Tag Archives: tension

Development, Anchorage, and Splices of Reinforcement

Steel reinforcement must be bonded to the concrete sufficiently so that the steel will yield before it is freed from the concrete. Despite assumptions made in the past to the contrary, bond stress between concrete and reinforcing bars is not uniform over a given length, not directly related to the perimeter of the bars, not equal in tension and compression, and may be affected by lateral confinement. The ACI 318 Building Code requirements therefore reflect the significance of average bond resistance over a length of bar or wire sufficient to develop its strength (development length).
The calculated tension or compression force in each reinforcing bar at any section [Eqs. (9.53) to (9.61) and (9.64)] must be developed on each side of that section by a development length Ld, or by end anchorage, or both. Hooks can be used to assist in the development of tension bars only.
The critical sections for development of reinforcement in flexural members are located at the points of maximum stress and where the reinforcement terminates or is bent.
The following requirements of the ACI 318 Building Code for the development of reinforcement were proposed to help provide for shifts in the location of maximum moment and for peak stresses that exist in regions of tension in the remaining bars wherever adjacent bars are cut off or bent. In addition, these requirements help minimize any loss of shear capacity or ductility resulting from flexural cracks that tend to open early whenever reinforcement is terminated in a tension zone.

Development for All Flexural Reinforcement

Reinforcement should extend a distance of d of 12db, whichever is larger, beyond the point where the steel is no longer required to resist tensile stress, where d is the effective depth of the member and db is the nominal diameter of the reinforcement.
This requirement, however, does not apply at supports of simple spans and at the free end of cantilevers.
Continuing reinforcement should extend at least the development length Ld beyond the point where terminated or bent reinforcement is no longer required to resist tension.
Reinforcement should not be terminated in a tension zone unless one of the following conditions is satisfied:

Development for Positive-Moment Reinforcement

A minimum of one-third the required positive-moment reinforcement for simple beams should extend along the same face of the member into the support, and in beams, for a distance of not less than 6 in.
A minimum of one-fourth the required positive-moment reinforcement for continuous members should extend along the same face of the member into the support, and in beams, for a distance of at least 6 in.
For lateral-load-resisting members, the positive-moment reinforcement to be extended into the support in accordance with the preceding two requirements should be able to develop between the face of the support and the end of the bars the yield strength ƒy of the bars.
Positive-moment tension reinforcement at simple supports and at points of inflection should be limited to a diameter such that the development length, in computed for ƒy with Eqs. (9.54) to (9.58) and (9.61) does not exceed

The value of Mn /Vu can be increased by 30% when the ends of the reinforcement are confined by a compressive reaction. It is not necessary to satisfy Eq. (9.53) for reinforcing bars that terminate beyond the center of simple supports with a standard hook, or terminate with a mechanical anchorage equivalent to a standard hook.

Development for Negative-Moment Reinforcement

Negative-moment reinforcement in continuous, restrained, or cantilever members should be developed in or through the supporting member.
Negative-moment reinforcement should have sufficient distance between the face  of the support and the end of each bar to develop its full yield strength.
A minimum of one-third of the required negative-moment reinforcement at the face of the support should extend beyond the point of inflection the greatest of d, 12db, or one-sixteenth of the clear span.

Computation of Development Length

Tension development length, Ld, is the length of deformed bar or deformed wire required to develop, or to transfer to the concrete, the full tensile capacity of the bar or wire. The tension development length of an uncoated bar or wire in normal weight concrete is expressed as a function of yield strength of the bar; ƒy; the square

Increased Ld is required for bundled bars: in 3-bar bundles, 20%; in 4-bar bundles, 33%. For determining the appropriate modifying factors for use with bundled bars, a unit of bundled bars should be treated as a single bar with a diameter derived from the equivalent total area.
Application of all the various interdependent tension development length requirements to each structural element in design would be extremely difficult and a waste of design time. The authors recommend that the designer check the actual dimensions available for tension development in the connection (or from a cutoff point established as a fraction of the span on typical design drawing details), compare to a table of development lengths required for each bar size, and select the bar size allowable. Table 9.8, which is based on the direct short-cut method, presents values of tension Ld for each size bar for normal-weight concrete with compressive strengths of 3000, 4000 and 5000 psi. Note that separate values are tabulated for ‘‘top bars’’ and ‘‘other bars.’’

Anchorage with Hooks

For rebars in tension, standard 90 and 180 end hooks can be used as part of the length required for development or anchorage of the bars. Table 9.9 gives the minimum tension embedment length Ldh required with standard end hooks (Fig. 9.17 and Table 9.9) and Grade 60 bars to develop the specified yield strength of the bars.

Development for Welded-Wire Fabric in Tension

For deformed welded-wire fabric (WWF) with at least one cross wire within the development length not less than 2 in. from the point of critical section (Fig. 9.18), the tension development length is the length calculated from Eqs. (9.54) and (9.56) using the direct short-cut method or from Eq. (9.58) using the more rigorous method and then multiplied by a wire fabric factor. The wire fabric factor is the larger of

The resulting development length should be at least 8 in except for determining lap splice lengths. When using Eqs. (9.54), (9.56) or (9.58), an epoxy-coated welded wire fabric factor of 1.0 can be taken for B . For deformed WWF with no cross wires within the development length or with a single cross wire less than 2 in from the point of the critical section, the wire fabric factor should also be taken as 1.0.

Tension Lap Splices

Bar sizes No. 11 or less and deformed wire may be spliced by lapping. Tension lap splices are classified in two classes, A and B, depending on the stress in the bars to be spliced. The minimum lap length Ls is expressed as a multiple of the tension development length Ld of the bar or deformed wire (Art. 9.49.4).
Class A tension lap splices include splices at sections where the tensile stress due to factored loads does not exceed 0.5ƒy and not more than one-half the bars at these sections are spliced within one Class A splice length of the section. For Class A splices,

Compression development length Ld is calculated by multiplying Ldb by optional modification factors. When bars are enclosed by a spiral at least 1⁄4 in in diameter and with not more than a 4-in pitch, or by ties at least size No. 4 with a spacing not more than 4 in., a modification factor of 0.75 may be used but the lap should be at least 8 in. It excess reinforcement is provided, Ldb may be reduced by the ratio of the area of steel required to area of steel provided. For general practice, with concrete compressive strength psi, use 22db ƒ’c => 3000 for compression em- c bedment of dowels (Table 9.11).
For bundled bars in compression, the development length of each bar within the bundle should be increased by 20% for a three-bar bundle and 33% for a four-bar bundle.

Compression Lap Splices

Minimum lap-splice lengths of rebars in compression Ls vary with nominal bar diameter db and yield strength ƒy of the bars. For bar sizes No. 11 or less, the compression lap-splice length is the largest of 12 in or the values computed from Eqs. (9.65a) and (9.65b):

When is less than 3000 psi, the length of lap should be one-third greater than ƒc the values computed from the preceding equations.
When the bars are enclosed by a spiral, the lap length may be reduced by 25%.
For general practice, use 30 bar diameters for compression lap splices (Table 9.11).
Spiral should conform to requirements of the ACI 318 Building Code: Spirals should extend from top of footing or slab in any story to the level of the lowest horizontal reinforcement in members supported above. The ratio of volume of spiral reinforcement to the total volume of the concrete core (out-to-out of spirals) should be at least that given in Art. 9.83. Minimum spiral diameter in cast-in-place construction is 3⁄8 in. Clear spacing between spirals should be limited to 1 to 3 in.

Spirals should be anchored by 11⁄2 extra turns of spiral bar or wire at each end of a spiral unit. Lap splices, or full mechanical or welded splices can be used to splice spiral reinforcement. Lap splice lengths should comply with Table 9.12, but not be less than 12 in.

The ACI 318 Building Code contains provisions for lap splicing bars of different sizes in compression. Length of lap should be the larger of the compression development length required for the larger size bar or the compression lap-splice length required for the smaller bar. It is permissible to lap-splice the large bar sizes, Nos. 14 and 18, to No. 11 and smaller bars.

Mechanical and Welded Splices

As an alternative to lap splicing, mechanical splices or welded splices may be used.
When traditional lap splices satisfy all requirements, they are generally the most economical. There are conditions, however, where they are not suitable: The ACI 318 Building Code does not permit lap splices of the large-size bars (Nos. 14 and 18) except in compression to No. 11 and smaller bars. Lap splices cause congestion at the splice locations and their use then may be impracticable. Under certain conditions, the required length of tension lap splices for No. 11 and similar-size bars can be excessive and make the splices uneconomical. For these reasons, mechanical splices or welded splices may be suitable alternatives.
Mechanical splices are made with proprietary devices. The ACI 318 Building Code requires a full mechanical splice to have a capacity, in tension or compression, equal to at least 125% of the specified ƒy of the bar. End-bearing mechanical splices may be used where the bar stress due to all conditions of factored loads is compressive.
For these types of compression-only splices, the ACI 318 Building Code prescribes requirements for the squareness of the bars ends. Descriptions of the commercially-available proprietary mechanical splice devices are given in ‘‘Mechanical Connections of Reinforcing Bars,’’ ACI 439.3R, and ‘‘Reinforcement Anchorages, and Splices,’’ Concrete Reinforcing Steel Institute.
For a full-welded splice, the ACI 318 Building Code requires the butt-welded bars to have a tensile capacity of at least 125% of the specified ƒy of the bar.
Welding should conform to ‘‘Structural Welding Code—Reinforcing Steel’’ (ANSI/  AWS D1.4), American Welding Society.

Anchorage of Web Reinforcement

Stirrups are reinforcement used to resist shear and torsion. They are generally bars, wire or welded-wire fabric, either single leg or bent into L, U, or rectangular shapes.
Stirrups should be designed and detailed to be installed as close as possible to the compression and tension surfaces of a flexural member as concrete cover requirements and the proximity of other reinforcing steel will permit. They should be installed perpendicular or inclined with respect to flexural reinforcement and spaced closely enough to cross the line of every potential crack. Ends of singleleg, simple U stirrups, or transverse multiple U stirrups should be anchored by one of the following means:
1. A standard stirrup hook around a longitudinal bar for stirrups fabricated from No. 5 bars or D31 wire or smaller sizes. Stirrups fabricated from bar sizes Nos. 6, 7, and 8 in Grade 40 can be anchored similarly.

Each leg of simple U stirrups made of plain welded-wire fabric should be anchored by one of the following means:

1. Two longitudinal wires located at the top of the U and spaced at 2 in.
2. One longitudinal wire located at a distance of d/4 or less from the compression face and a second wire closer to the compression face and spaced at least 2 in from the first wire. (d  distance, in from compression surface to centroid of tension reinforcement.) The second wire can be located on the stirrup leg beyond a bend, or on a bend with an inside diameter of at least 8db.
Each end of a single-leg stirrup, fabricated from plain or deformed welded-wire fabric, should be anchored by two longitudinal wires spaced at 2 in minimum. The inner wire of the two longitudinal wires should be located at least the larger of d/4 or 2 in from the middepth of the member d/2. The outer longitudinal wire at the tension face of the member should be located not farther from the face than the portion of primary flexural reinforcement closest to the face.
Between anchored ends, each bend in the continuous portion of a simple U or multiple U stirrup should enclose a longitudinal bar.

Stirrup Splices

Pairs of U stirrups or ties placed to form a closed unit may be considered properly spliced when the legs are lapped over a minimum distance of 1.3Ld. In members at least 18 in deep, such splices may be considered adequate for No. 3 bars of Grade 60 and Nos. 3 and 4 bars of Grade 40 if the legs extend the full available depth of the member.

Bearing-Type Bolted Connections

When some slip, although very small, may occur between connected parts, the  fasteners are assumed to function in shear. The presence of paint on contact surfaces is therefore of no consequence. Fasteners may be A307 bolts or high-strength bolts or any other similar fastener not dependent on development of friction on the contact surfaces.
Single shear occurs when opposing forces act on a fastener as shown in Fig. 7.39a, tending to slide on their contact surfaces. The body of the fastener resists this tendency; a state of shear then exists over the cross-sectional area of the fastener.
Double-shear takes place whenever three or more plates act on a fastener as illustrated in Fig. 7.40b. There are two or more parallel shearing surfaces (one on each side of the middle plate in Fig. 7.40b). Accordingly, the shear strength of the fastener is measured by its ability to resist two or more single shears.
Bearing on Base Metal. This is a factor to consider; but calculation of bearing stresses in most joints is useful only as an index of efficiency of the net section of tension members.

Eccentric Loading. Stress distribution is not always as simple as for the joint in Fig. 7.40a where the fastener is directly in the line of significant. Sometimes, the load is applied eccentrically, as shown in Fig. 7.41. For such connections, tests show that use of actual eccentricity to compute the maximum force on the extreme fastener is unduly conservative because of plastic behavior and clamping force generated by the fastener. Hence, it is permissible to reduce the actual eccentricity to a more realistic ‘‘effective’’ eccentricity.
For fasteners equally spaced on a single gage line, the effective eccentricity in inches is given by

Tension and Shear. For fastener group B in Fig. 7.41b, use actual eccentricity l2 since these fasteners are subjected to combined tension and shear. Here too, the load P can be resolved into an axial shear force through the fasteners and a couple.
Then, the stress on each fastener caused by the axial shear is P/n, where n is the number of fasteners. The tensile forces on the fasteners vary with distance from the center of rotation of the fastener group.
A simple method, erring on the safe side, for computing the resistance moment of group B fasteners assumes that the center of rotation coincides with the neutral axis of the group. It also assumes that the total bearing pressure below the neutral  axis equals the sum of the tensile forces on the fasteners above the axis. Then, with these assumptions, the tensile force on the fastener farthest from the neutral axis is

Tension Members

These are proportioned so that their gross and net areas are large enough to resist imposed loads. The criteria for determining the net area of a tension member with bolt holes is the same for allowable stress design and load-and-resistance-factor design. In determination of net area, the width of a bolt hole should be taken 1⁄16 in larger than the nominal dimension of the hole normal to the direction of applied stress. Although the gross section for a tension member without holes should be taken normal to the direction of applied stress, the net section for a tension member with holes should be chosen as the one with the smallest area that passes through any chain of holes across the width of the member. Thus, the net section may pass through a chain of holes lying in a plane normal to the direction of applied stress or through holes along a diagonal of zigzag line.
Net section for a member with a chain of holes extending along a diagonal or zigzag line is the product of the net width and thickness. To determine net width, deduct from the gross width the sum of the diameters of all the holes in the chain, then add, for each gage space in the chain, the quantity

s^2 /4g

where s  longitudinal spacing (pitch, in) of any two consecutive holes and g  transverse spacing (gage, in) of the same two holes.
The critical net section of the member is obtained from that chain with the least net width.
When a member axially stressed in tension is subjected to nonuniform transfer of load because of connections through bolts to only some of the elements of the cross section, as in the case of a W, M, or S shape connected solely by bolts through the flanges, the net area should be reduced as follows: 10% if the flange width is at least two-thirds the beam depth and at least three fasteners lie along the line of stress; 10% also for structural tees cut from such shapes; 15% for any of the preceding shapes that do not meet those criteria and for other shapes that have at least three fasteners in line of stress; and 25% for all members with only two fasteners in the line of stress.

ASD of Tension Members

Unit tensile stress Ft on the gross area should not exceed 0.60Fy, where Fy is the minimum yield stress of the steel member (see Table 7.11). Nor should Ft exceed 0.50Fu, where Fu is the minimum tensile strength of the steel member, when the allowable stress is applied to the net area of a member connected with fasteners requiring holes. However, if the fastener is a large pin, as used to connect eyebars, pin plates, etc., Ft is limited to 0.45Fy on the net area. Therefore, for the popular  A36 steel, the allowable tension stresses for gross and net areas are 22.0 and 29.0 ksi, respectively, and in the case of pin plates, 16.2 ksi.

LRFD of Tension Members

Design tensile strength Pn, kips, of the gross area Ag, in2, should not exceed 0.90Fy, where Fy is the minimum yield stress of the steel (Table 7.9) and Pn  AgFy. Nor should the design tensile strength Pn, kips, exceed 0.75Fu on the net area Ae, in2, of the member. Other criteria control the design tensile strength of pinconnected members. (Refer to the AISC specification for LRFD.)

Member Design Example-LRFD

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.

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 permitted in AASHTO LRFD Art., is taken as 0.125 in greater than the hole size specified in AASHTO LRFD Art. The net width is determined for each chain of holes extending across the member along any transverse, diagonal, or zigzag line, as discussed in Art. 13.9.
In designing a tension member, it is conservative and convenient to use the least net width for any chain together with the full tensile force in the member. It is sometimes possible to achieve an acceptable, but slightly less conservative design, by checking each possible chain with a tensile force obtained by subtracting the force removed by each bolt ahead of that chain (bolt closer to midlength of the member), from the full tensile force in the member.
This approach assumes that the full force is transferred equally by all bolts at one end.
Members and splices subjected to axial tension must be investigated for two conditions:
yielding on the gross section (Eq. 13.11), and fracture on the net section (Eq. 13.12). Determination of the net section requires consideration of the following:
• The gross area from which deductions will be made, or reduction factors applied, as appropriate
• Deductions for all holes in the design cross-section
• Correction of the bolt hole deductions for the stagger rule
• Application of a reduction factor U, to account for shear lag
• Application of an 85% maximum area efficiency factor for splice plates and other splicing elements
The factored tensile resistance, Pr, is the lesser of the values given by Eqs. 13.11 and 13.12.

The reduction factor, U, does not apply when checking yielding on the gross section because yielding tends to equalize the non-uniform tensile stresses over the cross section caused by shear lag.
Unless a more refined analysis or physical tests are utilized to determine shear lag effects, the reduction factors specified in the AASHTO LRFD Specifications may be used to account for shear lag in connections as explained in the following.
The reduction factor, U, for sections subjected to a tension load transmitted directly to each of the cross-sectional elements by bolts or welds may be taken as:

U=  1.0

For bolted connections, the following three values of U may be used depending on the details of the connection:
For rolled I-shapes with flange widths not less than two-thirds the depth, and structural tees cut from these shapes, provided the connection is to the flanges and has no fewer than three fasteners per line in the direction of stress,
U = 0.90

For all other members having no fewer than three fasteners per line in the direction of stress,
U = 0.85

For all members having only two fasteners per line in the direction of stress,
U = 0.75

Due to strain hardening, a ductile steel loaded in axial tension can resist a force greater than the product of its gross area and its yield strength prior to fracture. However, excessive elongation due to uncontrolled yielding of gross area not only marks the limit of usefulness, it can precipitate failure of the structural system of which it is a part. Depending on the ratio of net area to gross area and the mechanical properties of the steel, the component can fracture by failure of the net area at a load smaller than that required to yield the gross area.
General yielding of the gross area and fracture of the net area both constitute measures of component strength. The relative values of the resistance factors for yielding and fracture reflect the different reliability indices deemed proper for the two modes.
The part of the component occupied by the net area at fastener holes generally has a negligible length relative to the total length of the member. As a result, the strain hardening is quickly reached and, therefore, yielding of the net area at fastener holes does not constitute a strength limit of practical significance, except, perhaps, for some built-up members of unusual proportions.
For welded connections, An is the gross section less any access holes in the connection region.
Compression Members. Bridge members in axial compression are generally proportioned with width/ thickness ratios such that the yield point can be reached before the onset of local buckling. For such members, the nominal compressive resistance, Pn, is taken as:

To avoid premature local buckling, the width-to-thickness ratios of plate elements for compression members must satisfy the following relationship:

Members Under Tension and Flexure. A component subjected to tension and flexure must satisfy the following interaction equations:

Interaction equations in tension and compression members are a design simplification. Such equations involving exponents of 1.0 on the moment ratios are usually conservative. More exact, nonlinear interaction curves are also available and are discussed in the literature. If these interaction equations are used, additional investigation of service limit state stresses is necessary to avoid premature yielding.
A flange or other component subjected to a net compressive stress due to tension and flexure should also be investigated for local buckling.

Members Under Compression and Flexure. For a component subjected to compression and flexure, the axial compressive load, Pu, and the moments, Mux and Muy, are determined for concurrent factored loadings by elastic analytical procedures. The following relationships must be satisfied:

The moments about the axes of symmetry, Mux and Muy, may be determined by either (1) a second order elastic analysis that accounts for the magnification of moment caused by the factored axial load, or (2) the approximate single step adjustment specified in AASHTO LRFD Art.

LRFD Design of Truss Hanger

The following example, prepared in the SI system of units, illustrates the design of a tensile member that also supports a primary live load bending moment. The existence of the bending moment is not common in truss members, but can result from unusual framing. In this example, the bending moment serves to illustrate the application of various provisions of the LRFD Specifications.
A fabricated H-shaped hanger member is subjected to the unfactored design loads listed in Table 13.7. The applicable AASHTO load factors for the Strength-I Limit State and the Fatigue Limit State are listed in Table 13.8. The impact factor, I, is 1.15 for the fatigue limit state and 1.33 for all other limit states.
For the overall bridge cross section, the governing live load condition places three lanes of live load on the structure with a distribution factor, DF, of 2.04 and a multiple presence factor, MPF, of 0.85. For the fatigue limit state, the placement of the single fatigue truck produces a distribution factor of 0.743. The multiple presence factor is not applied to the fatigue limit state.
The factored force effect, Q, in the member is calculated for the axial force and the moment in Table 13.7 from the following equation to obtain the factored member load and moment:

Basic Allowable Stresses

Table 11.29 lists the allowable stresses for railroad bridges recommended in the AREMA Manual. The stresses, ksi, are related to the specified minimum yield stress Fy , or the specified minimum tensile strength Fu , ksi, of the material except where stresses are independent of the grade of steel. The basic stresses may be increased for loading combinations (Art. 11.35.12), or may be superseded by allowable fatigue stresses (Art. 11.38).
Allowable stresses for welds for railroad bridges are given in Table 11.30. These stresses may also be increased for loading combinations (Art. 11.35.12), or may be superseded by allowable fatigue stresses (Art. 11.38). The designer should review the AREMA Manual for complete provisions, including prohibited types of welds and joints. Special provisions may apply for fracture critical members.

Allowable Bearing Pressures on Masonry

For bearing assemblies with specified edge distances, with or without shock pads, the following allowable bearing stresses may be used for the indicated supporting material:
Concrete —0.25 of specified compressive strength
Granite —800 psi
Sandstone—400 psi
Limestone—400 psi
11.37.2 High Strength Bolts
Steel fabrication may be detailed for 7⁄8 in diameter A325 or A490 bolts in 15⁄16 in diameter holes. The designer should determine the owner’s requirements for fastener sizes, materials, use of oversize or slotted holes, etc. Often, 7⁄8 in diameter A325 high strength bolts are used because bridge owners generally have maintenance equipment for installing and removing these fasteners. Attention is directed to the AREMA Manual, Chapter 15 Commentary, for additional information.
High strength bolts must be installed to specified minimum tension values. The required tension for installed bolts of various sizes is given in Table 11.31.

Criteria for Built-Up 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 allowance for holes. The diameter of a hole for a fastener should be taken as 1⁄8 in greater than the nominal fastener diameter. The chain of holes that is critical is the one that requires the largest deduction for holes and may lie on a straight line or in a zigzag pattern. The deduction for any chain of holes equals the sum of the diameters of all the holes in the chain less, for each gage space in the chain, s2/4g, where s is the pitch, in, of any two successive holes and g is the gage, in, of those holes.
For angles, the gross width should be taken as the sum of the widths of the legs less the thickness. The gage for holes in opposite legs is the sum of the gages from back of angle less the thickness. If a double angle or tee is connected with the angles or flanges back to back on opposite sides of a gusset plate, the full net section may be considered effective.
But if double angles, or a single angle or tee, are connected on the same side of a gusset plate, the effective area should be taken as the net section of the connected leg or flange plus one-half the area of the outstanding leg. When angles connect to separate gusset plates, as in a double-webbed truss, and the angles are interconnected close to the gussets, for example, with stay plates, the full net area may be considered effective. Without such interconnection, only 80% of the net area may be taken as effective.
For built-up tension members with perforated plates, the net section of the plate through the perforation may be considered the effective area.
In pin-connected tension members other than eyebars, the net section across the pinhole should be at least 140%, and the net section back of the pinhole at least 100% of the required net section of the body of the member. The ratio of the net width, through the pinhole normal to the axis of the member, to thickness should be 8 or less. Flanges not bearing on the pin should not be considered in the net section across the pin.
To meet stress requirements, the section at pinholes may have to be reinforced with plates.
These should be arranged to keep eccentricity to a minimum. One plate on each side should be as wide as the outstanding flanges will allow. At least one full-width plate on each segment should extend to the far side of the stay plate and the others at least 6 in beyond the near edge. These plates should be connected with fasteners or welds arranged to distribute the bearing pressure uniformly over the full section.

Eyebars should have constant thickness, no reinforcement at pinholes. Thickness should be between 1⁄2 and 2 in, but not less than 1⁄8 the width. The section across the center of the pinhole should be at least 135%, and the net section back of the pinhole at least 75% of the required net section of the body of the bar. The width of the body should not exceed the pin diameter divided by 3⁄4 +  Fy /400, where Fy is the steel yield strength, ksi. The radius of transition between head and body of eyebar should be equal to or greater than the width of the head through the center of the pinhole.
Eyebars of a set should be symmetrical about the central plane of the truss and as nearly parallel and close together as practicable. But adjacent bars in the same panel should be at least 1⁄2 in apart. The bars should be held against lateral movement.
Stitching. In built-up members, welds connecting plates in contact should be continuous.
Spacing of fasteners should be the smaller of that required for sealing, to prevent penetration of moisture (Art. 5.11), or stitching, to ensure uniform action. The pitch of stitch fasteners on any single line in the direction of stress should not exceed 24t, where t = thickness, in, of the thinner outside plate or shape. If there are two or more lines of fasteners with staggered pattern, and the gage g, in, between the line under consideration and the farther adjacent line is less than 24t, the staggered pitch in the two lines, considered together, should not exceed 24t or 30t  + 3g/4. The gage between adjacent lines of stitch fasteners should not exceed 24t.

Cover Plates. When main components of a tension member are tied together with cover plates, the shear normal to the member in the planes of the plates should be assumed equally divided between the parallel plates. The shearing force should include that due to the weight of the member plus other external forces.
When perforated cover plates are used, the openings should be ovaloid or elliptical (minimum radius of periphery 11⁄2 in). Length of perforation should not exceed twice its width.
Clear distance between perforations in the direction of stress should not be less than the distance l between the nearer lines of connections of the plate to the member. The clear distance between the end perforation and end of the cover plate should be at least 1.25l. For plates groove-welded to the flange edge of rolled components, l may be taken as the distance between welds when the width-thickness ratio of the flange projection is less than 7; otherwise, the distance l should be taken between the roots of the flanges. Thickness of a perforated plate should be at least 1⁄50 of the distance between nearer lines of connection.
When stay plates are used to tie components together, the clear distance between them should be 3 ft or less. Length of end stay plates between end fasteners should be at least 1.25l, and length of intermediate stay plates at least 0.563l. Thickness of stay plates should not be less than l /50 in main members and l /60 in bracing. They should be connected by at least three fasteners on each side to the other components. If a continuous fillet weld is used, it should be at least 5⁄16 in.
Tension-member components also may be tied together with end stay plates and lacing bars like compression members. The last fastener in the stay plates preferably should also pass through the end of the adjacent bar.

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).
Allowable Stresses in Welds. Standard specifications require that weld metal used in bridges conform to the ‘‘Bridge Welding Code,’’ ANSI/AASHTO/AWS D1.5, American Welding Society.
Yield and tensile strengths of weld metal usually are specified to be equal to or greater than the corresponding strengths of the base metal. The allowable stresses for welds in bridges generally are as follows:
Groove welds are permitted the same stress as the base metal joined. When base metals of different yield strengths are groove-welded, the lower yield strength governs.
Fillet welds are allowed a shear stress of 0.27Fu, where Fu is the tensile strength of the electrode classification or the tensile strength of the connected part, whichever is less. When quenched and tempered steels are joined, an electrode classification with strength less than that of the base metal may be used for fillet welds, but this should be clearly specified in the design drawings.
Plug welds are permitted a shear stress of 12.4 ksi.
These stresses may be superseded by fatigue requirements (Art. 11.10). The basic stresses may be increased for loading combinations as noted in Art. 11.5.
Effective area of groove and fillet welds for computation of stresses equals the effective length times effective throat thickness. The effective shearing area of plug welds equals the nominal cross-sectional area of the hole in the plane of the faying surface.
Effective length of a groove weld is the width of the parts joined, perpendicular to the direction of stress. The effective length of a straight fillet weld is the overall length of the full-sized fillet, including end returns. For a curved fillet weld, the effective length is the length of line generated by the center point of the effective throat thickness. For a fillet weld in a hole or slot, if the weld area computed from this length is greater than the area of the hole in the plane of the faying surface, the latter area should be used as the effective area.
Effective throat thickness of a groove weld is the thickness of the thinner piece of base metal joined. (No increase is permitted for weld reinforcement. It should be removed by grinding to improve fatigue strength.) The effective throat thickness of a fillet weld is the shortest distance from the root to the face, computed as the length of the altitude on the hypotenuse of a right triangle. For a combination partial-penetration groove weld and a fillet weld, the effective throat is the shortest distance from the root to the face minus 1⁄8 in for any groove with an included angle less than 60 at the root of the groove.
In some cases, strength may not govern the design. Standard specifications set maximum and minimum limits on size and spacing of welds. These are discussed in Art. 5.19.
Rollers and Expansion Rockers. The maximum compressive load, Pm, kips, should not exceed the following:
for cylindrical surfaces,

for spherical surfaces,

Allowable Stresses for Bolts. Bolted shear connections are classified as either bearing-type or slip-critical. The latter are required for connections subject to stress reversal, heavy impact, large vibrations, or where joint slippage would be detrimental to the serviceability of the bridge. These connections are discussed in Sec. 5. Bolted bearing-type connections are restricted to members in compression and secondary members.
Fasteners for bearing-type connections may be ASTM A307 carbon-steel bolts or A325 or A490 high-strength bolts. High-strength bolts are required for slip-critical connections and where fasteners are subjected to tension or combined tension and shear.
Bolts for highway bridges are generally 3⁄4 or 7⁄8 in in diameter. Holes for high-strength bolts may be standard, oversize, short-slotted, or long-slotted. Standard holes may be up to 1⁄16 in larger in diameter than the nominal diameters of the bolts. Oversize holes may have a maximum diameter of 15⁄16 in for 3⁄4-in bolts and 11⁄16 in for 7⁄8-in bolts. Minimum diameter of a slotted hole is the same as that of a standard hole. For 3⁄4-in and 7⁄8-in bolts, shortslotted holes may be up to 1 in and 11⁄8 in long, respectively, and long-slotted holes, a
maximum of 17⁄8 and 23⁄16 in long, respectively.
In the computation of allowable loads for shear or tension on bolts, the cross-sectional area should be based on the nominal diameter of the bolts. For bearing, the area should be taken as the product of the nominal diameter of the bolt and the thickness of the metal on which it bears.
Allowable stresses for bolts specified in ‘‘Standard Specifications for Highway Bridges’’ of the American Association of State Highway and Transportation Officials (AASHTO) are summarized in Tables 11.17 and 11.18. The percentages of stress increase specified for load combinations in Art. 11.5 also apply to high-strength bolts in slip-critical joints, but the percentage may not exceed 133%.

In addition to satisfying these allowable-stress requirements, connections with highstrength bolts should also meet the requirements for combined tension and shear and for fatigue resistance.
Furthermore, the load PS, kips, on a slip-critical connection should be less than

where Fs  allowable stress, ksi, given in Table 11.17 for a high-strength bolt in a slipcritical
Ab  area, in2, based on the nominal bolt diameter
Nb  number of bolts in the connection
Ns  number of slip planes in the connection

Surfaces in slip-critical joints should be Class A, B, or C, as described in Table 11.17, but coatings providing a slip coefficient less than 0.33 may be used if the mean slip coefficient is determined by test. In that case, Fs for use in Eq. (11.14) should be taken as for Class A coatings but reduced in the ratio of the actual slip coefficient to 0.33.
Tension on high-strength bolts may result in prying action on the connected parts. See Art. 5.25.3.
Combined shear and tension on a slip-critical joint with high-strength bolts is limited by the interaction formulas in Eqs. (11.15) and (11.16). The shear ƒv , ksi (slip load per unit area of bolt), for A325 bolts may not exceed

Fatigue may control design of a bolted connection. To limit fatigue, service-load tensile stress on the area of a bolt based on the nominal diameter, including the effects of prying action, may not exceed the stress in Table 11.19. The prying force may not exceed 80% of the load.

Screw Connections

Screws are frequently used for connections in cold-formed steel because they can be driven with a hand-held drill, usually without punching a hole. The AISI Specification gives provisions for calculating nominal strength for self-tapping screws with 0.08

The distance between the centers of fasteners, and the distance from the center of a fastener to the edge of any part, must not be less than 3d. However, if the connection is subjected to shear force in one direction only, the minimum edge distance in the direction perpendicular to the force is 1.5d. Nominal strength equations are given for shear and for tension using the following notation:
Pns = nominal shear strength per screw
Pnt = nominal tension strength per screw
Pnot = nominal pull-out strength per screw
Pnov = nominal pull-over strength per screw
t1 = thickness of member in contact with the screw head

t2  thickness of member not in contact with the screw head
Fu1  tensile strength of member in contact with the screw head
Fu2  tensile strength of member not in contact with the screw head



For screws that carry tension the diameter of the head of the screw, or of the washer if one is used, must be at least 5⁄16 in (7.94 mm). Washers must be at least 0.05 in (1.27 mm) thick.
Two conditions must be checked: (1) pull-out of the screw and (2) pull-over of the sheet. In

Bolted Connections

Bolted connections of cold-formed steel members are designed as bearing type connections.
Bolt pretensioning is not required and installation should be to the snug-tight condition. The AISI Specification gives applicable provisions when the thickness, t, of the thinnest connected part is less than 3⁄16 in (4.76 mm). For thicker members, the AISC Specification applies. The most commonly used grades are A307 carbon steel bolts and A325 high strength bolts, but other types can also be used. Standard hole diameter is d + 1⁄32 in for d mm for d < 12.7 mm) where d is bolt diameter. Standard hole diameter is d + 1⁄16 in for d => 1⁄2 in (d + 1.6 mm for d => 12.7 mm). See the AISI Specification for information on slotted holes.
Several conditions must be checked for a bolted connection, including shearing strength of sheet (edge distance and spacing effects), tension strength in each connected part, bearing strength, bolt shear strength, and bolt tension strength. Each of these is treated in the following articles.

Sheet Shearing (Spacing and Edge Distance)

If bolts are too close to the ends of members, or if the bolts are spaced too closely, the connection may be limited in strength by the shear strength along a line parallel to the member force. Minimum center-to-center spacing of bolts is 3d and minimum center-to-edge distance is 1.5d. Additionally, the nominal strength, Pn, is limited to

where t = thickness of thinnest part and e = distance in line of force from center of hole
to nearest edge of adjacent hole or end of connected part.

Tension in Connected Part

For components in tension, limit states of both yielding and fracture must be considered,
with the smaller value controlling. The nominal tension strength, Pn, on the net section, An,
of each connected part must not exceed


The bearing strength varies from to Pn = 2.22Fudt to Pn = 3.33fudt depending on whether washers are used, the type of joint, and the Fu /Fsy ratio of the connected part. The AISI provisions are summarized in Tables 10.5 and 10.6.

Shear and Tension in Bolts

The nominal bolt strength resulting from shear, tension, or a combination thereof is calculated as follows:

Tension Members

The nominal tensile strength, Tn, of an axial loaded tension member is the smallest of three limit states: (1) yielding in the gross section, Eq. 10.22; (2) fracture in the net section away from the connections, Eq. 10.23; and (3) fracture in the net section at connections (Art. 10.18.2)

where Ag is the gross cross section area, An is the net cross section area, Fy is the design yield stress and Fu is the tensile strength.
As with all of the member design provisions, these nominal strengths must be divided by a safety factor, , for ASD (Art. 10.4.1) or multiplied by a resistance factor, , for LRFD (Art. 10.4.2). See Table 10.1 for  and  values for the appropriate member or connection category.