## 1124 Stringer Or Girder Spacing

One of the major factors affecting the economy of highway bridges with a concrete deck on stringers or longitudinal girders is spacing of the main members. Older bridges typically had spacing of 8 ft or less. Now, however, longer concrete-deck spans (up to 15 ft) are practicable through use of such devices as stay-in-place metal or precast-concrete forms. This makes possible fewer girders. (To eliminate the potential for fracture criticality when I-shape girders are used, there should be at...

## Gj

The factor GJ L represents the stiffness of the member in resisting twisting loads. It gives the magnitude of a torque needed to produce a unit rotation. Noncircular shafts behave differently under torsion from the way circular shafts do. In noncircular shafts, cross sections do not remain plane, and radial lines through the centroid do not remain straight. Hence the direction of the shear stress is not normal to the radius, and the distribution of shear stress is not linear. If the end...

## 810 Lightweight Steel Framing

Cold-formed steel structural members can provide an extremely lightweight floor framing system. These members, usually C or Z shapes, are normally spaced 24 in center to center (c to c) and can span up to about 30 ft between supports. Because of their light weight, these members can be handled and installed easily and quickly. Connections of cold-formed members are usually accomplished by welding or by the use of self-drilling screws. This type of floor-framing system is frequently used in...

## 1162

FIGURE 12.68 Maximum moments in interior stringer S2. With an allowable bending stress of 20 ksi, the cover-plated beam must provide a section modulus of at least _ 2,740 X 12 . 3 S -20- 1,644 in3 Try a W36 X 280. It provides a moment of inertia of 18,900 in4 and a section modulus of 1,030 in3, with a depth of 36.50 in. The cover plates must increase this section modulus by at least 1,644 - 1,030 614 in3. Hence, for an assumed distance between plates of 37 in, area of each plate should be about...

## 149 Guidelines For Preliminary Designs And Estimates

The usual procedure followed by most designers in preliminary designs of bridges involves the following steps 1. Preliminary layout of structure 2. Preliminary design of floor system and calculation of weights and dead load 3. Preliminary layout of bracing systems and estimates of weights and loads 4. Preliminary estimate of weight of main load-bearing structure 6. Check of initial assumptions for dead load Preliminary Weight of Arch. The ratios given in Art. 14.6 can guide designers in making...

## L

FIGURE 3.74 Calculation of end rotations of a simple beam by the unit-load method. (a) Moment applied at one end. (b) Bending-moment diagram for the applied moment. (c) Unit load applied at end where rotation is to be determined. (d) Bendingmoment diagram for the unit load. FIGURE 3.74 Calculation of end rotations of a simple beam by the unit-load method. (a) Moment applied at one end. (b) Bending-moment diagram for the applied moment. (c) Unit load applied at end where rotation is to be...

## 410 Cable Suspension Systems

Single cables, such as those analyzed in Art. 4.9, have a limited usefulness when it comes to building applications. Since a cable is capable of resisting only tension, it is limited to transferring forces only along its length. The vast majority of structures require a more complex ability to transfer forces. Thus it is logical to combine cables and other load-carrying elements into systems. Cables and beams or trusses are found in combination most often in suspension bridges (see Sec. 15),...

## 95 Dynamic Method Of Seismic Load Distribution

The Uniform Building Code'' static-force method (Art. 9.4) is based on a single-mode response with approximate load distributions and corrections for higher-mode response. These simplifications are appropriate for simple. regular structures. However, they do not consider the full range of seismic behavior in complex structures. The dynamic method of seismic analysis is required for many structures with unusual or irregular geometry, since it results in distributions of seismic design forces...

## 99 Member And Connection Design For Lateral Loads

Wind loads on steel structures are determined by first establishing the pressure distributions on structures after considering the appropriate design wind velocity, the exposure condition, and the local variation of wind pressure on the structure (Art. 9.2). Then, the wind loads on frames and structural elements are determined by distributing the wind pressure in accordance with the tributary areas and relative stiffness of the various components. Seismic design loads are determined by the...

## Info

FIGURE 12.10 Position of loads for maximum shear 25 ft from the support. FIGURE 12.10 Position of loads for maximum shear 25 ft from the support. FIGURE 12.11 Shear connector spacing along the top flange of a strinser. FIGURE 12.11 Shear connector spacing along the top flange of a strinser. Deflections. Dead-load deflections may be needed so that concrete for the deck may be finished to specified elevations. Cambering of rolled beams to offset dead-load deflections usually is undesirable...

## 2

Source Adapted from AREMA Manual, American Engineering and Maintenance-of-Way Association, 8201 Corporate Drive, Suite 1125, Landover, MD 20785-2230. Source Adapted from AREMA Manual, American Engineering and Maintenance-of-Way Association, 8201 Corporate Drive, Suite 1125, Landover, MD 20785-2230. assumed that the structure has been designed for specified loadings in accordance with recognized acceptable practices. As indicated in Table 11.32, the number of stress cycles specified for the...

## 1135 Design Loadings

Bridges must be designed to carry the specified dead loads, live loads and impact, as well as centrifugal, wind, other lateral loads, loads from continuous welded rail, longitudinal loads and earthquake loads. The forces and stresses from each of these specified loads should be a separate part of the design calculations. Also, because rail cars have changed in size and weight over the years and frequently are run in unit consists, the designer should be alert to live loadings that may be more...

## 11271 Minimum Steel Thickness

Because structural steel in bridges is exposed to the weather, minimum-thickness requirements are imposed on components to obtain a long life despite corrosion. Where steel will be exposed to unusual corrosive influences, the component should be increased in thickness beyond required thickness or specially protected against corrosion. In highway bridges, structural steel components, except railings, fillers, and webs of certain rolled shapes, should be at least 5 i6 in thick. Web thickness of...

## 616 Compression

Compressive forces can produce local or overall buckling failures in a steel member. Overall buckling is the out-of-plane bending exhibited by an axially loaded column or beam (Art. 6.17). Local buckling may manifest itself as a web failure beneath a concentrated load or over a reaction or as buckling of a flange or web along the length of a beam or column. Local buckling characteristics of the cross section of a member subjected to compression may affect its strength. With respect to potential...

## 21 Shop Detail Drawings

Bidding a structural fabrication project demands review of project requirements and assembly of costs. A take-off is made listing each piece of material and an estimate of the connection material that will be attached to it. An estimate of the labor to fabricate each piece is made. The list is sorted, evaluated, and an estimate of the material cost is calculated. The project estimate is the sum of material, fabrication labor, drafting, inbound and outbound freight, purchased parts, and...

## 1013 Concentrically Loaded Compression Members

These provisions are for members in which the resultant of all loads is an axial load passing through the effective section calculated at the stress Fn as subsequently defined. Concentrically loaded angle sections should be designed for an additional moment according to the AISI Specification. The slenderness ratio, KL r, of all compression members should preferably be limited to 200 (300 during construction). The nominal axial strength, Pn, is where Ae is the effective area at the stress Fn,...

## 15212 Criteria for Aerodynamic Design

Because the factor relating bridge movement to wind conditions depends on specific site and bridge conditions, detailed criteria for the design of favorable bridge sections cannot be written until a large mass of data applicable to the structure being designed has been accumulated. But, in general, the following criteria for suspension bridges may be used A truss-stiffened section is more favorable than a girder-stiffened section. Deck slots and other devices that tend to break up the...

## 21

Tool to the drafter, but other software calculates geometric and mechanical properties for the connections. Work is underway to promote a standard computer interface for design and detail information. The detailer works from the engineering and architectural drawings and specifications to obtain member sizes, grades of steel, controlling dimensions, and all information pertinent to the fabrication process. After the detail drawings have been completed, they are meticulously checked by an...

## A27

FIGURE 9.18 Forces at midspan of beams and midheight of columns in the frame of Fig. 9.17 as determined by the portal method. Setting the sum of the vertical forces equal to zero gives Setting the sum of the horizontal forces equal to zero results in A1 25 - 4.17 20.83 For the central top subassemblage 2 (S + S2) 8.33 h or S2 h (8.33 - 4.17) 4.16 y (9.42) The remaining axial and shear forces can be determined by this procedure, and bending moments can be determined directly from these forces...

## S7

1.22 wheel loads 0.61 axle loads Maximum moment induced in a 20-ft span by a standard HS20 truck load is 160 ft-kips. Hence, the maximum live-load moment in S1 is TABLE 12.45 Dead Load on S1, kips per ft Railing 0.070 X 9.83 7 0.098 Sidewalk 0.150 X 1 X 3 X 8 7 0.514 Slab 0.150 X 8 X 7.5 12 X 4 7 0.428 Stringers, brackets, framing details assume 0.110 Maximum shear caused by the truck is 41.6 kips. Therefore, maximum live-load shear in S1 is Impact for a 20-ft span is 30 of live-load stress....

## 710 Examplelrfd For Floorbeam With Unbraced Top Flange

A beam of grade 50 steel with a span of 20 ft is to support the concentrated load of a stub pipe column at midspan. The factored concentrated load is 55 kips. No floor deck is present on either side of the beam to brace the top flange, and the pipe column is not capable of bracing the top flange laterally. The weight of the beam is assumed to be 50 lb ft. Mu 55 x 20 4 + 0.050 x 202 8 277.5 kip-ft A beam size for a first trial can be selected from a load-factor design table for steel with Fy 50...

## Lower Cable

FIGURE 4.17 Forces acting at joints of a cable system with spreaders. bending moment at the low point equal to zero. Similarly, the cable and spreader forces at adjoining joints (joint 2, Fig. 4.17b and d) can be determined. Suppose now vertical loads are applied to the system. They can be resolved into concentrated vertical loads acting at the nodes, such as the load P at a typical joint Ob of the bottom cable, shown in Fig. 4.18b. The equations of Art. 4.9 can be used for the purpose. The...

## 1114 Criteria For Builtup Compression Members

Compression members should be designed so that main components are connected directly to gusset plates, pins, or other members. Stresses should not exceed the allowable for the gross section. The radius of gyration and the effective area of a member with perforated cover plates should be computed for a transverse section through the maximum width of perforation. When perforations are staggered in opposite cover plates, the effective area should be considered the same as for a section with...

## 0330e

The strength of rectangular sections in the slenderness range between compact and non-compact is expressed in terms of the plastic moment Mp and the yield moment Mr _ FyS. where Seff is the effective section modulus with the effective width of the compression flange taken as

## 11444 Considerations for Flanges

Where not fully supported laterally, the compression flange of a flexural member should be supported at points so that the ratio of the distance between points and radius of gyration of the flange plus the part of the web on the compression side of the neutral axis does not exceed 29,000 Wy, where Fy is the yield point of the material, psi. In open deck construction, ties may be seated on the top flange. Tie deflection loads the flange non-uniformly with the passage of each wheel. The minimum...

## 11452 End Bearings

In accord with current practice, spans more than 70 ft long should have hinged bearings at both ends and rollers or rockers at the expansion end. Spans 70 ft or less should be designed to slide on self-lubricating bronze plates at least V2 in thick. All end bearings should be secure against lateral and vertical movement and, when founded on masonry, should be raised above the seat on metal bolsters or pedestals. New provisions are being developed by a committee of AREMA established to formulate...

## 1494 6585

The maximum bending-stress range in the gross section of the web splice plates then is Fatigue in base-metal gross section at high-strength-bolted, slip-critical connections is classified by AASHTO as category B. For a redundant-load-path structure and 2,000,000 loading cycles, the allowable stress range is 18 ksi > 11.80 ksi. Thus, the two 27 X 3 8-in plates are satisfactory for fatigue. Stringer Flange Splice. Each stringer flange is spliced with a V2-in-thick plate on the outer surface and...

## 112

D is the diameter of the bolt (in) and fp is the computed bearing stress due to the service load (ksi). Maximum edge distances are set for sealing and stitch purposes. AISC specifications limit the distance from center of fastener to nearest edge of parts in contact to 12 times the thickness of the connected part, with a maximum of 6 in. The AASHTO maximum is 5 in or 8 times the thickness of the thinnest outside plate. (AISC gives the same requirement for unpainted weathering steel.) The AREMA...

## Vq 733 X 141

The allowable stress on the weld is 18.9 ksi. So the allowable load per weld is 18.9 X 0.707 13.4 kips per in, and for two welds, 26.7 kips per in. Therefore, the weld size required is 5.30 26.7 0.20 in. Use 1 4-in fillet welds. Floorbeam Connections to Girders. Since the bottom flange of the floorbeam is in compression, it can be connected to the inner web of each box girder with a splice plate of the same area. Use a 10 X 2-in plate, shop-welded to the girder and field-bolted to the...

## 722 ASD for Double Angle Hanger

The dead load on the hanger is 55 kips, and the live load plus impact is 45 x 1.33 60 kips (Art. 7.2.1). The total axial tension then is 55 + 60 115 kips. With the allowable tensile stress on the gross area of the hanger F1 0.6Fy 0.6 x 36 21.6 ksi, the gross area Ag required for the hanger is With the allowable tensile stress on the effective net area Ft 0.5Fu 0.5 x 58 29 ksi, Two angles 5 X 3 X 3 8 in provide Ag 5.72 in2 > 5.32 in2 OK. For 1-in-diameter bolts in holes 1 46 in in diameter,...

## 103

Combined, centrifugal forces and wind induce in G2 a maximum shear This is less than 25 of the total shear without these forces and may be ignored. Similarly, the combined maximum moment in G1 is This is less than 25 of the total moment without these forces and may be ignored. The maximum moments and shears for design therefore are as given in Tables 22.36 and 22.37. TABLE 12.33 V-Load Reactions, kips, and Final Midspan Moments Mn for Truck in One Lane Only, ft-kips Rv 1.33 x 5 6 + 2.67 x 4 6 +...

## 52

Stresses in the concrete are determined with the section moduli of the composite section with n 24 for SDL from Table 12.83a and n 8 for LL + I from Table 12.83b (Table 12.84). Since the bending stresses in steel and concrete are less than the allowable, the assumed steel section is satisfactory for the end span. Properties of Center-Span Section for Maximum Positive Moment. For maximum positive moment in the middle portion of the center span, the rolled beam will be made composite with the...

## 819 Plate Girders

For long spans or heavy loadings that exceed the capacity of standard rolled shapes, plate girders can be used. Plate girders are composed of individual steel plates that can vary in width, thickness, and grade of steel along their length to optimize the cross section. However, it is important to recognize that a minimum weight design is not always the most cost effective design. For example, it is often more economical to use a thicker web plate, rather than a thinner one with multiple...

## 7378

Podolny, Jr., and J. B. Scalzi, ''Construction and Design of Cable-Stayed Bridges,'' 2d ed., John Wiley & Sons, Inc., New York. f Stays No. 1, 2, and 3 combined into one back stay. Maximum live load. Per plane of a two-plane structure. * Reprinted with permission from W. Podolny, Jr., and J. B. Scalzi, ''Construction and Design of Cable-Stayed Bridges,'' 2d ed., John Wiley & Sons, Inc., New York. f Stays No. 1, 2, and 3 combined into one back stay....

## 624 Design Parameters For Tension Members

To prevent undue vibration of tension members, AISC specifications for ASD and LRFD suggest that the slenderness ratio LIr be limited to 300. This limit does not apply to rods. Tension members have three strength-limit states, yielding in the gross section, fracture in the net section, and block shear (see Table 6.17 and Art 6.15.3). For fracture in the net section, as defined by the AISC specifications, the critical net section is the critical cross section over which failure is likely to...

## 1 1

Where ID is the moment of inertia of girder AD. Similarly, the deflection of girder 9-9 at node 1 (Fig. 4.25d) equals (P - X1) + ( 1) (P - X4) + S9 (4.149) where I9 moment of inertia of girder 9-9 S9 deflection of girder AB at node 9 Girder AB carries the reactions of the interior girders spanning in the y direction (Fig. 4.25e) where IAB is the moment of inertia of girder AB. The equation for vertical displacement at node 1 is obtained by equating the right-hand side of Eqs. (4.147) and...

## 84 Metal Roof Deck

Steel-framed buildings often utilize a roof deck composed simply of metal deck. When properly sloped for drainage, the metal deck itself can serve as a watertight enclosure. Alternatively, roofing materials can be placed on top of the deck. In either case, diaphragm action can be achieved by proper sizing and attachment of the metal deck. A fire rating can be provided by applying spray-on fire protection to the underside of the roof deck, or by installing a fire-rated ceiling system below the...

## 12

The moment at C from the cantilever is MCD 12.50 ft-kips. If E 29,000 ksi, IAB 200 in4, and D 600 in4, then 2EIAB LAB 8055.6 ft-kips and 2EIbc Lbc 16,111.1 ft-kips. With dA 0, BA 0, and CB 0, Eq. (3.135) yields Mba 2 X 8,055.60b - 14.40 (3.137) Mbc 2 X 16,111.10B + 16,111.10C + 18.75 (3.138) Mcb 16,111.10B + 2 X 16,111.10C - 18.75 (3.139) Also, equilibrium of joints B and C requires that Substitution of Eqs. (3.137) and (3.138) in Eq. (3.140) and Eq. (3.139) in Eq. (3.141) gives 48,333.40 +...

## 225

*The shear stress fv, must also satisfy Table 10.7. Source Specification for the Design of Cold-Formed Steel Structural Members, American Iron and Steel Institute, Washington, DC, 1996, with permission. TABLE 10.11 Nominal Tension Stress, F'nt (MPa), for Bolts Subject to Combination of Shear and Tension LRFD Method* Threads not excluded Threads excluded from Resistance Description of bolts from shear planes shear planes factor A325 Bolts A354 Grade BD Bolts A449 Bolts A490 Bolts A307 Bolts,...

## 200

This is resisted by a couple compromising a downward vertical force on G1 and an upward vertical force on G3 By proportion, the maximum moment MC in G1 due to the centrifugal forces can be obtained from the maximum moment Mp1 previously computed for a truck load in lane 1, 1,340 ft-kips. Similarly, the maximum shear in G1 due to the centrifugal forces is

## 59 Minimum Number Of Fasteners

In buildings, connections carrying calculated stresses, except lacing, sag bars, and girts, should be designed to support at least 6 kips. In highway bridges, connections, including angle bracing but not lacing bars and handrails, should contain at least two fasteners. Web shear splices should have at least two rows of fasteners on each side of the joint. In railroad bridges, connections should have at least three fasteners per plane of connection. Long Grips. In buildings, if A307 bolts in a...

## 127 Effects Of Welding

Failures in service rarely, if ever, occur in properly made welds of adequate design. If a fracture occurs, it is initiated at a notchlike defect. Notches occur for various reasons. The toe of a weld may form a natural notch. The weld may contain flaws that act as notches. A welding-arc strike in the base metal may have an embrittling effect, especially if weld metal is not deposited. A crack started at such notches will propagate along a path determined by local stresses and notch toughness of...

## 1510 Cablesuspended Bridges For Rail Loading

Because of flexibility and susceptibility to vibration under dynamic loads, pure suspension bridges are rarely constructed for railway spans. They are sometimes used, however, where dead load constitutes a relatively large proportion of the total load. Where provisions for both railway and highway traffic is necessary, as for the future extension of the Salazar Bridge (Fig. 15.7), the addition of inclined cable stays from the pylon to the stiffening girder is advantageous or a cable-stayed...

## 169

(Fractional parts of design lanes are not used.) Roadway widths from 20 to 24 ft, however, should have two design lanes, each equal to one-half the roadway width. Truck and lane loadings are assumed to occupy a width of 10 ft placed anywhere within the design lane to produce maximum effect. If curbs, railings, and wearing surfaces are placed after the concrete deck has gained sufficient strength, their weight may be distributed equally to all stringers or beams. Otherwise, the dead load on the...

## 51 Limitations On Use Of Fasteners And Welds

Structural steel fabricators prefer that job specifications state that shop connections shall be made with bolts or welds'' rather than restricting the type of connection that can be used. This allows the fabricator to make the best use of available equipment and to offer a more competitive price. For bridges, however, standard specifications restrict fastener choice. High-strength bolts may be used in either slip-critical or bearing-type connections (Art. 5.3), subject to various limitations....

## 098

1.0 for U.S. customary units, kips and in 6.9 for metric units, N and mm 0.7 + 0.3(0 90)2 design yield stress of the web, ksi (MPa) depth of the flat portion of the web measured along the plane of the web, in (mm) t 0.075, when t is in inches t 1.91, when t is in mm web thickness, in (mm) actual length of bearing, in (mm). For the case of two equal and opposite concentrated loads distributed over unequal bearing lengths, the smaller value of N applies 0 angle between the plane of the web and...

## 515 Welding Materials

Weldable structural steels permissible in buildings and bridges are listed with required electrodes in Tables 5.10 and 5.11. Welding electrodes and fluxes should conform to AWS 5.1, 5.5, 5.17, 5.18, 5.20, 5.23, 5.25, 5.26, 5.28, or 5.29 or applicable provisions of AWS D1.1 or D1.5. Weld metal deposited by electroslag or electrogas welding processes should conform to the requirements of AWS D1.1 or D1.5 for these processes. For bridges, the impact requirements in D1.5 are mandatory. Welding...

## 20

Since T + Q 15 + 3.51 18.5 kips < 31.0 kips, the bolts are OK. The tee flange, however, should be checked independently. This can be done as follows. Assume that the prying force Q 3.51 acts at a distance a from the bolt line. The moment at the bolt line then is and that at the toe of the fillet, with T + Q 18.5 kips, is Mf 3.51 X (1.777 + 1.1875) - 18.5 X 1.1875 -11.6 kip-in The maximum moment in the flange is thus 11.6 kip-in, and the bending stress in the flange is 32.0 < 0.75 X 50 37.5...

## 11441 Lateral Bracing

A system of bottom lateral bracing should be provided for all spans more than 50 ft in length. Deck spans employing four or more beams per track, where the beams are less than 72 in deep, and where a reinforced concrete deck is integrated with the beams by shear connectors or where a cast in place concrete deck engages not less than 1 in of the beam flange thickness, do not require the bottom lateral bracing. There should be top lateral bracing in all deck spans and in through spans, provided...

## 11446 Flangeto Web Connections

Flange-to-web joints of welded plate girders should be the same for top and bottom flanges. For open deck construction, use full penetration groove welds. For ballast deck construction, with either steel plate or composite concrete, use full penetration groove welds or continuous fillet welds. Flange angles in riveted or bolted construction should be connected to the web with enough fasteners to transfer the horizontal shear force to the flange section. The connection must also be designed for...

## 127 X

Parapets, railings, and safety walks will be placed after the concrete slab has cured. Their weights may be equally distributed to all stringers. In addition, provision will be made for a future wearing surface, weight 20 psf. The total superimposed dead load will be designated SDL. Table 12.27 lists for the superimposed load on the composite section the dead loads, the preliminary bending moments, and the V loads, Table 12.28 gives the bending moments due to the V loads, and Table 12.29, the...

## 11066[D L Lr or S or R W or E T

L floor live load, including impact Lr roof life load A loads from cranes and materials handling systems S roof snow load R rain load W wind load E earthquake load T restraint loads Instead of the factors 0.75 and 0.66, allowable stresses may be increased one-third and one-half, respectively. S in load combination 7 may be taken as zero for snowloads < 13 psf, as 0.5S for 13 < snowload < 31 psf, and as 0.75S for snowloads > 31 psf. For the case of D + E + A for load combination 7, the...

## 1521 Aerodynamic Analysis Of Cablesuspended Bridges

The wind-induced failure on November 7, 1940, of the Tacoma Narrows Bridge in the state of Washington shocked the engineering profession. Many were surprised to learn that failure of bridges as a result of wind action was not unprecedented. During the slightly more than 12 decades prior to the Tacoma Narrows failure, 10 other bridges were severely damaged or destroyed by wind action (Table 15.12). As can be seen from Table 12a, wind-induced failures have occurred in bridges with spans as short...

## M2 fe2

Where r) column slenderness of built-up member acting as a unit a separation ratio h 2rib h distance between centroids of individual components perpendicular to member axis of buckling a distance between connectors rib radius of gyration of individual angle relative to its centroidal axis parallel to member axis of buckling In this case, h 1.03 + 0.375 + 1.03 2.44 in and a 2.44 (2 X 1.13) 1.08. Assume maximum spacing between connectors is a 80 in. With K 1, substitution in Eq. 7.11 yields KL (...

## 13 Relative Cost Of Structural Steels

Because of the many strength levels and grades now available, designers usually must investigate several steels to determine the most economical one for each application. As a guide, relative material costs of several structural steels used as tension members, beams, and columns are discussed below. The comparisons are based on cost of steel to fabricators (steel producer's price) because, in most applications, cost of a steel design is closely related to material costs. However, the total...

## 6318 Combined Flexure and Axial Force

HSS members under combined bending and axial force are subject to the same LRFD design requirements as other members (see Art. 6.19.1, Eqs. 6.65 6.66, and Art. 6.20). In these interaction equations the effects of bending moments about the x and y axis are additive, and this can be very conservative for round HSS. Therefore, for round HSS members in biaxial flexure, laterally unbraced with the same effective length factor for any direction of loading, it is permissible to replace the moment...

## 139 457 137 733

Allowable shear stress in the web for Grade 50W steel is 17 ksi. Average shear stress in the web is Transverse stiffeners are not required. Flange-to-Web Welds. The web will be connected to the deck plate and the bottom flange by a fillet weld on opposite sides of the web. These welds must resist the horizontal shear between flange and web. For the weld to the 10 X y2-in bottom flange, the minimum size TABLE 12.80 Bending Stresses in Member III fb 221 X 12 658 4.03 ksi (compression) fb 221 X 12...

## 0060 0080 0103 0133 0136 0138

*As given in ''Wind Forces on Structures,'' Transactions, vol. 126, part II, p. 1180, American Society of Civil Engineers. preclude vibrations. It does not directly compute the amplitude of vibration and, hence, it does not directly lead to determination of vibratory stresses. Solutions for amplitude are available in the literature. See, for example, M. Paz, Structural Dynamics Theory and Computation,'' Van Nostrand Reinhold, New York R. J. Melosh and H. A. Smith, New Formulation for Vibration...

## 629 Builtup Tension Members

The design strength and allowable stresses for prismatic built-up members subjected to axial tension by static forces are the same as for tension members given in Art. 6.13. Components of a built-up tension member should be connected at frequent intervals to ensure that they act together, that faying surfaces intended to be in contact stay in contact, that excessive vibration of relatively thin parts does not occur, and that moisture will not penetrate between faying surfaces and cause...

## F F F

Where _, y indexes representing the bending axis to which the applicable stress applies Fa allowable stress for axial force alone, ksi Fb allowable compression stress for bending moment alone, ksi F'e Euler stress divided by a safety factor, ksi 12n2E 23(KM rb)2 M unbraced length in plane of bending, in rb radius of gyration about bending plane, in K effective length factor in plane of bending fa axial compression stress due to loads, ksi fb compression bending stress at design section due to...

## 58 Fastener Holes

Standard specifications require that holes for bolts be z i6 in larger than the nominal fastener diameter. In computing net area of a tension member, the diameter of the hole should be taken Vi6 in larger than the hole diameter. Standard specifications also require that the holes be punched or drilled. Punching usually is the most economical method. To prevent excessive damage to material around the hole, however, the specifications limit the maximum thickness of material in which holes may be...

## R

Where R is the applied concentrated load or reaction (kip). Bearing stiffeners should be provided on the web when the applied concentrated load or reaction exceeds the following web crippling limits. When the concentrated load is applied at a distance of at least d 2 from the member end, R 67.5tw2 1 + 3(N d )(tj tf)15 VT fT (6.50) When the concentrated load is applied less than d 2 from the member end,

## 1494

Thus, the web bolts must be designed for a moment of 112.8 + 33.2 146.0 ft-kips. For determining bolt loads, the polar moment of inertia is first computed, as the sum of the moments of inertia of the bolts about two perpendicular axes (Fig. 14.37). 2 X 2 X 270 1080 9 X 2(1.5)2 _41 The maximum bolt loads are resolved into horizontal and vertical components PH and PV, respectively. Also, shear imposes a vertical load on the 18 bolts of

## 12152 Design of Ribs

Select Grade 50W steel for the ribs and deck plate for atmospheric corrosion resistance. This steel has a yield strength of 50 ksi in thicknesses up to 4 in. The trapezoidal section chosen for the ribs is shown in Fig. 12.61. Stresses in the ribs, and in the deck plate as part of the ribs (member II). may be determined by orthotropic-plate theory (Art. 4.12). In the first stage of the calculations, the ribs are assumed to be continuous and supported by rigid floor-beams. In the second stage,...

## 81 Concrete Fill On Metal Deck

The most prevalent type of floor deck used with steel frames is concrete fill on metal deck. The metal deck consists of cold-formed profiles made from steel sheet, usually having a yield strength of at least 33 ksi. Design requirements for metal deck are contained in the American Iron and Steel Institute's Specification for the Design of Cold-Formed Steel Structural Members.'' The concrete fill is usually specified to have a 28-day compressive strength of at least 3000 psi. Requirements for...

## 111k

The bending moment produced by the V loads at any section of a girder Gn must be added to the preliminary moment at that section to produce the final bending moment Mn there. Thus, where Mvn bending moment produced by V loads. Similarly, the shear due to the V loads must be added to the preliminary shears to yield the final shears. Stresses are computed in the same way as for straight girders. Between diaphragms, the girder flanges resist the torsion. At any section, the stresses in the top and...

## 2 E

W weight of bridge, lb per lin ft Hw horizontal component of cable load due to dead load (half bridge), kips b distance between centerlines of cables, or centerlines of pairs of cables, ft d vertical distance between top and bottom planes of lateral bracing, ft E modulus of elasticity of truss steel, ksf Av area of the diagonals in one panel of vertical truss, ft2 Ah area of diagonals in one panel of horizontal lateral bracing (two members for X yh angle between diagonals and chord of...

## 2f

In a similar manner, the magnitudes of the components of the acceleration vector a are Transformation of Eq. (3.27) into the form provides a condition in dynamics that often can be treated as an instantaneous condition in statics i.e., if a mass is suddenly accelerated in one direction by a force or a system of forces, an inertia force ma will be developed in the opposite direction so that the mass remains in a condition of dynamic equilibrium. This concept is known as d'Alembert's principle....

## 117 Distribution Of Loads Through Decks

Specifications of the American Association of State Highway and Transportation Officials (AASHTO) require that the width of a bridge roadway between curbs be divided into design traffic lanes 12 ft wide and loads located to produce maximum stress in supporting members. TABLE 11.11 Minimum Required Bolt Tension

## 337 Slopedeflection Method

One of several displacement methods for analyzing statically indeterminate structures that resist loads by bending involves use of slope-deflection equations. This method is convenient for analysis of continuous beams and rigid frames in which axial force effects may be neglected. It is not intended for analysis of trusses. Consider a beam AB (Fig. 3.77a) that is part of a continuous structure. Under loading, the beam develops end moments MAB at A and MBA at B and end rotations dA and 0b. The...

## I

BEAM AND GIRDER BRIDGES TABLE 12.3 Stresses in the Composite Section, ksi, at Section of Maximum Moment fb 804 X 12 752 12.83 fb 267 X 12 2,316 1.38 fb 1,201 X 12 7,744 1.86 fb 804 X 12 1,125 8.58 fb 267 X 12 1,473 2.18 fb 1,201 X 12 1,666 8.66 SDL fc 267 X 12 (1,460 X 24) 0.09 LL + I fc 1,201 X 12 (3,228 X 8) 0.56 Since the bending stresses in steel and concrete are less than the allowable, the assumed steel section is satisfactory. Use the W36 X 194 with 10 X 17 s-in bottom cover plate. Total...

## Roof Decks

The systems used for floor decks (Arts. 8.1 to 8.3) can also be used for roof decks. When used as roof decks, these systems are overlaid by roofing materials, to provide a weathertight enclosure. Other roof deck systems are described in Arts. 8.4 to 8.7. FIGURE 8.8 Minimum requirements for composite action with concrete-encased steel framins. FIGURE 8.8 Minimum requirements for composite action with concrete-encased steel framins.

## 190 L 190

Then, the estimated required area of the steel top flange is TABLE 12.36 Midspan Bending Moments, ft-kips TABLE 12.37 End Shear, kips, in Girder G, Vdl Vsdl Vll + V Total V Try a 18 X 1V2-in top flange, area 27 in2. The trial section is shown in Fig. 12.27. Its neutral axis can be located by taking moments of web and flange areas about middepth of the web. This computation and that for the section moduli Sst and Ssb of the plate girder alone are conveniently tabulated in Table 12.38. In...

## X

At the root of the threads extending into the tensile stress area load plus prying action when applicable Source Adapted from Load and Resistance Factor Design Specification for Structural Steel Buildings, American Institute of Steel Construction, 1999. load plus prying action when applicable Source Adapted from Load and Resistance Factor Design Specification for Structural Steel Buildings, American Institute of Steel Construction, 1999. fluctuations per day X 365 X years of design life. For...

## 104 Design Methods

The AISI Specification is structured such that nominal strength equations are given for various types of structural members such as beams and columns. For allowable stress design (ASD), the nominal strength is divided by a safety factor and compared to the required strength based on nominal loads. For Load and Resistance Factor Design (LRFD), the nominal strength is multiplied by a resistance factor and compared to the required strength based on factored loads. These procedures and pertinent...

## 33

V043 'V 29500 0.947 > 0.673 p (1 - 0.22 A) A p (1 - 0.22 0.947) 0.947 p 0.811 The effective width of the top flange is The next step is to determine whether the web is fully effective. To do this, first determine the location of the neutral axis. Because the top flange is not fully effective, the neutral axis will be located below the centroidal axis of the gross cross section. Table 10.13 shows the calculations to determine the distance of the neutral axis from the top fiber, y, and the...

## 615 Combined Tension And Shear

Combined tension and shear stresses are of concern principally for fasteners, plate-girder webs, and ends of coped beams, gusset plates, and similar locations. The AISC Load and Resistance Factor Design (LRFD) Specification for Structural Steel Buildings'' contains interaction formulas for design of bolts subject to combined tension and shear in bearing-type connections. The specification stipulates that the tension stress applied by factored loads must not exceed the design tension stress Ft...

## 1092 Unstiffened Elements and Edge Stiffeners with Stress Gradient

The effective width for unstiffened elements (including edge stiffeners) with a stress gradient is calculated in the same manner as for uniformly loaded stiffened elements (Art. 10.9.1) except that (1) k in Eq. 10.4 is taken as 0.43, and (2) the stress 3 is taken as the maximum compressive stress in the element. Figure 10.7 shows the location of 3 and the effective width for an edge stiffener consisting of an inclined lip. (Such lips are more structurally efficient when bent at 90 , but...

## 10128 Combined Bending and Web Crippling Strength

For beams with unreinforced flat webs, combinations of bending and web crippling near concentrated loads or reactions must satisfy interaction equations given in the A S Specifi- cation. Equations are given for two types of webs and for nested Z-sections, with separate equations for ASD and LRFD. See the AISI Specification for various exceptions and limitations that may apply. Symbols have common definitions except as noted. (a) For shapes having single unreinforced webs (b) For shapes having...

## 1

Fe 25 ( F + t) - ViF FtFtt (10.62) As an alternative to Eq. 10.62, a conservative estimate can be calculated from the following In the above, aex and at are given by Eqs. 10.31 and 10.33, and where ro is given by Eq. 10.36 and xo distance from shear center to centroid along principal x-axis taken as negative. For singly-symmetric sections, the x-axis is assumed to be the axis of symmetry. Doubly-Symmetric Sections. For doubly-symmetric sections, such as back-to-back C-sections, subject to...

## 313 Types Of Structural Members And Supports

Structural members are usually classified according to the principal stresses induced by loads that the members are intended to support. Axial-force members (ties or struts) are those subjected to only tension or compression. A column is a member that may buckle under compressive loads due to its slenderness. Torsion members, or shafts, are those subjected to twisting moment, or torque. A beam supports loads that produce bending moments. A beam-column is a member in which both bending moment...

## Figure 1411

SHEARMAN MINTON BRIDGE LOCATION On Interstate 64 over the Ohio River between Louisville, Ky., and New Albany, Ind. TYPE Tied, through, truss arch, 22 panels at 36.25 ft SPAN 800 ft RISE 140 ft RISE SPAN 1 5.7 NO. OF LANES OF TRAFFIC 6, double deck HINGES 2 CROWN DEPTH 30 ft DEPTH SPAN 1 27 Deck slab and surfacing for Slabs for Railings and parapets Floor steel for roadway and sidewalks Floor Arch trusses Arch bracing Arch hangers and bracing Arch ties Miscellaneous utilities, excess, etc....

## D 608

Where tw is the web thickness, in, and D is the clear distance, in, between the flanges. For composite beams used in simple spans, D may be replaced by 2Dcp, the distance, in, from the compression flange to the neutral axis in plastic bending. The compression depth of the composite section in plastic bending, including the slab, may not exceed where d is the depth of the steel girder, in, and ts is the thickness, in, of slab. Therefore, the maximum allowed Dcp 9.47 - 8.5 0.97 in. From Eq....

## 1545 1546 1513 1550

Bridge suspension (Cont.) Brighton Chain Pier Bronx-Whitestone Brooklyn Chesapeake Bay (second) Cincinnati Cologne-Mulheim Deer Isle Delaware Memorial I Dryburgh Abbey First Tacoma Narrows Forth Road Fykesesund Galashiels General U. S. Grant George Washington Gilbraltar Straits Golden Gate Hennepin Avenue Humber Jacob's Creek Klamath River Long's Creek Mackinac Manhattan Menai Straits Messina Straits Montrose Nassau Newport Niagara Falls Niagara-Clifton Niagara-Lewiston Oder River Ohio River...

## 0026

FIGURE 3.70 (a) Loaded gable frame. (b) Internal forces hold portion of frame in equilibrium. FIGURE 3.70 (a) Loaded gable frame. (b) Internal forces hold portion of frame in equilibrium. 2Fx 8 + PA cos 30 + VA sin 30 0 (3.129) Simultaneous solution of Eqs. (3.128) and (3.129) gives VA 3.96 hips and PA -11.53 kips. The negative value indicates that the rafter is in compression.

## 791 LRFD for Simple Span Floorbeam

If the beam's self-weight is assumed to be 45 lb ft, the factored uniform load is the larger of the following Wu 1.4 73(40 + 25) 2 + 45 3384.5 lb per ft Wu 1.2 73(40 + 25) 2 + 45 + 1.6 x 30(40 + 25) 2 4461 lb per ft (governs) The factored moment then is To select for beam AB a wide-flange section with Fy 50 ksi, the top flange being braced by joists, the required plastic modulus Zx is determined as follows The factored moment Mu may not exceed the design strength of < pMr, and A wide-flange...

## P

For Fu Fsy > 1.08, use T 2.0 (ASD) and 0 0.70 (LRFD). For Fu Fsy < 1.08, use T 2.22 (ASD) and 0 0.60 (LRFD). In the above, P required strength per weld (nominal force), Pu required strength per weld (factored force), t thickness of thinnest connected sheet, and Fsy specified yield stress. For tension, such as caused by uplift, the nominal strength is the smaller of the limit based on the strength of the weld and that based on the strength of the connected part. For weld strength, For...

## Fkq

Where Ac area of compression flange, 12 in2 b 4.64 for members with compression flange area less than tension flange area fc stress in compression flange due to the factored loading under investigation, ksi For this design, Lb 25 ft X 12 300 in, fc 18.8 and ar 2(38.17)(7 16) 12.0 2.78. Therefore,

## 1s Resistance To Longitudinal Forces

Acceleration and braking of vehicular loads, and longitudinal wind, apply longitudinal loads to bridges. In highway bridges, the magnitudes of these forces are generally small enough that the design of main truss members is not affected. In railroad bridges, however, chords that support the floor system might have to be increased in section to resist tractive forces. In all truss bridges, longitudinal forces are of importance in design of truss bearings and piers. In railway bridges,...

## 11356 Longitudinal Load

The longitudinal loads from trains on bridges are generally attributed to tractive or braking effort. With the current use of high adhesion locomotives and the development of better braking systems, bridges may be subject to greater longitudinal loads than in the recent past. The current AREMA recommendation is to assume the longitudinal load as 15 of the specified live load without impact for braking and 25 for traction. Field measurements are being made on selected bridges to determine...

## 10124 Beams C or Z Section Having One Flange Fastened to a Standing Seam Roof System

If the flange of a supporting beam is fastened to a standing seam roof system, the bending strength generally lies between that for a fully braced member and an unbraced member, but may equal that for a fully braced member. The strength depends on the details of the system, as well as whether the loading is gravity or uplift, and cannot be readily calculated. Therefore, the AISI Specification allows the nominal strength to be calculated by Eq. 10.40, but with the reduction factor R determined...

## Figure 1423

COLORADO RIVER ARCH BRIDGE LOCATION Utah State Route 95 over Colorado River, near Garfield-San Juan county line TYPE Half-through, solid-ribbed arch, 21 panels, 19 at 27.5 ft SPAN 550 ft RISE 90 ft RISE SPAN 1 6.1 NO. OF LANES OF TRAFFIC 2 HINGES 0 DEPTH 7 ft DEPTH SPAN 1 79 Deck slab and surfacing for roadway Railings and parapets Floor steel for roadway Floor Arch ribs Arch bracing Arch hangers and EQUIVALENT LIVE + IMPACT LOADING ONE EACH ARCH FOR FULLY LOADED STRUCTURE 952 lb per ft STEEL...

## 1020 Other Limit States At Connections

The AISI Specification gives procedures for checking certain other important limit states at member end connections. Included are shear-lag effects in bolted and welded connections where not all elements of the cross section are connected, shear strength along a plane through fasteners in beam webs where one or both flanges are coped, and block shear rupture where a connecting element can fail through a combination of shear on one plane and tension on a perpendicular plane. Many of these...

## 74 Compression Members

Steel members in buildings subject to compressive axial loads include columns, truss members, struts, and diagonal braces. Slenderness is a major factor in design of compression members. The slenderness ratio L r is preferably limited to 200. Most suitable steel shapes are pipes, tubes, or wide-flange sections, as designated for columns in the AISC Steel Construction Manual.'' Double angles, however, are commonly used for diagonal braces and truss members. Double angles can be easily connected...

## Figure 357

Integration is carried out over the path the force travels, which may not be a straight line. The work done by the weight of a body, which is the force, when it is moved in a vertical direction is the product of the weight and vertical displacement. According to Eq. (3.91) and with a the angle between the downward direction of gravity and the imposed displacement, the weight does positive work when movement is down. It does negative work when movement is up. In a similar fashion, the rotation...

## 1875 3875 5875 6875

MLL 2,030 3,429 4,096 4,149 Mr 386 651 778 788 FIGURE 12.37 Moment diagram for deck girder and capacities of various sections. FIGURE 12.37 Moment diagram for deck girder and capacities of various sections. R, - 0.19 X 134 - 25.4 kips The total maximum reaction is R - 468.1 kips, say 470 kips. Shears. Maximum live-load shears at floorbeam locations occur with truck loading between the beam and the far support. A heavy wheel should be at the beam in each design lane. The shears are readily...

## R mr

Where Nr number of studs in one rib at a beam, not to exceed 3 in computations wr average width of concrete rib or haunch, at least 2 in but not more than the minimum clear width near the top of the steel deck, in hr nominal rib height, in Hs length of stud in place but not more than hr + 3 in computations, in When the ribs of the steel deck are parallel to the steel beam and wr hr < 1.5, a reduction factor R should be applied to Qn computed from Eq. (7.28) For this orientation of the deck...

## 117 Welded Splices In Heavy Sections

Shrinkage during solidification of large welds in structural steel members causes, in adjacent restrained metal, strains that can exceed the yield-point strain. In thick material, triaxial stresses may develop because there is restraint in the thickness direction as well as in planar directions. Such conditions inhibit the ability of a steel to act in a ductile manner and increase the possibility of brittle fracture. Therefore, for members subject to primary tensile stresses due to axial...

## 11123 326

Axially stressed members in 5.40 5.96 5.97 13.3 13.5 lap 5.40 (See also Connections Knee braces Nodes Splices Trusses, joints in) Knee braces 5.89 5.90 12.113 12.114 load combinations in Load factors (see LFD LRFD) Load-and-resistance-factor design bridge lateral locomotive bridge longitudinal sidewalk building occupancy buoyancy centrifugal-force combinations of for bridges for buildings concentrated construction factored Cooper railway bridge crane runway culvert dead for bridges for...

## 11357 Centrifugal Load

In that case, the actual superelevation, in, is given by On curves, each axle load on each track should be applied vertically through the point defined above, 6 ft above top of rail. Impact should be computed and applied as indicated previously. Preferably, the section of the stringer, girder, or truss on the high side of the superelevated track should be used also for the member on the low side, if the required section of the low-side member is smaller than that of the high-side member. If the...