Military

6-1. Design is a two-phase 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.

6-2. 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).

6-3. 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 end-bearing components.

Step 10. Design the connections.

6-4. 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.

6-5. After determining the specifications, design the superstructure of the bridge as discussed below. Design the substructure according to the procedures outlined in Chapter 7.

6-6. 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 center-to-center stringer spacing. The goal is to produce the most economical, safe bridge design using the least number of stringers possible.

6-7. Determine the minimum number of stringers by using the maximum center-to-center stringer spacing and the roadway width (Figure 6-1). Stringer spacing should not exceed 6 feet for timber-deck bridges and 8 feet for concrete-deck bridges. Use Table 6-1 to determine the number of stringers required according to the bridge classification, the roadway width, and the deck type.

6-8. The number of stringers required can also be determined if the roadway width and the desired stringer spacing is known. Compute as follows:

6-9. After finding the number of stringers required (by either method), compute the actual stringer spacing as follows:

6-10. 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.

6-11. For a deck supported on timber stringers, first compute for the clear distance between the support stringers (equation 6-3) and then compute for the effective span length (equation 6-4).

6-12. 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 6-5) and then for the effective span length (equation 6-6).

6-13. 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.

6-14. 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 6-2 shows a sketch of both timber-deck orientations. Install a wearing surface to prevent wear. On timber-deck bridges, the wearing surface should consist of a 2- or 3-inch-thick timber treadway. On one-lane bridges, the treadway should be limited to the path of the wheels or tracks. On two-lane bridges, the treadway should fully cover the deck. Place the treadway between the curbs rather than under the curbs.

6-15. 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 low-volume or special-use roads. They are not suitable for asphalt pavement because of large live-load deflections and movements from moisture changes in the planks.

6-16. Determine the required deck thickness by using Figure 6-3. Plot the effective span length (equation 6-4) 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.

6-17. Normally, install the decking in a perpendicular direction to the bridge's centerline for ease and speed of construction. Install the decking with a 1/4-inch space between the planks for expansion, better drainage, and air circulation.

6-18. 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.

6-19. 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 6-6) 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 6-3 (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.

6-20. Lamination. The performance of live-load 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 well-nailed 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.

6-21. To build a more permanent structure, use a concrete deck (Figure 6-4). 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.

6-22. 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 6-2 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.

6-23. Reinforcing Steel Yield Strength. Steel reinforcement may consist of bars, welded-wire fabric, or wires. In the US, reinforcing bars are available in sizes of 3/8 to 2 1/4 inches nominal diameter. Table 6-3 lists various steel yield strengths for reinforcing steel used in structural design.

6-24. Slab Dimensions. Design a concrete deck as a one-way slab (continuous at both ends) with a design span equal to the effective span length (equation 6-6). In designing a one-way slab, consider, for example, a typical 12-inch-wide 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.

6-25. Wearing Surface. If desired, use a wearing surface such as asphalt. If asphalt is used, the wearing-surface thickness should be 1 1/2 inches.

6-26. Dead Load. Compute the dead-load weight of the slab by considering its own weight and any wearing surface for a 12-inch-wide strip. Compute the slab's dead-load weight and dead-load bending moment as follows:

6-27. Live Load. Determine the live-load bending moment acting on a 12-inch-wide 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.

6-28. Compute the critical, concentrated live load per wheel used for design and the live-load moment for the slabs as follows:

and-

6-29. Required Nominal Strength. Compute the required nominal strength as follows:

6-30. Reinforcing Steel Ratio. For a concrete compressive strength of 3,000 psi, use 0.85 for the B-factor to find the maximum reinforcement ratio in Table 6-5. Use the concrete compressive strength (f'c) and the B-factor to find the reinforcing steel ratio from Table 6-5.

6-31. Strength Coefficient of Resistance. Compute the strength coefficient of resistance as follows:

6-32. 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:

6-33. 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 half-inch, whichever is closest). This will become the final thickness of the concrete deck. Compute the effective depth as follows:

6-34. 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:

6-35. Bar Selection and Placement. Select the actual number of bars that will meet the tension steel area (equation 6-16) using Table 6-6. 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).

6-36. 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 6-6), whichever is greater.
• For two or more layers of bars, the minimum clear spacing is equal to or greater than 1 inch.

6-37. Ensure that the bar spacing obtained with equation 6-16 is greater than the minimum clear spacing obtained previously with equation 6-15. Compute the actual spacing between the bars as follows:

6-38. Design Check. Compute the depth of the equivalent rectangular stress block (equation 6-18) and then the design strength of the section (equation 6-19). First compute-

6-39. The section is acceptable in flexure if m' from equation 6-19 is greater than or equal to m from equation 6-11. If the condition is not satisfied, go back to equation 6-14 and increase the effective depth of slab slightly and redo all the necessary calculations until the condition is satisfied.

6-40. 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.

6-41. Compute the area of temperature and shrinkage steel as follows:

6-43. A curb system guides traffic on the bridge. For timber-deck bridges, place 6- x 6-inch timbers on 5-foot centers on the curb risers. Risers of 6- x 12- x 30-inch material provide an adequate curb system. Rigidly attach the curbs to the decking. Figure 6-5 shows the minimum specifications for a curb system on timber-deck 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 concrete-deck 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 10-foot intervals on both sides of the bridge.

6-44. 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 4-inch posts with reflectors at 10-foot intervals along both sides of the bridge. Figure 6-5 shows the minimum specifications for handrails on timber-deck bridges.

6-45. Stringer design involves computing the dead-load weight, the live-load moment, and the total design moment. Various factors must be considered in the stringer selection (timber or steel).

6-46. 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.

6-47. For the initial design calculations on a timber-deck bridge, assume a dead-load weight of 0.1 kpf for any accessories and a weight equal to 0.2 kpf per stringer. For a concrete-deck bridge, assume a dead-load weight of 0.4 kpf for any accessories (includes curbs and handrails) and a weight equal to 0.3 kpf per stringer. Compute the dead-load weight of the deck (equation 6-21) and the estimated design dead load (equation 6-22). First compute:

6-48. Assume that the dead load of the bridge is equally shared by all of the stringers. Compute the design dead-load moment per stringer as follows:

6-49. 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 3-1 to determine the equivalent MLC of the civilian traffic for design calculations.

6-50. NATO traffic restrictions apply for design purposes, which is 25 mph and 100-foot 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 1-foot width. Post these line loads in all locations that lines of people might be expected.

6-51. Determine the total live-load moment according to the design vehicle class (Table B-2,). Compute the live-load moment that a stringer must resist (including impact effects) as follows:

6-52. The total design moment that each stringer resists is the summation of the dead- and live-load moments per stringer. Compute as follows:

6-53. If the species and grade of timber is known, use the allowable stresses from Table C-1 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.

6-54. Apply some modification factors (see the notes in Table C-1) 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 solid-sawn timber cannot be determined, assume an allowable bending stress equal to 1.75 ksi and an allowable horizontal-shear stress equal to 0.095 ksi. For glue-laminated timber, assume an allowable bending stress equal to 2.16 ksi and an allowable horizontal-shear stress equal to 0.2 ksi. These values must be adjusted for the various applicable conditions stated in the notes of Table C-1. The modification for lower traffic volume has already been considered in those assumed values.

6-55. The allowable bending stress for steel members is 0.75 times the steel yield strength (Table 6-7), assuming that the stringers are braced properly (paragraph 6-59). The allowable shear stress for steel members is 0.45 times the steel yield strength.

6-56. 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:

6-57. Select a stringer (Table C-2 for timber and Table D-2 for steel) with a section modulus greater than or equal to the required section modulus from equation 6-26. 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 6-23). Compute the total design moment per stringer (equation 6-25) and the required section modulus (equation 6-26) until a suitable steel stringer size (as listed in Appendix D) is obtained.

6-58. 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).

6-59. 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 6-6 shows the lateral-buckling effect in a beam (timber or steel).

6-60. To prevent lateral buckling in a beam, use cross frames or diaphragms and bracing systems for lateral support. One of the primary factors affecting lateral-beam stability is the distance between the points of a lateral support along the beam's length (the unsupported or unbraced length).

6-61. For timber beams, provide lateral support by locating transverse bracing at the beam's end supports and at every one-third point along the beam span (Figure 6-7). This distance (spacing) between the lateral braces along the length of the beam is the unbraced length. For simple-span beams and any loading condition, compute the effective beam length and then the beam slenderness factor as follows:

6-62. If the result of equation 6-30 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 lateral-bracing design.

6-63. 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.

6-64. 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:

6-65. 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:

6-66. Spacing of Lateral-Bracing. 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.

6-68. Diaphragms are rolled shapes used in a lateral-bracing system (Figure 6-8). 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 I-beam) 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 3/4-inch or 7/8-inch bolts at a minimum spacing along a single row) may also be used. See Chapter 9 for more information.

6-69. 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 6-9). 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 one-tenth 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.

6-70. After designing the deck and selecting the stringer size, check the initial dead-load 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 dead-load value may result in an increase or decrease of the required section modulus.

6-71. Compute the dead load for the deck as follows:

6-72. Compute the dead load for the wearing surface as follows:

6-73. Compute the dead load for the stringers as follows:

6-74. 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:

6-75. Compute the dead load due to accessories as follows:

6-76. Compute the length of the lateral bracing as follows:

6-77. Compute the total actual dead load as follows:

6-78. Compute the actual dead load carried per stringer as follows:

6-79. Compare the actual dead load to the estimated design dead load per stringer as follows:

6-80. If the results of equation 6-45 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 6-45 do not work, adjust the stringer size by redoing all the necessary calculations as follows:

• Replace the estimated design dead load (equation 6-22) with the total actual dead load (equation 6-43).
• Recompute all related equations to obtain a new section modulus, and select a new stringer section.
• Check the dead-load requirements with the values and continue recomputing until the results of equation 6-45 work.

6-81. After selecting a stringer size, check the stringer's shear capacity. In most timber-stringer bridges with spans of less than 20 feet, shear controls the design. In steel-stringer bridges with a high design classification and short spans (20 feet or less), shear may be a critical factor.

6-82. Assume that the design dead-load shear is equally distributed among all the stringers. Compute the design dead-load shear per stringer as follows:

6-83. Determine the design live-load shear. Use Table B-3.

6-84. Effective Live-Load Shear per Stringer. The effective live-load shear must account for the loads at the abutments or intermediate supports and for those further out on the span. Since steel-stringer bridges act very similarly to glue-laminated timber bridges, the equations used to compute the effective live-load shear per stringer are the same. The live-load shear per stringer corresponds to the largest value from the following equations:

• Wheeled vehicle, one traffic lane.

6-85. Design Live-Load Shear per Stringer. Compute the design live-load shear per stringer as follows:

6-86. Design Shear per Stringer. Compute the design shear per stringer and the actual shear stress acting on the stringer as follows:

6-87. If the actual shear stress (equation 6-53) 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.

6-88. 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 6-10). Compute the actual bearing stress as follows:

6-89. The actual bearing stress should not exceed the allowable bearing stress. The values for allowable bearing stress for timber are shown in Table 6-8. These design values are given for the wet- and dry-service 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.

6-90. Bearing plates are designed to transmit the loads from the superstructure into the substructure. If the bearing-seat area is insufficient to carry the load, failure will occur. Bearing failure causes the materials that bear together to crush, which may lead to stringer-flange 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 6-11 shows various types of end-bearing failures. Bearing plates are designed to prevent flange failure and crushing of the supports. Web crippling can be prevented by designing end-bearing stiffeners.

6-91. End-bearing 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 6-45] is greater than the estimated design dead load [equation 6-22]).

6-92. Bearing-Plate Area. The required bearing-plate area is determined by the allowable bearing stress of the support and the design shear that is carried to the support. Compute as follows:

6-93. 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 stringer-flange width. The minimum seat length is 6 inches. Therefore, the minimum plate area is six times the flange width.

6-94. Plate Thickness. Use these steps to determine the plate thickness.

Step 1. Compute the actual bearing stress as follows:

6-95. Web Crippling. Check for web crippling. If the actual bearing stress in the web exceeds the allowable bearing stress, use end-bearing stiffeners or increase the length of the bearing plate. Compute the actual bearing stress as follows:

6-96. End-bearing stiffeners are normally not required for standard, rolled shapes unless abutment or intermediate-support dimensions restrict the length of the bearing plate. However, the web may have to be stiffened to prevent it from buckling. If end-bearing 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 6-12). Compute the minimum required thickness of the end-bearing stiffeners as follows:

6-97. 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.