary load-carrying members is not concrete, the E loading used for the concrete design shall be that used for the primary members.

(2) The axle loads on structures may be assumed as uniformly distributed longitudinally over a length of 3 feet (900 mm), plus the depth of ballast under the tie, plus twice the effective depth of slab, limited, however, by the axle spacing.

(3) Live load from a single track acting on the top surface of a structure with ballasted deck or under fills shall be assumed to have uniform lateral distribution over a width equal to the length of track tie plus the depth of ballast and fill below the bottom of tie, unless limited by the extent of the structure.

D = Dead Load F = Longitudinal Force due to Friction or

Shear Resistance at Expansion Bearings

L = Live Load

I = Impact

CF = Centrifugal Force EQ = Earthquake (Seismic)

E = Earth Pressure SF = Stream Flow Pressure

B = Buoyancy ICE = Ice Pressure

W = Wind Load on Structure OF = Other Forces (Rib Shortening, Shrinkage,

Temperature and/or Settlement of Supports)

WL = Wind Load on Live Load

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(4) The lateral distribution of live load from multiple tracks shall be as specified for single tracks and further limited so as not to exceed the distance between centers of adjacent tracks.

(5) The lateral distribution of the live load for structures under deep fills carrying multiple tracks, shall be assumed as uniform between centers of outside tracks, and the loads beyond these points shall be distributed as specified for single track. Widely separated tracks shall not be included in the multiple track group.

(6) In calculating the maximum live loads on a structural member due to simultaneous loading on two or more tracks, the following proportions of the specified live load shall be used:

• For two tracks – full live load,

• For three tracks – full live load on two tracks and one-half on the other track,

• For four tracks – full live load on two tracks, one-half on one track, and one-fourth on the remaining track. (7) The tracks selected for full live load in accordance with the listed limitations shall be those tracks which will

produce the most critical design condition on the member under consideration. d. Impact Load.1

(1) Impact forces, applied at the top of rail, shall be added to the axle loads specified. For rolling equipment without hammer blow (diesels, electric locomotives, tenders alone, etc.), the impact shall be equal to the following percentages of the live load:

(U.S. Customary)

Figure 8-2-1. Cooper E 80 (EM 360) Axle Load Diagram

For L

d

14 feet I = 60

For 14 feet < L

d

127 feet I =

For L > 127 feet I = 20

(Metric)

Where L is the span length in feet (meters).

This formula is intended for ballasted-deck spans and substructure elements as required.

(2) For continuous structures, the impact value calculated for the shortest span shall be used throughout.

(3) Impact may be omitted in the design for massive substructure elements which are not rigidly connected to the superstructure.

(4) For steam locomotives with hammer blow, the impact calculated according to Article 2.2.3d(1) shall be increased by 20%.

e. Centrifugal Force.

(1) On curves, a centrifugal force corresponding to each axle load shall be applied horizontally through a point 8 feet (2450 mm) above the top of rail measured along a line perpendicular to the line joining the tops of the rails and equidistant from them. This force shall be the percentage of the live load computed from the formulas below. (2) On curves, each axle load on each track shall be applied vertically through the point defined in the first paragraph

of this article.

(3) The greater of loads on high and low sides of a superelevated track shall be used for the design of supports under both sides.

(4) The relationships between speed, degree of curve, centrifugal force and a superelevation which is 3 inches (75 mm) less than that required for zero resultant flange pressure between wheel and rail are expressed by the formulas:

EQ 2-3

where:

C = Centrifugal force in percentage of the live load

D = Degree of curve (Degrees based on 100 foot (30 m) chord)

For L

d

4 meters I = 60

For 4 meters < L

d

39 meters I =

For L > 39 meters I = 20 125e L C = 0.00117 S2D EQ 2-1 C = 0.000452 S2D EQ 2-1M E = 0.0007 S2D – 3 EQ 2-2 E = 0.0068 S2D – 75 EQ 2-2M S E 3+ 0.0007D --- = S E 75+ 0.0068D --- = EQ 2-3M

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f. Earth Pressure. Earth pressure forces to be applied to the structure shall be determined in accordance with the

provisions of Part 5 Retaining Walls, Abutments and Piers.

g. Buoyancy. Buoyancy shall be considered as it affects the design of either substructure, including piling, or the superstructure.

h. Wind Load on Structure. The base wind load acting on the structure is assumed to be 45 lb per square foot (2160 Pa) on the vertical projection of the structure applied at the center of gravity of the vertical projection in any horizontal direction. A base wind velocity of 100 miles per hour (160 km/h) was used to determine the base wind load. If an increase in the design wind velocity is made, the design wind velocity and design wind load shall be shown on the plans.

For Group II and Group V loadings, when a design wind velocity greater than 100 miles per hour (160 km/h) is advisable the base wind load may be increased by the ratio of the square of the design wind velocity to the square of the base wind velocity. This increase shall not apply to Group III and Group VI Loadings.

i. Wind Load on Live Load. A wind load of 300 lb per linear foot (4.4 kN/m) on the train shall be applied 8 feet (2450

mm) above the top of rail in a horizontal direction perpendicular to the centerline of the track. j. Longitudinal Force.1

(1) The longitudinal force for E-80 (EM-360) loading shall be taken as the larger of:

– Force due to braking, as prescribed by the following equation, acting 8 feet (2450 mm) above top of rail.

– Force due to traction, as prescribed by the following equation, acting 3 feet (900 mm) above top of rail.

For design of superstructure elements, L shall be taken as the length in feet (meters) of the span under consideration. For design of substructure elements, L shall be as follows:

– Where rail is continuous across the bridge, or where load transfer devices that are approved by the Engineer are employed at discontinuities in the rail, L shall be the total bridge length in feet (meters). Longitudinal force shall be distributed to individual substructure units as described in Article 2.2.3(j)(2) below.

– Where rail is not continuous across the bridge, and approved load transfer devices are not employed, L shall be taken as the length in feet (meters) of each bridge segment with rail continuity. The substructure units for each segment shall be evaluated and the longitudinal force computed for that segment shall be distributed to individual substructure units as described in Article 2.2.3(j)(2) below.

E = Actual superelevation in inches (mm) S = Permissible speed in miles per hour (km/hr)

Longitudinal braking force (kips) = 45 + 1.2L (Longitudinal braking force (kN) = 200 + 17.5L)

Longitudinal traction force (kips) (Longitudinal traction force (kN)

25 L =

200 L

– For design loads other than E-80 (EM-360), these forces shall be scaled proportionally. The points of force application shall not be changed.

(2) The effective longitudinal force shall be distributed to the various components of the supporting structure, taking into account their relative stiffness. The resistance of the backfill behind the abutments shall be utilized where applicable. The mechanisms (rail, bearings, load transfer devices, etc.) available to transfer the force to the various components shall also be considered.

(3) The longitudinal deflection of the superstructure due to longitudinal force computed in (1) above shall not exceed 1 inch (25 mm) for E-80 (EM 360) loading. For design loads other than E-80 (EM 360), the maximum allowable longitudinal deflection shall be scaled proportionally. In no case, however, shall the longitudinal deflection exceed 1-1/2 inches (38 mm).

k. Longitudinal Force Due to Friction or Shear Resistance at Expansion Bearings. Provisions shall be made to accommodate forces due to friction or shear resistance due to expansion bearings.

l. Earthquake. In regions where earthquakes may be anticipated, structures may be designed to resist earthquake motions

by considering the relationship of the site to active faults, the seismic response of the soils at the site, and the dynamic response characteristics of the total structure. Refer to Chapter 9 Seismic Design for Railway Structures for additional guidance.

m. Stream Flow Pressure. All piers and other portions of structures which are subject to the force of flowing water or drift shall be designed to resist the maximum stresses induced thereby.

(1) Stream Pressure

The effect of flowing water on piers and drift build up, assuming a second-degree parabolic velocity distribution and thus a triangular pressure distribution, shall be calculated by the formula:

Pavg = K(Vavg)2 EQ 2-4

where:

The maximum stream flow pressure, P_max, shall be equal to twice the average stream flow pressure, P_avg,

computed by EQ 2-4. Stream flow pressure shall be a triangular distribution with P_max located at the top of water elevation and a zero pressure located at the flow line.

(2) The stream flow forces shall be computed by the product of the stream flow pressure, taking into account the pressure distribution, and the exposed pier area. In cases where the corresponding top of water elevation is above the low beam elevation, stream flow loading on the superstructure shall be investigated. The stream flow pressure acting on the superstructure may be taken as P_max with a uniform distribution.

(3) Pressure Components

P_avg = average stream pressure, in pounds per square foot, (Pa)

V_avg = average velocity of water in feet per second, (m/s) computed by dividing the flow rate by the flow area,

K = a constant, being 1.4 (or 725 for metric) for all piers subjected to drift build up and square-ended piers, 0.7 (or 360 for metric) for circular piers, and 0.5 (or 260 for metric) for angle-ended piers where the angle is 30 degrees or less.

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When the direction of stream flow is other than normal to the exposed surface area, or when bank migration or a change of stream bed meander is anticipated, the effects of the directional components of stream flow pressure shall be investigated.

(4) Drift Lodge Against Pier

Where a significant amount of drift lodge against a pier is anticipated, the effects of this drift build up shall be considered in the design of the bridge opening and the bridge components. The overall dimensions of the drift build up shall reflect the selected pier locations, site conditions, and known drift supply upstream. When it is anticipated that the flow area will be significantly blocked by drift build up, increases in high water elevations, stream velocities, stream flow pressures, and the potential increases in scour depths shall be investigated. n. Ice Pressure. The effects of ice pressure, both static and dynamic, shall be accounted for in the design of piers and

other portions of the structure where, in the judgment of the Engineer, conditions so warrant.

(1) General. Ice forces on piers shall be selected having regard to site conditions and the mode of ice action to be expected. Consideration shall be given to the following modes:

(a) dynamic ice pressure due to moving ice sheets and floes carried by streamflow, wind or currents; (b) static ice pressure due to thermal movements of continuous stationary ice sheets onlarge bodies of water; (c) static pressure resulting from ice jams;

(d) static uplift or vertical loads resulting from adhering ice in waters of fluctuating level.

The expected thickness of ice, the direction of its movement, and the height at which it acts shall be determined by field investigations, published records, aerial photography and other means. Consideration shall be given to the worst expected combination of height, thickness and pressure, to the possibility of unusual thicknesses resulting from special circumstances or operations, and to the natural variability of ice conditions from year to year. (2) Dynamic Ice Pressure. Horizontal forces resulting from the pressure of moving ice are to be calculated by the

formula:

F = Cnptw EQ 2-5

where:

Table 8-2-1. Coefficient for Nose Inclination F = horizontal ice force on pier; pounds (N)

C_n = coefficient for nose inclination from Table 8-2-1; p = ice pressure as indicated below; psi (MPa)

t = thickness of ice in contact withpier; inches (mm)

w = width of pier or diameter of circular-shaft pier at the level of ice action; inches (mm)

Inclination of Nose to Vertical Cn

0 degrees to 15 degrees 1.00

15 degrees to 30 degrees 0.75

(3) The ice pressure “p” shall normally be taken in the range of 100 psi (0.7 MPa) to 400 psi (2.8 MPa) on the assumption that crushing or splitting of the ice takes place on contact with the pier. The value used shall be based on an assessment of the probable condition of the ice at time of movement, on previous local experience, and on assessment of existing structure performance. Relevant ice conditions include the expected temperature of the ice at time of movement, the size of moving sheets and floes and the velocity at contact. Due consideration shall be given to probability of extreme rather than average conditions at the site in question.

NOTE: The following values of ice pressure appropriate to various situations may be used as a guide:

(a) In the order of 100 psi (0.7 MPa) where break-up occurs at melting temperatures and where the ice runs as small “cakes” and is substantially disintegrated in its structure;

(b) In the order of 200 psi (1.4 MPa) where break-up occurs at melting temperatures, but the ice moves in large pieces and is internally sound;

(c) In the order of 300 psi (2.1 MPa) where at break-up there is an initial movement of the ice sheet as a whole or where large sheets of sound ice may strike the piers;

(d) In the order of 400 psi (2.8 MPa) where break-up or major ice movement may occur with ice temperature significantly below the melting point.

(4) The ice pressure values listed above apply to piers of substantal mass and dimensions. The values shall be modified as necessary for variations inpier width or pile diameter, and design ice thickness by multiplying by the appropriate coefficient obtained from Table 8-2-2.

Table 8-2-2. Coefficient for Design Ice Thickness

where:

(5) Piers should be placed with their longitudinal axes parallel to the principal direction of ice action. The force calculated by the formula shall then be taken to act along the direction of the long axis. A force transverse to the longitudinal axis and amounting to not less than 15% of the longitudinal force shall be considered to act

simultaneously.

(6) Where the longitudinal axis of a pier cannot be placed parallel to the principal direction of ice action, or where the direction of ice action may shift, the total force on the pier shall be figured by the formula and resolved into vector components. In such conditions, forces transverse to the longitudinal axis of the pier shall in no case be taken as less than 20% of the total force.

b/t Coefficient 0.5 1.8 1.0 1.3 1.5 1.1 2.0 1.0 3.0 0.9 4.0 or greater 0.8

b = width of pier or diameter of pile; t = design ice thickness.

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(7) In the case of slender and flexible piers, consideration should be given to the vibrating nature of dynamic ice forces and to the possibility of high momentary pressures and structural resonance.

(8) Ice pressure on piers frozen into ice sheets on large bodies of water shall receive special consideration where there is reason to believe that the ice sheets are subject to significant thermal movements relative to the piers.

o. Other Forces (Rib Shortening, Shrinkage, Temperature and/or Settlement of Supports).

(1) The structure shall be designed to resist the forces caused by rib shortening, shrinkage, temperature rise and/or drop and the anticipated settlement of supports.

(2) The range of temperature shall generally be as shown in Table 8-2-3.

In document AREMA MRE Chapter 8 2015.pdf (Page 99-107)