## 770

* Equivalent to 1 in 10,000 hours. t Equivalent to 1 in 100,000 hours. Not recommended for use where temperatures exceed 800 F. * Equivalent to 1 in 10,000 hours. t Equivalent to 1 in 100,000 hours. Not recommended for use where temperatures exceed 800 F. A shear fracture is indicated by a dull or fibrous appearance. A shiny or crystalline appearance is associated with a cleavage fracture. The data obtained from a Charpy test are used to plot curves, such as those in Fig. 1.11, of energy or...

## Edge Of Fillet

FIGURE 5.30 Column splice with butt plate. FIGURE 5.31 Column splice with partial-penetration groove welds. FIGURE 5.31 Column splice with partial-penetration groove welds. lifting. The lifting-lug detail in Fig. 5.33 takes advantage of the constant distance between inside faces of flanges of W14 sections, and allows for welding the flanges and web of the splice, as shown in Fig. 5.32. Bolted column splices generally are made with flange plates. Fillers are inserted (Fig. 5.34) when the...

## 523 Welding Clearance And Space

Designers and detailers should detail connections to ensure that welders have ample space for positioning and manipulating electrodes and for observing the operation with a protective hood in place. Electrodes may be up to 18 in long and 3 s in in diameter. In addition, adequate space must be provided for deposition of the required size of fillet weld. For example, to provide an ade- FIGURE 5.21 Minimum landing tor a nllet weld. , , c ,, ,,,, , c 6 quate landing c (in) for the fillet weld of...

## 1955

1 Under Construction. 2 Railroad & Highway. 3 Double Deck. 43 pylons, 4 4 span continuous. 1 Under Construction. 2 Railroad & Highway. 3 Double Deck. 43 pylons, 4 4 span continuous. spans over that required for strictly navigation clearance requirements. One of the most obvious is the economic trade off of shorter spans requiring deep water foundations, as opposed to longer spans requiring shallow water foundations or foundations completely out of the water and on land. Another reason is...

## Ei

6 angle through which one end of beam rotates with respect to the other end L length over which the deformation takes place I moment of inertia E modulus of elasticity For beams carrying transverse loads, the total strain energy is the sum of the energy for bending and that for shear. Virtual Forces. Virtual work also may be created when a system of virtual forces is applied to a structure that is in equilibrium. In this case, the principle of virtual work requires that external virtual work,...

## 0259 0400

Channel sections, made with two angle segments, with solid web, perforated web, or web of stay plates and lacing. These are seldom used on modern bridges. Single box sections, made with side channels, beams, angles and plates, or side segments of plates only. The side elements may be connected top and bottom with solid plates, perforated plates, or stay plates and lacing. Alternatively, they may be connected at the top with solid cover plates and at the bottom with perforated plates, or stay...

## Charles W Roeder PE

Professor of Civil Engineering, University of Washington, Seattle, Washington Design of buildings for lateral forces requires a greater understanding of the load mechanism than many other aspects of structural design. To fulfill this need, this section provides a basic overview of current practice in seismic and wind design. It also discusses recent changes in design provisions and recent developments that will have an impact on future design. There are fundamental differences between design...

## 717 Base Plate Design

Base plates are usually used to distribute column loads over a large enough area of supporting concrete construction that the design bearing strength of the concrete will not be exceeded. The factored load Pu is considered to be uniformly distributed under a base plate. The nominal bearing strength fp (ksi) of the concrete is given by fp 0.85fCVaJa, and VaJa, < 2 (7.41) where fc specified compressive strength of concrete, ksi A1 area of the base plate, in2 A2 area of the supporting concrete...

## Vs

Where V is the wind speed, fps, D is a characteristic dimension, ft, and S is the Strouhal number, the ratio of velocity of vibration of the obstruction to the wind velocity (Table 13.3). When the obstruction is a member of a truss, self-exciting oscillations of the member in the direction perpendicular to the wind stream may result when the frequency of vortex shedding coincides with a natural frequency of the member. Thus, determination of the torsional frequency and bending frequency in the...

## 1041 ASD Requirements

A design satisfies the requirements of the AISI Specification when the allowable design strength of each structural component equals or exceeds the required strength, determined on the basis of the nominal loads, for all applicable load combinations. This is expressed as Rn nominal strength (specified in Chapters B through E of the Specification) n safety factor (see Table 10.1) Rn n allowable design strength ASD Load Combinations. In the absence of an applicable code...

## Fabrication And Erection

Director, Fabricating & Standards American Institute of Steel Construction, Inc., Chicago, Illinois Designers of steel-framed structures should be familiar not only with strength and serviceability requirements for the structures but also with fabrication and erection methods. These may determine whether a design is practical and cost-efficient. Furthermore, load capacity and stability of a structure may depend on design assumptions made as to type and magnitude of stresses and strains...

## 1113 Criteria For Builtup Tension Members

A tension member and all its components must be proportioned to meet the requirements for maximum slenderness ratio given in Table 11.24. The member also must be designed to ensure that the allowable tensile stress on the net section is not exceeded. The net section of a high-strength-bolted tension member is the sum of the net sections of its components. The net section of a component is the product of its thickness and net width. Net width is the minimum width normal to the stress minus an...

## 43 Fixed Arches

In a fixed arch, translation and rotation are prevented at the supports (Fig. 4.3). Such an arch is statically indeterminate. With each reaction comprising a horizontal and vertical component and a moment (Art. 4.1), there are a total of six reaction components to be determined. Equilibrium laws provide only three equations. Three more equations must be obtained from a knowledge of the elastic behavior of the arch. One procedure is to consider the arch cut at the crown. Each half of the arch...

## 1518 Selfanchored Suspension Bridges

Self-anchored suspension bridges differ from the type discussed in Arts. 15.16 and 15.17 only in that external anchorages are dispensed with (see Art. 15.3). Unlike the externally anchored type, self-anchored suspension bridges may properly be analyzed by the elastic theory, since the effect of distortions of the structural geometry under live load is practically eliminated. The structure is also not stressed by uniform temperature change of cables and stiffening girders. The analysis is thus...

## 53 Highstrength Bolts Nuts And Washers

For general purposes, A325 and A490 high-strength bolts may be specified. Each type of bolt can be identified by the ASTM designation and the manufacturer's mark on the bolt head and nut (Fig. 5.1). The cost of A490 bolts is 15 to 20 greater than that of A325 bolts. Job specifications often require that main connections shall be made with bolts conforming to the Specification for Structural Joints Using ASTM A325 and A490 Bolts.'' This FIGURE 5.1 A325 high-strength structural steel bolt with...

## 56 Pins

A pinned connection is used to permit rotation of the end of a connected member. Some aspects of the design of a pinned connection are the same as those of a bolted bearing connection. The pin serves the same purpose as the shank of a bolt. But since only one pin is present in a connection, forces acting on a pin are generally much greater than those on a bolt. Shear on a pin can be resisted by selecting a large enough pin diameter and an appropriate grade of steel. Bearing on thin webs or...

## 630 Plastic Design

Structural steel members often have considerable reserve load-carrying capacity after yielding occurs, e.g., at the outer surfaces of a beam. For a flexural member, this reserve capacity is quantified by the shape factor Z S of the cross section, where Z is the plastic section modulus and S is the corresponding elastic section modulus. For W shapes, Z S ranges from 1.10 to 1.15. The AISC ASD and LRFD specifications recognize that for structures with continuous framing, additional reserve...

## 713 Lrfd For Composite Beam With Uniform Loads

The typical floor construction of a multistory building is to have composite framing. The floor consists of 31 4-in-thick lightweight concrete over a 2-in-deep steel deck. The concrete weighs 115 lb ft3 and has a compressive strength of 3.0 ksi. An additional 30 of the dead load is assumed for equipment load during construction. The deck is to be supported on FIGURE 7.6 Seven locations of the plastic neutral axis used for determining the strength of a composite beam. (a) For cases 6 and 7, the...

## 623 Local Plate Buckling

When compression is induced in an element of a cross section, e.g., a beam or column flange or web, that element may buckle. Such behavior is called local buckling. Provision to prevent it should be made in design because, if it should occur, it can impair the ability of a member to carry additional load. Both the AISC ASD and LRFD specifications for structural steel buildings recognize the influence of local buckling by classifying steel sections as compact, noncompact, or slender-element. A...

## 353 Vibration Of Singledegreeoffreedom Systems

Several dynamic characteristics of a structure can be illustrated by studying single-degree-of-freedom systems. Such a system may represent the motion of a beam with a weight at center span and subjected to a time-dependent concentrated load P(t) (Fig. 3.100a). It also may approximate the lateral response of a vertically loaded portal frame constructed of flexible columns, fully restrained connections, and a rigid beam that is also subjected to a time-dependent force P(t) (Fig. 3.100b). In...

## 2

15.16.2 Static Analysis Deflection Theory Distortions of structural geometry of long suspension spans under live load may be very large. As a consequence, the elastic theory (Art. 15.16.1) gives unduly conservative moments, shears, and deflections. For economy, therefore, a deflection theory, also referred to as an exact or second-order theory, that accounts for effects of deformations should be used. With the notation and assumptions given for the elastic theory in Art. 15.16.1, a differentia...

## 712 Composite Beams

Where As area of the steel section (not applicable to hybrid sections), in Fy yield strength of the steel, ksi Equation (7.26) expresses the strength of the shear connectors where l,Qn is the sum of the nominal strength of the shear connectors between the point of maximum positive moment and zero moment on either side. For full composite design. three locations of the plastic neutral axis are possible. The location depends on the relationship of Cc to the yield strength of the web, Pyw AwFy,...

## 1116 Composite Construction With I Girders

With shear connectors welded to the top flange of a beam or girder, a concrete slab may be made to work with that member in carrying bending stresses. In effect, a portion of the slab, called the effective width, functions much like a steel cover plate. In fact, the effective slab area may be transformed into an equivalent steel area for computation of composite-girder stresses and deflection. This is done by dividing the effective concrete area by the modular ratio n, the ratio of modulus of...

## 711 Examplelrfd For Floorbeam With Overhang

A floorbeam of A36 steel carrying uniform loads is to span 30 ft and cantilever over a girder for 7.5 ft (Fig. 7.4). The beam is to carry a dead load due to the weight of the floor plus assumed weight of beam of 1.5 kips per ft and due to partitions, ceiling, and ductwork of 0.75 kips per ft. The live load is 1.5 kips per ft. Negative Moment. The cantilever is assumed to carry full live and dead loads, while the back span is subjected to the minimum dead load. This loading produces maximum...

## Figure 1415

FORT PITT BRIDGE LOCATION Pittsburgh, Pennsylvania, over the Monongahela River TYPE Solid-ribbed, tied, through arch, 30 panels at 25 ft SPAN 750 ft RISE 122.2 ft RISE SPAN 1 6.2 NO. OF LANES OF TRAFFIC 4, each level of double deck HINGES 2 DEPTH 5.4 ft DEPTH SPAN 1 139 Deck slab and surfacing for roadways, slabs for sidewalks, railings and parapets, 16,100 on both decks Floor steel for roadway and sidewalks, on both decks Floor bracing (truss bracing) Arch ribs Arch bracing Arch hangers...

## 1112 Detailing For Buckling

Prevention of buckling is important in bridge design, because of the potential for collapse. Three forms of buckling must be considered in bridge design. The first, and most serious, is primary buckling of an axially loaded compression member. Such column buckling may include Euler-type elastic buckling and inelastic buckling. This is a rare occurrence with highway bridges, attesting to the adequacy of the current design provisions. A second form of buckling is local plate buckling. This form...

## A4 3a5

Setting the sum of the moments equal to zero gives Axial forces in the columns can be determined at other levels by the same procedure. Other shear forces and bending moments can be determined by application of the equations of equilibrium for individual subassemblages, as for the portal method. FIGURE 9.20 Cantilever method of determining the forces at midspan of beams and midhheight of columns in the frame of Fig. 9.17. FIGURE 9.20 Cantilever method of determining the forces at midspan of...

## 413 Orthotropic Plates

Plate equations are applicable to steel plate used as a deck. Between reinforcements and supports, a constant-thickness deck, loaded within the elastic range, acts as an isotropic elastic plate. But when a deck is attached to reinforcing ribs or is continuous over relatively closely spaced supports its properties change in those directions. The plate becomes anis-tropic. And if the ribs and floorbeams are perpendicular to each other, the plate is orthog-onal-anistropic, or orthotropic for...

## Mr V1 V1 X2 Fm2

Ry radius of gyration about the minor axis E modulus of elasticity of steel 29,000 ksi A area of the cross section of the member G shear modulus of elasticity of steel 11,000 ksi J torsional constant for the section Fl smaller of (Fy, - F) or Fyw Fyf yield stress of flange, ksi Fw yield stress of web, ksi Iy moment of inertia about minor axis Cw warping constant Fr compressive residual stress in flange 10 ksi for rolled shapes, 16.5 ksi for welded shapes For singly symmetrical I-shaped members...

## 113512 Combination Loads Or Wind Load Only

Every component of substructure and superstructure should be proportioned to resist all combinations of forces applicable to the type of bridge and its site. Members subjected to stresses from dead, live, impact, and centrifugal loads should be designed for the smaller of the basic allowable unit stress or the allowable fatigue stress. With the exception of floorbeam hangers, members subjected to stresses from other lateral or longitudinal forces, as well as to dead, live, impact, and...

## 116 Lamellar Tearing

In a structural steel member subjected to tension, elongation and reduction of area in sections normal to the stress are usually much lower in the through-thickness direction than in the planar direction. This inherent directionality is of small consequence in many applications, but it does become important in design and fabrication of structures with highly restrained joints because of the possibility of lamellar tearing. This is a cracking phenomenon that starts underneath the surface of...

## 12183 Loads Moments and Shears

There are fewer load combinations specified in LRFD than LFD and some of the load combinations apply only to concrete superstructures. The following Strength I Limit State load combination will govern in this example problem Strength I Limit State yp (Dead Load) + 1.75(LL + IM) Different load factors are applied to different types of dead loads. In addition, AASHTO specifies minimum and maximum values for these loads factors, and the most unfavorable load factor must be used in the design. yp...

## 35 Frictional Forces

Suppose a body A transmits a force FAB onto a body B through a contact surface assumed to be flat (Fig. 3.8a). For the system to be in equilibrium, body B must react by applying an equal and opposite force FBA on body A. FBA may be resolved into a normal force N and a force Ff parallel to the plane of contact (Fig. 3.8b). The direction of Ff is drawn to resist motion. The force F is called a frictional force. When there is no lubrication, the resistance to sliding is referred to as dry...

## 29

Fa - 6.19 ksi < 0.9 x 50 45 ksi OK. fv 29 3.5 ksi < 27 ksi OK. Jv .75 x 11 fa 13.0 ksi < 45 ksi OK. Ja .75 x 11 Associated Shear Connections Beams 3 and 4. The specified shear for these beams is R 107 kips. First consider the weld to the beam web. As with the strong axis beam web connection, this is a field welded connection with bolts used for erection only. The design load (required strength) is R 107 kips. The beam web shear R is essentially constant in the area of the connection and...

## 6252 Web Area

Webs are the shear-carrying elements of beams and girders. At any point along the length of a flexural member, the applied shear must be less than the strength of the gross web area, the product of the overall depth d and thickness tw of the web. Generally, shear is not a controlling limit state for the design of a rolled shape. Webs of rolled shapes are thick enough that shear buckling does not occur. However, the shear strength of the web is a major design issue when proportioning a plate...

## David H LeRoy PE

Modjeski and Masters, Inc., Harrisburg, Pennsylvania A truss is a structure that acts like a beam but with major components, or members, subjected primarily to axial stresses. The members are arranged in triangular patterns. Ideally, the end of each member at a joint is free to rotate independently of the other members at the joint. If this does not occur, secondary stresses are induced in the members. Also if loads occur other than at panel points, or joints, bending stresses are produced in...

## 15218 Stability Investigations

It is most important to note that the validation of stability of the completed structure for expected wind speeds at the site is mandatory. However, this does not necessarily imply that the most critical stability condition of the structure occurs when the structure is fully completed. A more dangerous condition may occur during erection, when the joints have not been fully connected and, therefore, full stiffness of the structure has not yet been realized. In the erection stage, the...

## 510 Clearances For Fasteners

FIGURE 5.6 Staggered holes provide clearance for high-strength bolts. Designs should provide ample clearance for tightening high-strength bolts. Detailers who prepare shop drawings for fabricators generally are aware of the necessity for this and can, with careful detailing, secure the necessary space. In tight situations, the solution may be staggering of holes (Fig. 5.6), variations from standard gages (Fig. 5.7), use of knife-type connections, or use of a combination of shop welds and field...

## Info

FIGURE 2.10 Field splices in girder bridges. FIGURE 2.10 Field splices in girder bridges. live loads, on the steel while the structure is partly erected. The structure must be erected safely and economically in a manner that does not overstress any member or connection. Erection stresses may be of opposite sign and of greater magnitude than the design stresses. When designed as tension members but subjected to substantial compressive erection stresses, the members may be braced temporarily to...

## 1 Aof Pushl 1 SPSP

2Pu required axial load strength of all columns in a story, kips Aoh translation deflection of the story under consideration, in 2H sum of all story horizontal forces producing Aoh, kips L story height, in P'e AgFy Ac2 (kips), where Ac is the slenderness parameter defined in Art. 6.16.2 with K > 1.0 in the plane of bending 6.19.2 ASD for Bending and Compression In ASD, the interaction of bending and axial compression is governed by Eqs. (6.68) and (6.69) or (6.70) When fa Fa < 0.15,...

## 514 Installation Of Fasteners

All parts of a connection should be held tightly together during installation of fasteners. Drifting done during assembling to align holes should not distort the metal or enlarge the holes. Holes that must be enlarged to admit fasteners should be reamed. Poor matching of holes is cause for rejection. FIGURE 5.11 Typical bolted splice of columns when depth Du of the upper column is nominally 2 in less than depth DL of the lower column. FIGURE 5.11 Typical bolted splice of columns when depth Du...

## 5419

For this shear, d 332(n 6) V683 87 in > 72 in. Use a stiffener spacing of 60 in. Try a pair of plates at each location, with the width equal at least to D 30 + 2 06 30 + 2 5.5 in < 6 in. Use 6 x 3 8-in plates welded to the web for the intermediate stiffeners. Change in Flange Size. At a sufficient distance from midspan, the bending moment decreases sufficiently to permit reducing the thickness of the flange plates to in. The net moment of inertia reduces to 265,000 in4 and the section...

## 20

0.9F *t 0.9F *t 1.1Fu*t 1.1F* 0.9F *t 0.9F * * Fu specified minimum tensile strength of connected parts. Connections with bolts in oversize holes or in slotted holes with the load applied less than about 80 or more than about 100 to the axis of the slot should be designed for a slip resistance less than that computed from Eq. 11.14. f Not applicable when the distance, parallel to the load, from the center of a bolt to the edge of the connected part is less than 1V2d, where d is the nominal...

## 1523 Erection Of Cablesuspended Bridges

The ease of erection of suspension bridges is a major factor in their use for long spans. Once the main cables are in position, they furnish a stable working base or platform from which the deck and stiffening truss sections can be raised from floating barges or other equipment below, without the need for auxiliary falsework. For the Severn Bridge, for example, 60-ft box-girder deck sections were floated to the site and lifted by equipment supported on the cables. Until the 1960s, the field...

## 329 Calculation Of Reactions In Statically Determinate Systems

For statically determinate systems, reactions can be determined from equilibrium equations Eq. (3.11) or (3.12) . For example, in the planar system shown in Fig. 3.66, reactions R1, H1, and R2 can be calculated from the three equilibrium equations. The beam with overhang carries a uniform load of 3 kips ft over its 40-ft horizontal length, a vertical 60-kip concentrated load at C, and a horizontal 10-kip concentrated load at D. Support A is hinged it can resist vertical and horizontal forces....

## 334 Methods For Analysis Of Statically Indeterminate Systems

For a statically indeterminate structure, equations of equilibrium alone are not sufficient to permit analysis (see Art. 3.28). For such systems, additional equations must be derived from requirements ensuring compatibility of deformations. The relationship between stress and strain affects compatibility requirements. In Arts. 3.35 to 3.39, linear elastic behavior is assumed i.e., in all cases stress is assumed to be directly proportional to strain. There are two basic approaches for analyzing...

## 146 Design Of Arch Ribs And Ties

Computers greatly facilitate preliminary and final design of all structures. They also make possible consideration of many alternative forms and layouts, with little additional effort, in preliminary design. Even without the aid of a computer, however, experienced designers can, with reasonable ease, investigate alternative layouts and arrive at sound decisions for final arrangements of structures. Rise-Span Ratio. The generally used ratios of rise to span cover a range of about 1 5 to 1 6. For...

## S8

* Standard Specifications for Highway Bridges,'' American Association of State Highway and Transportation Officials. * Standard Specifications for Highway Bridges,'' American Association of State Highway and Transportation Officials. 100 psf transverse 40 psf longitudinal Transverse and longitudinal loads should be applied simultaneously. Wind forces applied directly to the substructure should be assumed at 40 psf for 100-mph wind velocity. For wind directions skewed to the substructure, this...

## 7

8 TABLE 6.11 Design Wind Pressure Method 1 Components and Cladding Enclosed Building (Continued) Effective Basic wind speed V (mph) Location Zone (SF) 85 90 100 110 120 10 +5 -22 +6 -24 +7 -30 +9 -36 +11 -43 +12 -51 +14 -59 +16 -68 +19 -77 +21 -87 Roof 2 20 +5 -19 +6 -22 +7 -27 +8 -33 +10 -39 +12 -46 +13 -53 +15 -61 +18 -69 +20 -78 100 +4 -14 +5 -16 +6 -19 +7 -24 +8 -28 +10 -33 +11 -38 +13 -44 +15 -50 +17 -56 10 +5 -33 +6 -37 +7 -45 +9 -55 +11 -65 +12 -77 +14 -89 +16 -102 +19 -116 +21 -131 3 20...

## 1210 Through Plategirder Bridges With Floorbeams

For long or heavily loaded bridge spans, restrictions on depth of structural system imposed by vertical clearances under a bridge generally favor use of through construction. Through girders support the deck near their bottom flange. Such spans preferably should contain only two main girders, with the railway or roadway between them (Fig. 12.46). In contrast, deck girders support the deck on the top flange (Art. 12.8). The projection of the girders above the deck in through bridges may be...

## 63

The bottom flange of the W36 X 280 provides an area of 26.0 in2. Hence, the cover plate should supply an area of about 30.2 - 26.0 4.2 in2. Try a 10 X i 2-in plate, area 5.0 in2. The trial section is shown in Fig. 12.70. Properties of the cover-plated steel section alone are computed in Table 12.85. In determination of the properties of the composite section, use is made of the computations for the end-span composite section in Table 12.84. Calculations for the center-span section are given in...

## 0770

Because a' > 1, use a' 1 to calculate the design strength, fT. 4> T (f> B (-1 (1 + Sa') 40.6 ((1.69) 25.6 kips > 22.4 kips Bolts and bracket flange are OK for bending and prying action. Check web of W18 X 86 bracket for limit state of shear on gross section fRgv fs0.60FyAg 0.90 X 0.60 X 50 X 0.480 X 21 272 kips > 115 kips, OK. Check flange of W18 X 86 bracket for limit state of shear on net section 4> Rnv fs0.60FuAn 0.75 X 0.60 X 65 X 0.770 X (21 - 7 X 1.00) X 2 630 kips > 115...

## Figure 143

BAYONNE BRIDGE LOCATION Between Bayonne, N.J., and Port Richmond, Staten Island, N.Y. TYPE Half-through truss arch, 40 panels at 41.3 ft SPAN 1,675 ft RISE 266 ft RISE SPAN 1 6.3 NO. OF LANES OF TRAFFIC 4 plus 2 future rapid transit HINGES 2 CROWN DEPTH 37.5 FT DEPTH SPAN 1 45 Track, Floor steel and floor Arch truss and bracing Arch hangers SPECIFICATION LIVE LOADING LB PER FT 2 rapid-transit lines at 6,000 lb per ft 4 roadway lanes at 2,500 lb per 2 sidewalks at 600 lb EQUIVALENT LIVE + IMPACT...

## P qGCp qtGCJ67

Where q and qi velocity pressure as given by ASCE 7 G gust effect factor as given by ASCE 7 Cp external pressure coefficient as given by ASCE 7 GCpi internal pressure coefficient as given by ASCE 7 Codes and standards may present the gust factors and pressure coefficients in different formats. Coefficients from different codes and standards should not be mixed. Designers should exercise judgment in selecting wind loads for a building with unusual shape, response-to-load characteristics, or site...

## 168

FIGURE 12.47 Moment envelope for through girder and capacities of cross sections. FIGURE 12.47 Moment envelope for through girder and capacities of cross sections. Flange Size at Midspan. To select a trial size for the flange, assume an allowable bending stress Fb 20 ksi and distance between flange centroids of about 110 in. Then, for a maximum moment of 9,930 ft-kips, the required area of one flange is about Assume a 20 X 23 8-in plate for each flange, with an area of 47.5 in2. Width-thickness...

## 118 Basic Allowable Stresses For Bridges

Table 11.16 lists the basic allowable stresses for highway bridges recommended in AASHTO Standard Specifications for Highway Bridges'' for ASD. The stresses are related to the minimum yield strength Fy, ksi, or minimum tensile strength Fu, ksi, of the material in all cases except those for which stresses are independent of the grade of steel being used. The basic stresses may be increased for loading combinations (Art. 11.5). They may be superseded by allowable fatigue stresses (Art. 11.10)....

## Bolt In Shear And Tension Connected To A Bracket

Where P load, kips, on the bracket n total number of fasteners In addition, the moment is resisted by the upper fasteners in tension and the pressure of the lower part of the bracket against the support. The neutral axis is usually located above the bottom of the connection by about V6 of the connection length, but its exact location requires a trial-and-error approach. However, an alternative is to use a conservative plastic distribution, which is valid for both ASD and LRFD design methods....

## 98 Forces In Frames Subjected To Lateral Loads

Horizontal shear in each story is distributed in equal amounts to interior columns, while each exterior column is assigned half the shear for an interior column, since exterior columns do not share the loads of adjacent portals. If the bays are unequal, shear may be apportioned to each column in proportion to the lengths of the girders it supports. When bays are equal, the axial load in interior columns due to lateral load is zero. Inflection points (points of zero moment) are placed at...

## 114 Highway Design Loadings

The AASHTO Standard Specifications for Highway Bridges'' require bridges to be designed to carry dead and live loads and impact, or the dynamic effect of the live load. Structures should also be capable of sustaining other loads to which they may be subjected, such as longitudinal, centrifugal, thermal, seismic, and erection forces. Various combinations of these loads must be considered as designated in groups I through X. (See Art. 11.5.1.) The LRFD Specification separates loads into two...

## Fremont Bridge

TYPE Half-through, tied, solid ribbed arch, 28 panels at 44.83 ft SPAN 1,255 ft RISE 341 ft RISE SPAN 1 3.7 NO. OF LANES OF TRAFFIC 4 each upper and lower roadways HINGES 2 DEPTH 4 ft DEPTH SPAN 1 314 Decks and Railings and Floor steel for roadway Floor bracing Arch Arch Arch hangers or columns and bracing Arch tie girders TOTAL SPECIFICATION FOR LIVE LOADING AASHTO HS20-44 EQUIVALENT LIVE + IMPACT LOADING FOR ARCH FOR FULLY LOADED STRUCTURE 2,510 lb per ft TYPES OF STEEL IN STRUCTURE Arch ribs...

## 211 Cleaning And Painting

The AISC Specification for Structural Steel Buildings'' provides that, in general, steelwork to be concealed within the building need not be painted and that steel encased in concrete should not be painted. Inspection of old buildings has revealed that the steel withstands corrosion virtually the same whether painted or not. Paint is expensive to apply, creates environmental concerns in the shop and can create a slip hazard for erectors. Environmental requirements vary by region. Permitting...

## T Kane PE

Technical Manager, Cives Steel Company, Roswell, Ga. In this section, the term connections is used in a general sense to include all types of joints in structural steel made with fasteners or welds. Emphasis, however, is placed on the more commonly used connections, such as beam-column connections, main-member splices, and truss connections. Recommendations apply to buildings and to both highway and railway bridges unless otherwise noted. This material is based on the specifications of the...

## Ae

The factor AE L represents the stiffness of the member in resisting axial loads. It gives the magnitude of an axial load needed to produce a unit displacement. Equations (3.50) to (3.51) hold for both tension and compression members. However, since compression members may buckle prematurely, these equations may apply only if the member is relatively short (Arts. 3.46 and 3.49). FIGURE 3.19 Representation of types of ideal supports (a) roller, (b) hinged support, (c) fixed support. FIGURE 3.19...

## 15171 Preliminary Design by Steinman Baker Procedure

Analysis by elastic theory is sufficiently accurate for short spans and designs with deep, rigid stiffening systems that limit deflections to small amounts. The simple calculations of elastic theory are also useful, however, for preliminary designs and estimates if tubular percentage corrections are applied, based on experience with the deflection theory. The corrections depend principally on the magnitude of the dead load and on the flexibility of the structure. The magnitude of the...

## 151 Evolution Of Cablesuspended Bridges

Early cable-suspended bridges were footbridges consisting of cables formed from twisted vines or hide drawn tightly to reduce sag. The cable ends were attached to trees or other permanent objects located on the banks of rivers or at the edges of gorges or other natural obstructions to travel. The deck, probably of rough-hewn plank, was laid directly on the cable. This type of construction was used in remote ages in China, Japan, India, and Tibet. It was used by the Aztecs of Mexico, the Incas...

## 15172 Preliminary Design by Hardesty Wessman Procedure

FIGURE 15.51 Steinman-Baker correction curves for stresses obtained by elastic theory for suspension bridges. (Reprinted with permission form D. B. Steinman, A Practical Treatise on Suspension Bridges,'' 2d ed., John Wiley & Sons, Inc., New York.) FIGURE 15.51 Steinman-Baker correction curves for stresses obtained by elastic theory for suspension bridges. (Reprinted with permission form D. B. Steinman, A Practical Treatise on Suspension Bridges,'' 2d ed., John Wiley & Sons, Inc., New...

## 19 Hardness Tests

In the Brinell hardness test, a small spherical ball of specified size is forced into a flat steel specimen by a known static load. The diameter of the indentation made in the specimen can be measured by a micrometer microscope. The Brinell hardness number may then be calculated as the ratio of the applied load, in kilograms, to the surface area of the indentation, in square millimeters. In practice, the hardness number can be read directly from tables for given indentation measurements. The...

## 27 Camber

Camber is a curvature built into a member or structure so that when it is loaded, it deflects to a desired shape. Camber, when required, might be for dead load only, dead load and partial live load, or dead load and full live load. The decision to camber and how much to camber is one made by the designer. Rolled beams are generally cambered cold in a machine designed for the purpose, in a large press, known as a bulldozer or gag press, through the use of heat, or a combination of mechanically...

## 075

Price factors for shapes tend to be lower. A852 and A514 steels are not available in shapes. * Based on plates 3 4 X 96 X 240 in. Price factors for shapes tend to be lower. A852 and A514 steels are not available in shapes. section modulus. Their relative weight W2 W1 and relative cost C2 C1 are influenced by the web depth-to-thickness ratio d 1. For example, if the two members have the same d 1 values, such as a maximum value imposed by the manufacturing...

## 5833

Fy F' (-720,000 + 4200 - 2.75T2)10-6 800 F < T < 1200 F (1.10) E E' 1 - T50010()0 100 F < T < 700 F (1.11) E E' (500,000 + 1333T - 1.111T2)10-6 700 F < T < 1200 F (1.12) a (6.1 + 0.0019T)10-6 100 F < T < 1200 F (1.13) In these equations Fy Fy and E E are the ratios of elevated-temperature to room-temperature yield strength and modulus of elasticity, respectively, a is the coefficient of thermal expansion per degree Fahrenheit, and T is the temperature in degrees Fahrenheit....

## 46 Ribbed Domes

As pointed out in Art. 4.5, domes may be thin-shell, framed, or a combination. One type of framed dome consists basically of arch ribs with axes intersecting at a common point at the crown and with skewbacks, or bases, uniformly spaced along a closed horizontal curve. Often, to avoid the complexity of a joint with numerous intersecting ribs at the crown, the arch ribs are terminated along a compression ring circumscribing the crown. This construction also has the advantage of making it easy to...

## 1375 X

The distance from the neutral axis to the center of curvature of the rocker is With Rr as radius, live load causes an expansion of 60 X 0.005 0.30 in at each end of the girder. Thus, the rocker must be capable of accommodating a live-load expansion of 2 X 0.3 0.60 in. Addition of this to the thermal expansion yields a total expansion of Maximum shortening is 0.76 in. The 4-in web of the rocker (Fig. 12.43) permits movements up to 4 2 2 in, expansion or contraction. Rocker. The rocker has a...

## Moment At Midspan

FIGURE 3.85 Influence diagrams for a beam with overhang. FIGURE 3.86 Determination for moving loads on a simple beam (a) of maximum end reaction (b) and maximum midspan moment (c) from influence diagrams. FIGURE 3.86 Determination for moving loads on a simple beam (a) of maximum end reaction (b) and maximum midspan moment (c) from influence diagrams. Ra 12 X 1.0 X 60 X 1.0 + 16 X 1.0 + 16 X 0.767 + 4 X 0.533 60.4 kips Figure 3.86c is the influence diagram for midspan bending moment with a...

## 020

Mu 328.0 ft-kips, and the plastic modulus required is Z Mu 0.9Fy 328 X 12 (0.9 X 50) 87.5 in3. The least-weight section with larger modulus is a W21 X 44, with Z 95.4 Camber. This is computed for maximum deflection attributable to full construction dead loads. For this computation, the dead-load portion of the end moments is included. The loads are listed under construction dead load in Table 7.4. The corresponding deflection is 1.09 in. A camber of 1 in may be specified. Design for Maximum End...

## 11447 Stiffeners at Bearing Points

Stiffeners should be provided in pairs, opposite each other, at the centerline of the end bearing of plate girders and beams. Appropriately positioned pairs of stiffeners should be placed at all points of concentrated loads. Stiffener width should be as wide as the flange will accommodate, and the stiffener connection to the web should have the capacity to transmit the load. Angle stiffeners should not be crimped. Plate stiffeners should be clipped top and bottom to clear the fillet of the...

## Ae And Ei In Structure In Engg

Ma statically determinate moment due to unit horizontal force applied at cut end of cable Mo statically determinate moment due to loads Na statically determinate axial forces due to unit horizontal force applied at cut end of cable No statically determinate axial forces due to loads E modulus of elasticity of stiffening-truss steel I moment of inertia of stiffening truss A cross-sectional area of member subjected to axial force et coefficient of thermal expansion t temperature change Ac...

## R A LaBoube PE

Professor of Civil Engineering, University of Missouri-Rolla, Rolla, Missouri Building designs generally are controlled by local or state building codes. In addition, designs must satisfy owner requirements and specifications. For buildings on sites not covered by building codes, or for conditions not included in building codes or owner specifications, designers must use their own judgment in selecting design criteria. This section has been prepared to provide information that will be helpful...

## 121

FIGURE 12.1 Two-lane highway bridge with rolled-beam stringers. (a) Framing plan. (b) Typical cross section. FIGURE 12.1 Two-lane highway bridge with rolled-beam stringers. (a) Framing plan. (b) Typical cross section. Spacing. For railroad bridges, two stringers generally carry each track. They may, however, be more widely spaced than the rails, for stability reasons. If a bridge contains only two stringers, the distance between their centers should be at least 6 ft 6 in. When more stringers...

## 319 Shear Deflections In Beams

Shear deformations in a beam add to the deflections due to bending discussed in Art. 3.18. Deflections due to shear are generally small, but in some cases they should be taken into When a cantilever is subjected to load P (Fig. 3.51a), a portion dx of the span undergoes a shear deformation (Fig. 3.51b). For an elastic material, the angle y equals the ratio of the shear stress v to the shear modulus of elasticity G. Assuming that the shear on the element is distributed uniformly, which is an...

## 617 Bending Strength

For a member subjected to flexure, the bending strength depends on the shape of the member, width thickness or depth thickness ratios of its elements, location and direction of loading, and the support given to the compression flange. Higher strengths are assigned to symmetrical and compact shapes. Flexural strength may be reduced, however, based on the spacing of lateral supports that prevent displacement of the compression flange and twist of the cross section. The AISC LRFD and ASD...

## 36

FIGURE 3.24 For a rectangular beam (a) in the plastic range, strain distribution (b) is linear, while stress distribution (c) is rectangular. FIGURE 3.24 For a rectangular beam (a) in the plastic range, strain distribution (b) is linear, while stress distribution (c) is rectangular. To determine these stresses, consider the portion of a beam with length dx between vertical sections 1-1 and 2-2 (Fig. 3.25). At a horizontal section a distance y from the neutral axis, the horizontal shear force...

## 821 Arched Roofs

These are advantageous for long bays, especially if large clearances are desirable along the center. Such braced barrel vaults have been used for hangars, gymnasiums, and churches. While these roofs can be supported on columns, they also can be extended to the ground, thus eliminating the need for walls (Fig. 8.30). The roofs usually are relatively lightweight, FIGURE 8.30 Cylindrical arches. (a) Ribbed (b) diagonal grid (lamella) (c) pleated barrel. FIGURE 8.30 Cylindrical arches. (a) Ribbed...

## 618 Bearing

For bearing on the contact area of milled surfaces, pins in reamed, drilled, or bored holes, and ends of a fitted bearing stiffener, the LRFD design strength is tpRn (kips), where tp 0.75 and Rn l.8FyApb. The projected bearing area (in2) is represented by Apb, and Fy is the specified minimum yield stress (ksi) for the part in bearing with the lower yield stress. Expansion rollers and rockers are limited to an LRFD bearing strength 4> Rn, with tp 0.75 Rn 6.0(Fy - 13) Vd 20 (6.63b) where d...

## 1410 Buckling Considerations For Arches

Since all arches are subjected to large compressive stresses and also usually carry significant bending moments, stability considerations must be addressed. The American Association of State Highway and Transportation Officials (AASHTO) Standard Specifications for Highway Bridges'' contain provisions intended to ensure stability of structures. For true arches, the design should provide stability in the vertical plane of the arch, with the associated effective buckling length, and also provide...

## 256

(b - f) W-f l Vl2 + 4f2 sin a V2f (b + f) l Vh2 + l2 V2f (h + 2f) 2f Vl2 + 4f2 4a V1 + 16a2 TABLE 15.6 Equations for Catenary and Parabolic Cables* (Continued) Vertical component V of cable tension Horizontal component H of cable tension * Adapted from H. Odenhausen, ''Statical Principles of the Application of Steel Wire Ropes in Structural Engineering,'' Acier-Stahl-Steel, no. 2, pp. 51-65, 1965. x (x h)2 (x h)4 (x h)6 cosh - 1 +-- --1-----1-- --+ the parabolic profile (obtained by dropping...

## 1311 Member Design Examplelrfd

The design of a truss hanger by the AASHTO LRFD Specifications is presented subsequently. This is preceded by the following introduction to the LRFD member design provisions. 13.11.1 LRFD Member Design Provisions Tension Members. The net area, An, of a member is the sum of the products of thickness and the smallest net width of each element. The width of each standard bolt hole is taken as the nominal diameter of the bolt plus 0.125 in. The width deducted for oversize and slotted holes, where...

## 01801

Esslinger, Suspension Bridge Design Calculations by Electronic Computer,'' Acier-Stahl-Steel, no. 5, pp. 223-230, 1962. A. A. Jakkula, Theory of the Suspension Bridge,'' IABSE Publication, vol. 4, pp. 333358, 1936. C. P. Kuntz, J. P. Avery, and J. L. Durkee, Suspension-bridge Truss Analysis by Electronic Computer,'' ASCE Conference on Electronic Computation, Nov. 20-21, 1958. D. J. Peery, An Influence-line Analysis for Suspension Bridges,'' ASCE Transactions, vol. 121, pp. 463-510, 1956. T....

## 1

The allowable tensile load (kips) per fastener, including the effect of prying action, is given by B allowable bolt tension, including the effect of shear, if any, kips t thickness of thinnest connected flange or angle leg, in P length of flange or angle leg tributary to a bolt, in Fy flange or angle yield stress, ksi a' a + d 2 a distance from center of fastener to edge of flange or angle leg, in (not to exceed b distance from center of fastener to face of tee stem or angle leg, in P b' a' S 1...

## 812 Stub Girders

The primary advantage of the stub-girder system is that it provides ample space for routing mechanical ductwork throughout a floor while achieving a reduced floor construction depth as compared to conventional steel framing. This system utilizes floorbeams that are supported on top of, rather than framed into, stub girders. Thus, the floorbeams are designed as continuous members, which results in steel savings and reduced deflections. A stub girder consists of a shallow wide-flange member...

## 526 Tension Splices

Design rules for tension splices are substantially the same as those for hanger connections. In buildings, splices should develop the strength required by the stresses at point of splice. For groove welds, however, the full strength of the smaller spliced member should be developed. In highway bridges, splices should be designed for the larger of the following 75 of the strength of the member or the average of the calculated stress at point of splice and the strength of the member there. Where...

## 341 Elastic Flexural Buckling Of Columns

A member subjected to pure compression, such as a column, can fail under axial load in either of two modes. One is characterized by excessive axial deformation and the second by flexural buckling or excessive lateral deformation. For short, stocky columns, Eq. (3.48) relates the axial load P to the compressive stress . After the stress exceeds the yield point of the material, the column begins to fail. Its load capacity is limited by the strength of the material. In long, slender columns,...

## 315 Members Subjected To Torsion

Forces or moments that tend to twist a member are called torisonal loads. In shafts, the stresses and corresponding strains induced by these loads depend on both the shape and size of the cross section. Suppose that a circular shaft is fixed at one end and a twisting couple, or torque, is applied at the other end (Fig. 3.21a). When the angle of twist is small, the circular cross section remains circular during twist. Also, the distance between any two sections remains the same, indicating that...

## 131

These trusses were statically indeterminate. Stress analysis was difficult. Latter, simpler web systems were adopted, thus eliminating the need for tedious and exacting design procedures. To eliminate secondary stresses due to rigid joints, early American engineers constructed pin-connected trusses. European engineers primarily used rigid joints. Properly proportioned, the rigid trusses gave satisfactory service and eliminated the possibility of frozen pins, which induce stresses not usually...

## 138 Truss Design Procedure

The following sequence may serve as a guide to the design of truss bridges Select span and general proportions of the bridge, including a tentative cross section. Design the roadway or deck, including stringers and floorbeams. Design upper and lower lateral systems. Design portals and sway frames. Design posts and hangers that carry little stress or loads that can be computed without a complete stress analysis of the entire truss. Compute preliminary moments, shears, and stresses in the truss...

## S

5-5 5-5 1.454 wheels 0.727 axle Hence, the maximum live-load moment is While this moment does not occur at midspan as do the maximum dead-load moments, stresses due to Mll may be combined with those from Mdl and Msdl to produce the maximum stress, for all practical purposes. For maximum shear with the truck load, the outer 40-kip load should be placed at the support (Fig. 12.3c). Then, the shear is 90(74 - 14 + 4.66) VT -74-- 78.6 kips This loading governs, because the shear due to lane loading...

## 300

*In joints involving combinations of base metals, preheat as specified for the higher-strength steel being welded. f Use only low-hydrogen electrodes when welding A36 steel more than 1 in thick for dynamically loaded structures. When the base-metal temperature is below 32 F, the base metal should be preheated to at least 70 F and the minimum temperature maintained during welding. *In joints involving combinations of base metals, preheat as specified for the higher-strength steel being welded. f...

## 15191 Static Analysis Elastic Theory

Cable-stayed bridges may be analyzed by the general method of indeterminate analysis with the equations of virtual work. The degree of internal redundancy of the system depends on the number of cables, types of connections (fixed or movable) of cables with the pylons, and the nature of the pylon connection at its base with the stayed girder or pier. The girder is usually made continuous over three spans. Figure 15.55 shows the order of redundancy for various single-plane systems of cables. If...

## 330 Forces In Statically Determinate Trusses

A convenient method for determining the member forces in a truss is to isolate a portion of the truss. A section should be chosen such that it is possible to determine the forces in the cut members with the equations of equilibrium Eq. (3. 11) or (3.12) . Compressive forces act toward the panel point, and tensile forces act away from the panel point. To calculate the force in member a of the truss in Fig. 3.67a, the portion of the truss in Fig. 3.67b is isolated by passing section x-x through...

## Runner Line

Stiffleg derricks are extremely versatile in that they can be used in a permanent location as yard derricks or can be mounted on a wheel-equipped frame for use as a traveler in bridge erection. A stifleg derrick also can be mounted on a device known as a creeper and thereby lift itself vertically on a structure as it is being erected. Stiffleg derricks can range from small, 5-ton units to large, 250-ton units, with 80-ft masts and 180-ft booms. A guy derrick (Fig. 2.6) is...

## 111 Effect Of Strain Rate On Tensile Properties

Tensile properties of structural steels are usually determined at relatively slow strain rates to obtain information appropriate for designing structures subjected to static loads. In the design of structures subjected to high loading rates, such as those caused by impact loads, however, it may be necessary to consider the variation in tensile properties with strain rate. Figure 1.8 shows the results of rapid tension tests conducted on a carbon steel, two HSLA steels, and a constructional alloy...