PART THREE
Design
Military, semipermanent, nonstandard fixed highway bridges are designed for a given MLC. Simply supported stringer bridges are recommended since they are easy to design and construct. The materials available and the capabilities of the construction unit must be known before conducting the design process. The design should be economical in materials and construction effort but should not require excessive maintenance.
Chapter 6
Bridge Superstructures
Steel is not always readily available and requires special equipment for its use in construction. However, steel stringers are preferred over timber stringers because of their strength and capability for supporting longer spans. Use steel stringers for TO nonstandard fixed bridges whenever possible. The deck should normally be plank or laminated timber. The wearing surface should be either timber planks or asphalt. Use a concrete deck if concrete is available and a more durable structure is desired.
DESIGN PHASES
61. Design is a twophase process. The first phase involves determining the design loads and their effects in terms of moment and shear forces. The second phase involves selecting members that have sufficient strength to resist the effects of the intended loads on the bridge. Before considering the design process complete, the failure modes (lateral buckling, excessive deflection, end bearing, and so forth) as well as moment and shear must be checked.
DESIGN SEQUENCE
62. A logical design sequence is necessary to prevent design omissions and to eliminate unnecessary effort. Select and design members and accessories to prevent any of the five modes of beam failure (excessive vertical deflection, bending, shear, lateral deflection, and bearing).
63. The superstructure design sequence is discussed below and includes beam failure as part of the design process. The first nine steps are discussed in this chapter, and step 10 is discussed in Chapter 9.
Step 1. Perform a reconnaissance of the bridge site and determine the bridge's requirements.
Step 2. Determine the number of stringers.
Step 3. Design the deck.
Step 4. Design the stringers.
Step 5. Check the vertical deflection.
Step 6. Design the lateral bracing.
Step 7. Check the dead load.
Step 8. Check the shear forces.
Step 9. Design the endbearing components.
Step 10. Design the connections.
RECONNAISSANCE
64. Perform a reconnaissance of the bridge site as outlined in Chapter 2. Before proceeding with the bridge design, determine the—
 Span length of the bridge (in feet).
 Design classification (wheeled, tracked, or both).
 Number of lanes.
 Available construction materials.
 Equipment and personnel required.
 Site constraints.
65. After determining the specifications, design the superstructure of the bridge as discussed below. Design the substructure according to the procedures outlined in Chapter 7.
NUMBER OF STRINGERS DETERMINATION
66. After determining the bridge specifications, estimate the minimum number of stringers required for a given span length. The total number of stringers depends on the moment capacity of an individual stringer, the roadway width, and the centertocenter stringer spacing. The goal is to produce the most economical, safe bridge design using the least number of stringers possible.
67. Determine the minimum number of stringers by using the maximum centertocenter stringer spacing and the roadway width (Figure 61). Stringer spacing should not exceed 6 feet for timberdeck bridges and 8 feet for concretedeck bridges. Use Table 61 to determine the number of stringers required according to the bridge classification, the roadway width, and the deck type.
Figure 61. Stringer Spacing
Table 61. Number of Stringers Required
68. The number of stringers required can also be determined if the roadway width and the desired stringer spacing is known. Compute as follows:


69. After finding the number of stringers required (by either method), compute the actual stringer spacing as follows:


DECK DESIGN
610. The deck system includes the structural deck, the wearing surface, and the curb and handrail systems. The deck of a stringer bridge supports the vehicles and distributes the load to the stringers. In a deck design (for either timber or concrete decks), the effective span length over which the loads are distributed must be known. Use this measurement to compute the dead load that is supported by the stringers.
611. For a deck supported on timber stringers, first compute for the clear distance between the support stringers (equation 63) and then compute for the effective span length (equation 64).



612. For timber stringers, a standard stringer nominal width of 4 inches is suggested for initial design calculations. The effective span length should not exceed the distance between the edges of the top flange of the supporting stringers plus the thickness of the deck. If the deck is supported on steel stringers, compute for the distance between the edges of the top flange of the support stringers (equation 65) and then for the effective span length (equation 66).



613. For steel stringers, assume an initial flange width of 12 inches for the deck computations. The effective span length should not exceed the distance between the edges of the top flange of the supporting stringers plus the thickness of the deck.
Timber Deck
614. Timber decks are constructed with the long dimension of the planks placed either horizontally (flat) (plank deck) or vertically (on edge) (laminated deck). The vertically oriented planks of a laminated deck are nailed to each other. Figure 62 shows a sketch of both timberdeck orientations. Install a wearing surface to prevent wear. On timberdeck bridges, the wearing surface should consist of a 2 or 3inchthick timber treadway. On onelane bridges, the treadway should be limited to the path of the wheels or tracks. On twolane bridges, the treadway should fully cover the deck. Place the treadway between the curbs rather than under the curbs.
Figure 62. TimberDeck Orientations
Plank Deck
615. A plank deck is the simplest to design and construct. It consists of a series of sawn lumber planks placed flatwise across supporting beams. Each plank is normally 10 or 12 inches wide and 4 inches thick. Plank decks are used primarily on lowvolume or specialuse roads. They are not suitable for asphalt pavement because of large liveload deflections and movements from moisture changes in the planks.
616. Determine the required deck thickness by using Figure 63. Plot the effective span length (equation 64) and the desired MLC. The minimum deck thickness is 3 inches. Use a laminated deck when the required deck thickness exceeds 6 inches. Use deck planks made from dimensioned lumber having a thickness equal to or greater than the required deck thickness. If the available deck material is not thick enough, layer planks until achieving the required thickness plus 2 inches. The extra 2 inches will compensate for the structural inefficiencies of layered planks.
Figure 63. Required and Effective Deck Thicknesses (Timber Deck)
617. Normally, install the decking in a perpendicular direction to the bridge's centerline for ease and speed of construction. Install the decking with a 1/4inch space between the planks for expansion, better drainage, and air circulation.
Laminated Deck
618. Large stringer spacing and high design classifications usually require a thicker decking (laminated decks are more economical in this case). Although layering strengthens the plank decks, laminated decks are much stiffer.
619. Required Deck Thickness. Loads are spread out more effectively in a laminated deck than in a conventional plank deck. Lamination has the effect of shortening the effective deck span between stringers by about 25 percent. To design a laminated deck—
 Adjust the effective span length (equation 66) by multiplying its value by a factor equal to 0.75. This value will now become the adjusted effective span length.
 Determine the required deck thickness of the laminated deck from Figure 63 (assuming that it equals that for a plank deck). Use the adjusted effective span length and the MLC. The minimum deck thickness required is 3 inches.
620. Lamination. The performance of liveload deflections depends on the effectiveness of the nails in transferring loads between adjacent boards. To create a laminated deck, place the planks vertically. Make sure that the deck is wellnailed or glued to the adjacent board over the full length. Nails should be placed at a minimum of 1 1/2 inches on center along the length of the boards. The nail pattern should be staggered to prevent splitting of the lumber.
Reinforced Concrete Deck
621. To build a more permanent structure, use a concrete deck (Figure 64). Reinforced concrete decks can span greater distances than timber decks. Concrete decks use fewer stringers, which can be spaced up to 8 feet apart. The construction process is more difficult because of the required formwork, procuring and setting of steel, placing of concrete, and curing. However, if material and time are available, use concrete decking for a stronger flooring system.
Figure 64. Cross Section of a SteelStringer Bridge With a Concrete Deck
622. Concrete Compressive Strength. In the US, the design strength of concrete corresponds to the compressive strength (in psi) of test cylinders that are 6 inches in diameter and 12 inches high and are measured on the 28th day after they are placed. Table 62 lists various concrete compressive strengths used in structural design. In most situations, use a compressive strength equal to 3,000 psi for design purposes unless what will be available from the concrete source is known.
Table 62. Compressive Strength of Concrete
623. Reinforcing Steel Yield Strength. Steel reinforcement may consist of bars, weldedwire fabric, or wires. In the US, reinforcing bars are available in sizes of 3/8 to 2 1/4 inches nominal diameter. Table 63 lists various steel yield strengths for reinforcing steel used in structural design.
Table 63. Yield Strength of Reinforcing Steel
624. Slab Dimensions. Design a concrete deck as a oneway slab (continuous at both ends) with a design span equal to the effective span length (equation 66). In designing a oneway slab, consider, for example, a typical 12inchwide strip. The continuous slab may be designed as a continuous beam having a known width of 12 inches; the slab thickness is now the only unknown. For design calculations, assume a slab thickness equal to 7 inches.
625. Wearing Surface. If desired, use a wearing surface such as asphalt. If asphalt is used, the wearingsurface thickness should be 1 1/2 inches.
626. Dead Load. Compute the deadload weight of the slab by considering its own weight and any wearing surface for a 12inchwide strip. Compute the slab's deadload weight and deadload bending moment as follows:



Table 64. Unit Weights for a DeadLoad Computation
627. Live Load. Determine the liveload bending moment acting on a 12inchwide strip of slab with reinforcement perpendicular to the traffic. The live load is that for the desired wheeled vehicle (Appendix B) with the tire load positioned so that it produces the most critical loading between the stringers.
628. Compute the critical, concentrated live load per wheel used for design and the liveload moment for the slabs as follows:


629. Required Nominal Strength. Compute the required nominal strength as follows:

630. Reinforcing Steel Ratio. For a concrete compressive strength of 3,000 psi, use 0.85 for the Bfactor to find the maximum reinforcement ratio in Table 65. Use the concrete compressive strength (f'c) and the Bfactor to find the reinforcing steel ratio from Table 65.
Table 65. Reinforcing Steel Ratio (R_{s})
631. Strength Coefficient of Resistance. Compute the strength coefficient of resistance as follows:


632. Effective Depth. Assuming that number (No.) 6 steel bars are used (nominal diameter of the bar equals 3/4 inch plus an additional 3/4 inch for protective concrete cover) and that the bars will fit in one layer, compute the required overall depth as follows:

633. Increase the required overall depth by about 1/2 inch (or by an amount that will round the required overall depth to the next complete inch or halfinch, whichever is closest). This will become the final thickness of the concrete deck. Compute the effective depth as follows:


634. Revised Reinforcing Steel Ratio. Compute the required area of tension steel to be placed in the transverse direction of the slab. Compute the revised value of the reinforcing steel ratio and the required steel area as follows:

and

635. Bar Selection and Placement. Select the actual number of bars that will meet the tension steel area (equation 616) using Table 66. Use at least two bars wherever flexural reinforcement is required. Do not use more than two bar sizes at a given location in the span. The selected bars should not be more than two standard sizes apart (for example, No. 7 and No. 9 bars may be acceptable, but No. 4 and No. 9 would not).
636. Locate the bars symmetrically about the vertical axis of the beam section (in one layer if practical). Select a bar size so that no less than two and no more than five or six bars are put in one layer. When using several layers of different bar sizes, place the largest bars in the layer nearest to the face of the beam. When placing bars within the beam's width, follow these guidelines for determining the minimum clear spacing required between the bars that will allow for proper concrete placement around them:
 For one layer of bars, the minimum clear spacing is 1 inch or the nominal diameter of the larger bar (Table 66), whichever is greater.
 For two or more layers of bars, the minimum clear spacing is equal to or greater than 1 inch.
637. Ensure that the bar spacing obtained with equation 616 is greater than the minimum clear spacing obtained previously with equation 615. Compute the actual spacing between the bars as follows:

638. Design Check. Compute the depth of the equivalent rectangular stress block (equation 618) and then the design strength of the section (equation 619). First compute

then compute

639. The section is acceptable in flexure if m' from equation 619 is greater than or equal to m from equation 611. If the condition is not satisfied, go back to equation 614 and increase the effective depth of slab slightly and redo all the necessary calculations until the condition is satisfied.
640. Temperature and Shrinkage. Reinforcing bars (parallel to traffic) are required in the top of the slab. Use the following guidelines for computing the minimum temperature reinforcement ratio (denoted by R_{temp}):
 The R_{temp} is 0.0020 when using grade 40 or 50 bars for the slabs.
 The R_{temp} is 0.0018 when using grade 60 bars for the slabs.
641. Compute the area of temperature and shrinkage steel as follows:

Place the temperature reinforcement bars at a minimum spacing equal to three times the slab thickness. Do not exceed a spacing of 18 inches.
642. Shear Check. Because of practical space limitations, shear reinforcement is not used in a slab. Slabs designed for bending moment should be considered satisfactory in shear.
Curbs and Handrails
643. A curb system guides traffic on the bridge. For timberdeck bridges, place 6 x 6inch timbers on 5foot centers on the curb risers. Risers of 6 x 12 x 30inch material provide an adequate curb system. Rigidly attach the curbs to the decking. Figure 65 shows the minimum specifications for a curb system on timberdeck bridges. The curb system will not withstand the impact of a heavy vehicle that is out of control. To design such a system would require a curb system of excessive size and cost. For concretedeck bridges, form the curb as a part of the deck. Pour the curb at the same time as the main deck. Provide drain holes in the curb at 10foot intervals on both sides of the bridge.
Figure 65. Curb and Handrail Systems for TimberDeck Bridges
644. Include a handrail system if necessary. Place handrails on bridges with heavy foot traffic and where the danger of falling exists. If handrails are not used, mark the bridge edges. One marking method is to place 2 x 4inch posts with reflectors at 10foot intervals along both sides of the bridge. Figure 65 shows the minimum specifications for handrails on timberdeck bridges.
STRINGER DESIGN
645. Stringer design involves computing the deadload weight, the liveload moment, and the total design moment. Various factors must be considered in the stringer selection (timber or steel).
Dead Load
646. The dead load includes the weight of all the parts of a structure, including the deck and accessories (railings, curbs, lateral bracing, and connections) as well as the stringers. Since the stringers are not yet sized, their weight must be estimated. The dead load is considered to be uniformly distributed along the span and equally shared by each stringer.
647. For the initial design calculations on a timberdeck bridge, assume a deadload weight of 0.1 kpf for any accessories and a weight equal to 0.2 kpf per stringer. For a concretedeck bridge, assume a deadload weight of 0.4 kpf for any accessories (includes curbs and handrails) and a weight equal to 0.3 kpf per stringer. Compute the deadload weight of the deck (equation 621) and the estimated design dead load (equation 622). First compute:


then compute

648. Assume that the dead load of the bridge is equally shared by all of the stringers. Compute the design deadload moment per stringer as follows:


Live Load
649. Vehicle loads are assumed to be the only live load acting on the bridge. Find the design values for the live load by using the moment and shear curves in Appendix B. Use the larger value of wheeled and tracked moment and both values of wheeled and tracked shear for further calculations. If the bridge is for civilian traffic, use the provisions in Chapter 3, Section III, and Figure 31 to determine the equivalent MLC of the civilian traffic for design calculations.
650. NATO traffic restrictions apply for design purposes, which is 25 mph and 100foot spacing. Because of this long spacing, usually only one vehicle will be on any single span of a bridge at a time. If significant pedestrian traffic is expected (refugees and dismounted military units), treat these as line loads of 75 pounds per foot, each over a 1foot width. Post these line loads in all locations that lines of people might be expected.
651. Determine the total liveload moment according to the design vehicle class (Table B2,). Compute the liveload moment that a stringer must resist (including impact effects) as follows:

Total Design Moment per Stringer
652. The total design moment that each stringer resists is the summation of the dead and liveload moments per stringer. Compute as follows:


TimberStringer Selection
653. If the species and grade of timber is known, use the allowable stresses from Table C1 for the design. Convert these values from psi to ksi by dividing the tabulated stress by 1,000. Generally, the tabulated values assume that the material will be in continuously dry conditions. However, timber decking and stringers may retain moisture on their horizontal surfaces; therefore, consider its use under wet conditions.
654. Apply some modification factors (see the notes in Table C1) toward the tabulated allowable bending stress to account for various effects (lumber thickness/width ratios, edgewise or flatwise use, repetitive member use, and moisture content). For military loads, apply an additional factor equal to 1.33 to account for lower traffic volume (see Appendix I). Whenever the species and grade of solidsawn timber cannot be determined, assume an allowable bending stress equal to 1.75 ksi and an allowable horizontalshear stress equal to 0.095 ksi. For gluelaminated timber, assume an allowable bending stress equal to 2.16 ksi and an allowable horizontalshear stress equal to 0.2 ksi. These values must be adjusted for the various applicable conditions stated in the notes of Table C1. The modification for lower traffic volume has already been considered in those assumed values.
SteelStringer Selection
655. The allowable bending stress for steel members is 0.75 times the steel yield strength (Table 67), assuming that the stringers are braced properly (paragraph 659). The allowable shear stress for steel members is 0.45 times the steel yield strength.
Required Section Modulus
656. Once the total moment each stringer must resist is known, compute the section modulus a stringer requires for a given allowable bending stress as follows:


657. Select a stringer (Table C2 for timber and Table D2 for steel) with a section modulus greater than or equal to the required section modulus from equation 626. The available stringer sizes may not be large enough to provide sufficient section modulus. If this happens, add a stringer to the bridge section and recompute (equation 623). Compute the total design moment per stringer (equation 625) and the required section modulus (equation 626) until a suitable steel stringer size (as listed in Appendix D) is obtained.
VERTICALDEFLECTION CHECK
658. Compute the vertical deflection of the stringers due to the live load (including impact) as shown below. The deflection should not be greater than d max = (L/200) x 12 (in inches).


LATERALBRACING DESIGN
659. When a beam is loaded and deflected downward, the upper portion of the beam shortens and the lower portion of the beam lengthens. This reshaping results from the internal moments induced by the loading. The beam will experience compressive forces in the upper portion and tensile forces in the lower portion of the section. The upper portion of the member tends to compress or buckle, just as a column does with respect to its weaker axis. The buckling effect is always accompanied by some lateral twisting. This action is called lateral buckling. Figure 66 shows the lateralbuckling effect in a beam (timber or steel).
Figure 66. Lateral Buckling
660. To prevent lateral buckling in a beam, use cross frames or diaphragms and bracing systems for lateral support. One of the primary factors affecting lateralbeam stability is the distance between the points of a lateral support along the beam's length (the unsupported or unbraced length).
Timber Stringers
661. For timber beams, provide lateral support by locating transverse bracing at the beam's end supports and at every onethird point along the beam span (Figure 67). This distance (spacing) between the lateral braces along the length of the beam is the unbraced length. For simplespan beams and any loading condition, compute the effective beam length and then the beam slenderness factor as follows:


or




Figure 67. Lateral Bracing for Timber Stringers
662. If the result of equation 630 is not < 50, increase the number of braces along the beam's span to reduce the unsupported length and then recompute. When the unbraced length varies substantially along the beam's span, check the slenderness factor for each unsupported length. Typically, the slenderness factor at the center portion of the beam (where bending stress is higher) will control the lateralbracing design.
Steel Stringers
663. A steel beam should be braced laterally, perpendicular to the plane of the web. Lateral bracing provides adequate lateral stability of the compression flange so that the beam section can develop its maximum design bending strength.
664. Maximum Allowable Unbraced Length. Establish the maximum allowable unbraced length for a steel stringer by using the smaller of the values obtained from the following equations:


or


665. Number of Braces. The number of lateral braces needed will depend on the length of the beam's span and the maximum unbraced length for a given steel section. Compute for the number of lateral braces needed as follows:


666. Spacing of LateralBracing. Distribute the number of lateral braces by spacing them along the beam span at the distance computed below. Locate a lateral brace at each end support and the remaining braces along the beam's length.


667. BracingSystem Selection. The type of lateral bracing depends on the availability of materials. Diaphragms or cross frames are satisfactory braces. Diaphragms are generally more economical for rolled shapes that are less than 32 inches deep. Cross frames are generally more economical for builtup beams that are 32 inches and deeper.
668. Diaphragms are rolled shapes used in a lateralbracing system (Figure 68). The diaphragm depth should be at least half the depth of the steel stringer. Construct diaphragms from the lightest materials available. Although the most suitable diaphragms are constructed using channel sections, any rolled shape (such as an Ibeam) is satisfactory. Precut ends of stringers are available for fabricating diaphragms. Structural Ts can be used as diaphragms. Form these shapes by cutting the excess stringer material in half, along the centerline of the web. When using structural Ts, place the flange as close as possible to the stringer's compression flange (which is the top flange) and weld the connections. A bolted connection (with 3/4inch or 7/8inch bolts at a minimum spacing along a single row) may also be used. See Chapter 9 for more information.
Figure 68. HighwayBridge Diaphragm
669. Cross frames are used when the depth of the stringer exceeds 32 inches. Use equal leg angles configured into a cross frame as a more economical alternative to using diaphragms (Figure 69). However, the increased cost of cutting and fabrication outweighs any material savings. Minimum requirements of the angles are that—
 The dimensions of the member should not be smaller than 3 x 3 x 3 1/8 inches.
 The thickness of the member should be greater than onetenth the length of the longer leg.
 The ratio of the span length to the radius of gyration of the section used for bracing (12L/r, where L is in feet and r is in inches) must be less than or equal to 200.
Figure 69. CrossFrame Beam Bracing
DEADLOAD CHECK
670. After designing the deck and selecting the stringer size, check the initial deadload assumption for any necessary corrections. The total dead load per stringer consists of the combined dead loads of the deck system, the stringers, the lateral bracing, and any accessories. Any changes in the total deadload value may result in an increase or decrease of the required section modulus.
Component Loads
671. Compute the dead load for the deck as follows:


672. Compute the dead load for the wearing surface as follows:


673. Compute the dead load for the stringers as follows:


674. For steel stringers, the last number in the nomenclature of a steel section corresponds to its weight (in pounds per foot). For example, as shown in Appendix D, a W27x94 would indicate that this section weighs 94 pounds per foot. Compute the weight due to the steel stringers as follows:


675. Compute the dead load due to accessories as follows:


or


676. Compute the length of the lateral bracing as follows:


and


Actual Dead Loads
677. Compute the total actual dead load as follows:


678. Compute the actual dead load carried per stringer as follows:


679. Compare the actual dead load to the estimated design dead load per stringer as follows:


680. If the results of equation 645 work, then the selected bridge components are considered adequate based on the estimated dead load. Complete the design and classify the bridge as described in Chapter 3. If the results of equation 645 do not work, adjust the stringer size by redoing all the necessary calculations as follows:
 Replace the estimated design dead load (equation 622) with the total actual dead load (equation 643).
 Recompute all related equations to obtain a new section modulus, and select a new stringer section.
 Check the deadload requirements with the values and continue recomputing until the results of equation 645 work.
SHEARFORCE CHECK
681. After selecting a stringer size, check the stringer's shear capacity. In most timberstringer bridges with spans of less than 20 feet, shear controls the design. In steelstringer bridges with a high design classification and short spans (20 feet or less), shear may be a critical factor.
DeadLoad Shear per Stringer
682. Assume that the design deadload shear is equally distributed among all the stringers. Compute the design deadload shear per stringer as follows:


Design LiveLoad Shear
683. Determine the design liveload shear. Use Table B3.
684. Effective LiveLoad Shear per Stringer. The effective liveload shear must account for the loads at the abutments or intermediate supports and for those further out on the span. Since steelstringer bridges act very similarly to gluelaminated timber bridges, the equations used to compute the effective liveload shear per stringer are the same. The liveload shear per stringer corresponds to the largest value from the following equations:
 Wheeled vehicle, one traffic lane.


 Wheeled vehicle, two or more traffic lanes.


 Tracked vehicle, one traffic lane.

 Tracked vehicle, two or more traffic lanes.


685. Design LiveLoad Shear per Stringer. Compute the design liveload shear per stringer as follows:


686. Design Shear per Stringer. Compute the design shear per stringer and the actual shear stress acting on the stringer as follows:

and

687. If the actual shear stress (equation 653) is less than or equal to the allowable shear stress, the stringer will not have to be adjusted. However, if the actual shear stress is greater than the allowable shear stress, select a larger stringer size that satisfies the shear strength and moment capacity requirements.
ENDBEARING DESIGN (TIMBER STRINGERS)
688. Although bearing failure in timber stringers is rare, the bearing stress should still be checked. The minimum width of the cap (or sill) required for timber stringers is 6 inches (Figure 610). Compute the actual bearing stress as follows:


Figure 610. EndBearing Timber Stringer
689. The actual bearing stress should not exceed the allowable bearing stress. The values for allowable bearing stress for timber are shown in Table 68. These design values are given for the wet and dryservice conditions and were obtained as the average stress value from various species combinations. If the actual bearing stress exceeds the allowable bearing stress, then increase either the width of the cap or the width of the stringer to provide a sufficient bearing area.
ENDBEARING DESIGN (STEEL STRINGERS)
690. Bearing plates are designed to transmit the loads from the superstructure into the substructure. If the bearingseat area is insufficient to carry the load, failure will occur. Bearing failure causes the materials that bear together to crush, which may lead to stringerflange failure. Another type of failure is web crippling (failure of the web portion of the stringer). Web crippling occurs due to the stress concentrations at the junction of the flange and the web where the beam is trying to transfer compression from a wide flange to a narrow web. Figure 611 shows various types of endbearing failures. Bearing plates are designed to prevent flange failure and crushing of the supports. Web crippling can be prevented by designing endbearing stiffeners.
Figure 611. EndBearing Failures
Bearing Plates
691. Endbearing plates are typically required when steel stringers rest on concrete or timber supports. Their design is based on the design shear transmitted to the support (adjusted if the actual dead load [equation 645] is greater than the estimated design dead load [equation 622]).
692. BearingPlate Area. The required bearingplate area is determined by the allowable bearing stress of the support and the design shear that is carried to the support. Compute as follows:


693. Plate Width and Length. The most economical plate design results when the seat width (which is the length of the plate) is increased while the plate width is minimized. The minimum width of the plate should be equal to the stringerflange width. The minimum seat length is 6 inches. Therefore, the minimum plate area is six times the flange width.
694. Plate Thickness. Use these steps to determine the plate thickness.
Step 1. Compute the actual bearing stress as follows:


Step 2. Compute the required thickness of the bearing plate as follows:

Step 3. Select a bearingplate thickness from the following available standard thicknesses:
 1/32inch increments (up to 1/2 inch).
 1/16inch increments (from 1/2 up to 1 inch).
 1/8inch increments (from 1 up to 3 inches).
 1/4inch increments (for 3 inches or greater).
Step 4. Build the bearing plate to the required thickness by laminating the plates. Fully weld the perimeters of the plate.
695. Web Crippling. Check for web crippling. If the actual bearing stress in the web exceeds the allowable bearing stress, use endbearing stiffeners or increase the length of the bearing plate. Compute the actual bearing stress as follows:


EndBearing Stiffeners
696. Endbearing stiffeners are normally not required for standard, rolled shapes unless abutment or intermediatesupport dimensions restrict the length of the bearing plate. However, the web may have to be stiffened to prevent it from buckling. If endbearing stiffeners are needed, construct them of angles or plates on each side of the stringer web. Position them over the center of the bearing at the end of each stringer. Ensure that they fit tightly against the flanges being loaded. Mill the top and bottom of the stiffener to bear against the flanges of the stringer, and extend them out as far as possible toward the edges of the flange (Figure 612). Compute the minimum required thickness of the endbearing stiffeners as follows:


Figure 612. EndBearing Stiffener
697. Provide sufficient welding (or bolting) to transfer the total end shear through the web. Do not crimp the angles used as end stiffeners to fit over the flange angles. Instead, use filler plates between the web and the stiffeners.
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