SECTION II. DESIGN
4-22. Forms are the molds that hold the plastic concrete and support it until it hardens. They must keep deflections within acceptable limits, meet dimensional tolerances, prevent paste leakage, and produce a final product that meet appearance needs. Therefore, strength, rigidity, and watertightness are the most important form design considerations. In addition, forms must support all weights and stresses to which they are subject, including the dead load (DL) of the forms; the weight of people, equipment, and materials that transfers to the forms; and any impact due to vibration. Although these factors vary with each project, do not neglect any of them when designing a form. Ease of erection and removal are other important factors in economical form design. Sometimes you may want to consider using platforms and ramp structures that are independent of the formwork because they prevent form displacement due to loading, as well as impact shock from workers and equipment.
BASIS OF FORM DESIGN
4-23. Concrete is in a plastic state when placed in the designed form; therefore, it exerts hydrostatic pressure on the form. The basis of form design is to offset the maximum pressure developed by the concrete during placing. The pressure depends on the rate of placing and the ambient temperature. The rate of placing affects pressure because it determines how much hydrostatic head builds up in the form. The hydrostatic head continues to increase until the concrete takes its initial set, usually in about 90 minutes. However, because the initial set takes more time at low ambient temperatures, consider the ambient temperature at the time of placement. Knowing these two factors (rate of placement and ambient temperature) plus the specified type of form material, calculate a tentative design.
PANEL-WALL FORM DESIGN
4-24. It is best to design forms following a step-by-step procedure. Use the following steps to design a wood form for a concrete wall.
Step 6. Determine the maximum concrete pressure (MCP) using the rate of placing (see Figure 4-3 or the formula above the figure). Draw a vertical line from the rate of placing until it intersects the correct concrete-temperature line. Read left horizontally from the point of intersection to the left margin of the graph and determine the MCP in 100 pounds per square foot.
Figure 4-3. MCP graph
Table 4-1. Maximum stud (joist) spacing for board sheathing
Table 4-2. Maximum stud (joist) spacing for plywood sheathing, in inches
Table 4-3. Maximum spacing, in inches, for whales, ties, stringers,
Table 4-4. Maximum spacing, in inches, for ties and 4" x 4" or larger shores where member to be supported is a double member
Table 4-5. Average breaking load of tie material, in pounds
SAMPLE FORM DESIGN PROBLEM NUMBER ONE
4-25. Design a form for a concrete wall 40 feet long, 2 feet thick, and 10 feet high. An M919 concrete mobile mixer is available and the crew can produce and place a cubic yard of concrete every 10 minutes. The concrete placing temperature is estimated at 70° F. The form materials are 2 by 4s, 1-inch board sheathing, and number 9 black annealed wire. The solution steps are as follows:
Step 1. Lay out available materials.
Step 2. Calculate the production rate.
Step 3. Calculate the plan area of the form.
Step 4. Calculate the rate of placing.
Step 5. Determine the concrete-placing temperature.
Step 6. Determine the MCP (refer to Figure 4-3).
Step 7. Determine the MSS (refer to Table 4-1).
Step 8. Calculate the ULS.
Step 9. Determine the MWS (refer to Table 4-3).
Step 10. Calculate the ULW.
SAMPLE FORM DESIGN PROBLEM NUMBER TWO
4-26. Design the form for a concrete wall 40 feet long, 2 feet thick, and 10 feet high. An M919 concrete mobile mixer is available and the crew can produce and place a cubic yard of concrete every 7 minutes. The concrete placing temperature is estimated to be 70° F. The materials for constructing the form are 2 by 4s, 3/4-inch thick plywood, and 3,000-pound (breaking strength) snap ties. The following steps will be used:
Step 1. Lay out available needed materials.
Step 2. Calculate the production rate.
Step 3. Calculate the plan area of form.
Step 4. Calculate rate the of placing.
Step 5. Determine the concrete placing temperature.
Step 6. Determine the MCP (refer to Figure 4-3).
Step 7. Determine the MSS (refer to Table 4-2).
Step 8. Determine the ULS.
Step 9. Determine the MWS (refer to Table 4-3 using 700 pounds per foot load).
Step 10. Determine the ULW.
Step 11. Determine the tie spacing based on wale size (refer to Table 4-4, using 1,000 pounds per load).
Step 12. Determine the tie spacing based on tie-rod strength (refer to Table 4-5).
Step 13. Determine the maximum tie spacing.
Step 14. Insert the first tie-rod one-half the spacing from the end and one full spacing thereafter. Because tie-rods are being used, it is not necessary to adjust the tie/stud spacing.
Step 15. Calculate the number of studs per side.
BRACING FOR WALL FORMS
4-27. Braces are used against wall forms to keep them in place and in alignment and to protect them from mishaps due to external forces (wind, personnel, equipment, vibration, accidents). An equivalent force due to all of these forces (the resultant force) is assumed to be acting uniformly along the top edge of the form in a horizontal plane. For most military applications, this force is assumed to be 12.5 times the wall height, in feet. As this force can act in both directions, braces to be used should be equally strong in tension as in compression, or braces should be used on both sides of the wall forms. The design procedure is based on using a single row of braces and assumes that strong, straight, seasoned lumber will be used and that the braces are properly secured against the wall forms and the ground (both ends are secured). Once we know the height of the wall to be built and have selected a material (2 inches or greater) for the braces, we need to determine the maximum safe spacing of these braces (center-to-center) that will keep the formwork aligned.
4-28. The following terms are used in bracing for a form wall. See Figure 4-4.
Figure 4-4. Elements of diagonal bracing
Table 4-6. J factor
4-29. The design procedure can best be explained by the example problem that follows:
Step 1. Determine the spacing of braces for a wall 10 feet high. Use 2-by 6- inch by 10-foot material, attached 6 feet from the bottom of the form. The following selected materials are given:
J = 3,710 feet4 (from Table 4-6)
Lmax = 6 1/4 feet (because of the 2-inch material)
LB = 10 feet
h = 10 feet (from example problem)
y = 6 feet (from example problem)
Step 2. Determine the angle of placement, 0.
0 = sin-1 (.600) = 37o
Step 3. Determine the L which is the actual unsupported length of brace. Since the Lmax for all 2-inch material is 6 1/4 feet and the brace in this problem is 10 feet long, we will have to use something to support the braces (usually a 1 by 4 or a 1 by 6). The best position for this support would be in the middle of the brace, thus giving L = 5 feet.
Step 4. Determine the Smax from the formula.
4-30. Using 2- by 6- inches by 10-feet brace applied to the top edge of the wall form at y = 6 feet, place these braces no further apart than 7 feet. After the braces are properly installed, connect all braces to each other at the center so deflection does not occur.
NOTE: This procedure determines the maximum safe spacing of braces. There is no doctrine that states the braces must be placed 7 feet apart--they can be less.
4-31. To fully understand the procedure, the following points lend insight to the formula.
Derivation of the formula has a safety factor of 3.
For older or green lumber, reduce Smax according to judgment.
For maximum support, attach braces to the top edge of the forms (or as closely as practicable). Also, better support will be achieved when 0 = 45o
Remember to use intermediate supports whenever the length of the brace (LB) is greater than Lmax.
Whenever there are choices of material, the larger size will always carry greater loads.
To prevent overloading the brace, place supports a minimum of 2 feet apart for all 2-inch material and 5 feet apart for all 4-inch material. This is necessary to prevent crushing of the brace.
OVERHEAD SLAB FORM DESIGN
4-32. There may be instances where a concrete slab will have to be placed above the ground such as bunker and culvert roofs. Carefully consider the design of the formwork because of the danger of failure caused by the weight of plastic concrete and the live load (LL) of equipment and personnel on the forms. The overhead slab form design method employs some of the same figures used in the wall-form design procedure.
4-33. The following terms are used in the form design (see Figure 4-5).
Sheathing. Shapes and holds the concrete. Plywood or solid sheet metal is best for use.
Joists. Supports the sheathing against deflection. Performs the same function as studs in a wall form. Use 2-, 3-, or 4-inch thick lumber.
Stringers. Supports the joists against deflection. Performs the same function as wales in a wall form. Use 2-inch thick or larger lumber. Stringers do not have to be doubled as wales are.
Shores. Supports the stringers against deflection. Performs the same functions as ties in a wall form and also supports the concrete at the desired elevation above the ground. Lumber at least as large as the stringer should be used, but never use lumber smaller than 4 by 4s.
Lateral bracing. Bracing may be required between adjacent shores to keep shores from bending under load. Use 1 by 6s or larger material for bracing material.
Cross bracing. Cross bracing will always be required to support the formwork materials.
Wedges. Wood or metal shims used to adjust shore height
Mudsill. Board which supports shores and distributes the load. Use 2-inch thick or larger lumber.
Figure 4-5. Typical overhead slab forms
4-34. Use the following steps in determining form design:
Step 1. Lay out and specify the materials you will be using for the construction of the overhead roof slab. It is important that anyone using your design will know exactly the materials to use for each of the structural members.
Step 2. Determine the maximum total load (TL) the formwork will have to support.
The LL of materials, personnel, and equipment is estimated to be 50 pounds per square foot unless the formwork will support engine-powered concrete buggies or other power equipment. In this case, a LL of 75 pounds per square foot will be used. The LL is added with the DL of the concrete to obtain the maximum TL. The concrete's DL is obtained using the concrete's unit weight of 150 pounds per cubic foot. The formulas are--
TL = LL + DL
LL = 50 lb/sq ft, or 75 lb/sq ft with power equipment
Step 3. Determine the maximum joist spacing. Use Table 4-1, or Table 4-2 and determine the joist spacing based on the sheathing material used. This is the same procedure used in determining the MSS for wall-form design. Use the maximum TL in place of the MCP.
Step 4. Calculate the uniform load on the joists (ULJ). The same procedure is used as determining uniform loads on structural members in wall-form design.
Step 5. Determine the maximum stringer spacing. Use Table 4-3 and the ULJ calculated in step 4. Round this load up to the next higher load located in the left column of the table. Read right to the column containing the lumber material used as the joist. This is the member to be supported by the stringer. The value at this intersection is the on-center (OC) spacing of the stringer.
Step 6. Calculate the uniform load on the stringer (ULSstr).
Step 7. Determine the maximum shore spacing the following two ways:
Determine the maximum shore spacing based on the stringer strength. Use Table 4-3 orTable 4-4 (depending on the type of stringer) and the ULSstr, rounded to the next higher load shown in the left column of the table. Read right to the stringer material column. This intersection is the maximum OC spacing of the shore required to ensure the stringer is properly supported.
Determine the maximum shore spacing based on the allowable load. This determination is dependent on both the shore strength and the end bearing of the stringer on the shore. Using Tables 4-7 and Table 4-8, select the allowable load on the shore both ways as follows:
(NOTE: The unsupported length is equal to the height above the sill--sheathing thickness, joist thickness, and stringer thickness. This length is then rounded up to the next higher table value.)
Table 4-7. Allowable load (in pounds) on wood shores, based on shore strength
Table 4-8. Allowable load on specified shores, in pounds, based on bearing stresses
1. When the compression perpendicular to the grain of the member being supported is unknown, assume the most critical C is ^ to the grain.
2. R indicates rough lumber.
3. S4S indicates surfaced on four sides.
- First, determine the allowable load based on the shore strength. Select the shore material dimensions and determine the unsupported length in feet of the shore. See Table 4-7. The allowable load for shore is given in pounds at the intersection. Read down the left column to the unsupported length of the shore, then read right to the column of the size material used as the shore.
- Second, determine the allowable load based on end bearing area. Select the size of the shore material and the compression C perpendicular (^) to the grain of the stringer. If the C ^ to the grain is unknown, use the lowest value provided in Table 4-8. Read down the left column to the C ^ to the grain of the stringer material and then right of the column of the shore material. The allowable load between the stringer and the shore will be in pounds.
- Compare the two loads just determined and select the lower as the maximum allowable load on the shore to be used in the formula below.
Calculate shore spacing by the following formula:
Step 8. Determine the most critical shore spacing. Compare the shore spacing based on the stringer strength in step 7, with the shore spacing based on the allowable load in step 7. Select the smaller of the two spacings.
Step 9. Check the shore bracing.
Verify that the unbraced length (l) of the shore (in inches) divided by the least dimension (d) of the shore does not exceed 50. If l/d exceeds 50, the lateral and cross bracing must be provided. Table 4-7 indicates the l/d > 50 shore lengths and can be used if the shore material is sound and unspliced. It is good engineering practice to provide both lateral and diagonal bracing to all shore members if material is available.
SAMPLE FORM DESIGN PROBLEM NUMBER THREE
4-35. Design the form for the roof of a concrete water tank to be 6 inches thick, 20 feet wide, and 30 feet long. The slab will be constructed 8 feet above the floor (to the bottom of the slab). Available materials are 3/4-inch plywood and 4 by 4 (S4S) (surfaced on four sides) lumber. Mechanical buggies will be used to place concrete. Use the following steps in design:
Step 1. Lay out available materials for construction.
3/4-inch plywood (strong way)
4 x 4 (S4S)
4 x 4 (S4S)
4 x 4 (S4S)
Step 2. Determine the maximum TL.
LL = personnel and equipment = 75 lb/sq ft
TL = DL + LL
TL = 75 lb/sq ft + 75 lb/sq ft
TL = 150 lb/sq ft
Step 3. Determine the maximum joist spacing using Table 4-2.
3/4-inch plywood (strong way) and TL = 150 pounds per square foot
Joist spacing = 22 inches
Step 4. Calculate the ULJ.
Step 5. Determine the maximum stringer spacing using Table 4-3.
Load = 275 pounds per foot
Joist material = 4 x 4
Maximum stringer spacing = 55 inches
Step 6. Calculate the ULSstr.
Step 7. Determine the maximum shore spacing based on stringer strength. Use the maximum shore spacing shown in Table 4-3 single member stringers.
Load = 687.5 pounds per foot (round up to 700 pounds per foot)
Stringer material = 4 x 4 (S4S)
Maximum shore spacing = 35 inches, based on stringer strength
Step 8. Determine shore spacing based on allowable load. This determination is based on both the shore strength and end bearing stresses of the stringer to the shore. Determine both ways as follows:
Allowable loads based on shore strength are shown in Table 4-7.
Unsupported length = 8 feet - 3/4 inch - 3 1/2 inches - 3 1/2 inches = 7 feet 4 1/4 inches (round up to 8 feet).
For an 8-foot 4 by 4 (S4S), the allowable load = 5,400 pounds, based on shore strength.
For an allowable load based on end bearing stresses see Table 4-8. Since we do not know what species of wood we are using, we must assume the worst case. Therefore, the (C ^) to the grain = 250, and the allowable load for a 4 by 4 (S4S) = 3,100 pounds based on end bearing stresses.
Select the most critical of the two loads determined.
Since the (C ^) is less than the allowable load on the shore perpendicular to the grain (II), 3,100 pounds is the critical load.
Calculate the shore spacing as follows:
Step 9. Select the most critical shore spacing. The spacing determined in step 7 is less than the spacing determined in step 8; therefore, the shore spacing to be used is 35 inches.
Step 10. Check shore deflection.
Unsupported length = 8 feet - 3/4 inch - 3 1/2 inch - 3 1/2 inches = 7 feet 4 1/4 inches = 88.25 inches
d = least dimension of 4 x 4 (S4S) lumber = 3.5 inches
NOTE: Lateral bracing is not required. Cross bracing is always required.
4-36. Summary of materials needed for construction.
3/4-inch plywood (strong way)
4 x 4 (S4S) lumber spaced 22 inches OC
4 x 4 (S4S) lumber spaced 55 inches OC
4 x 4 (S4S) lumber spaced 35 inches OC
CONCRETE SLAB ON GRADE THICKNESS DESIGN
4-37. Concrete slabs on grade are the most often constructed concrete projects by engineer units. Many slabs that are constructed fail because the thickness of the slab is not adequate. In other cases, the slab thickness is so excessive that materials and personnel are wasted in the construction. Use the following procedure, tables, and figures for the design of concrete slab thickness in the field to eliminate possible failure or wasted materials.
4-38. The following three points apply to the design thickness:
The minimum slab thickness will be 4 inches for class 1, 2, and 3 floors, as listed in Table 4-9.
Only the load area and the flexural strength required will be considered using this method. Whenever the loaded area exceeds 80 square inches, the soil-bearing capacity must be considered. When the load will be applied at the edges of the concrete slab, either thicken the edge by 50 percent and taper back to normal slab thickness at a slope of not more than 1 in 10 or use a grade beam to support the edge.
The controlling factor in determining the thickness of a floor on ground is the heaviest concentrated load the slab will carry. The load is usually the wheel load plus impact loading caused by the vehicle.
Table 4-9. Concrete floor classifications
4-39. Use the following steps in design procedures for concrete slabs.
Step 1. Determine the floor classification. Use Table 4-9 with the usual traffic and use of the slab.
Step 2. Determine the minimum compressive strength. Using Table 4-10, read down the class of floors column until you find the floor classification selected. Read to the right and select the f 'c in psi. Note that this table gives the recommended slump range for the plastic concrete.
Table 4-10. Recommended slumps and compressive strengths
Step 3. Determine the allowable flexural tensile stress f 't after the concrete f 'c is determined. Use the formula:
Step 4. Determine the equivalent static load (ESL). The expected impact loading is needed for this step. The impact loading is 25 percent more than the static load (SL) for the vehicles.
ESL = (1 + 25%) x SL
Step 5. Evaluate and correct the ESL if f 't is not equal to 300 psi. When calculating the allowable flexural tensile f 'c in step 4 above, an f 't was determined. If this f 't is not equal to 300 psi, then the ESL must be corrected based on a ratio between the standard (300 psi) and the actual f 't. This correction is necessary so that the standard thickness (see Figure 4-6) may be used to determine the required slab thickness. The procedure for correction is as follows:
Figure 4-6. Maximum wheel loads for industrial floors
Step 6. Determine the slab thickness. Using Figure 4-6, read up the left side until the TL is the same as the design CESL from 5 above. Read to the right until the loaded area (in square inches) for the slab design is intersected. The slab thickness can then be determined by interpolating between the slanted slab thickness lines on the figure. Round up to the next 1/4 inch.
Step 7. Determine the minimum cement content and recommended air content for structures subjected to freeze-thaw cycles, depending upon the maximum size of CA to be used.
4-42. The slab thickness design procedure is now complete, and with the accumulated information you should proceed to the mix design procedure as detailed in Chapter 3 of this manual.
4-40. Slab construction is often spoiled by improper construction practices that can be easily prevented. Forms for slabs on grades are relatively simple to construct. See Section III of this chapter. The following practices should always be employed for ensuring that the slab will hold up under service load.
Always use non-frost susceptible (free-draining) material under the slab. Material such as silts and very fine sand expands under frost action if groundwater is present. Removing these types of soil and replacing them with a free-draining material (gravel or coarse sand) to one-half of the expected frost penetration, (in addition to providing adequate drainage at the edges of the structure), will prevent frost heave.
Always use some form of steel reinforcement. Welded-wire mesh is very desirable for preventing excessive cracking and preventing widening of cracks that do develop.
Always keep the slab moist and protect it from excessive heat and freezing for the required curing time. This will ensure the concrete is cured properly.
SAMPLE SLAB CONSTRUCTION PROBLEM
4-41. Determine the slab thickness for the floor of a wheeled-vehicle shop. The total weight on one wheel is 7,500 pounds and the loaded area equals 40 square inches. The surface will be exposed to foot and wheel traffic. Abrasive wear is expected. The maximum-size aggregate will be 1 inch.
Step 1. Determine the floor classification, see Class 5, Table 4-9.
Step 2. Determine the minimum compressive strength from Table 4-10.
Step 3. Determine the allowable flexural tensile stress.
Step 4. Determine the ESL.
ESL = (1 +.25) x SL = 1.25 x 7,500 = 9375 lbs
Step 5. Evaluate and correct the ESL if f 't ¹ 300 psi
Step 6. Determine the slab thickness from Figure 4-6.
Loaded area = 40 sq in
Slab thickness = 6.6 in
NOTE: Always round up to the next higher 1/4-inch thickness for convenience. Therefore, the thickness is rounded up to 6 3/4-inches.
4-42.The minimum cement content per cubic yard from, Table 4-11, with 1-inch maximum-size aggregate (MSA) is 520 pounds. Because the structure is a vehicle-shop floor, the air content may be less than the table allowance. The slab design information is now:
f 'c = 4,500 psi
Slab thickness = 6 3/4 inches
Minimum cement content = 520 lb/cu yd
Air content = 6%
Table 4-11. Minimum cement contents and percentages of entrained air
COLUMN FORM DESIGN
4-43. Use the following steps in determining design procedures of a wood form for a concrete column.
Step 1. Determine the materials you will use for sheathing, yokes, and battens. The standard materials for column forms are 2 by 4s and 1-inch sheathing.
Step 2. Determine the column height.
Step 3. Determine the largest cross-sectional column dimension.
Step 4. Determine the maximum yoke spacing by referring to Table 4-12. First, find the column height in feet in the first column. Then move right horizontally to the column heading of the largest cross-sectional dimension in inches of the column you are constructing. The center-to-center spacing between the second yoke and the base yoke is the lowest value in the interval that falls partly in the correct column height line. You can obtain all subsequent yoke spacing by reading up this column to the top. These are maximum yoke spacing; you can place yokes closer together. Adjust final spacing to be at the top of the column.
Table 4-12. Column yoke spacing using 2 by 4s and 1-inch cheathing
SAMPLE COLUMN FORM DESIGN PROBLEM
4-44. Determine the yoke spacing for a 9-foot column whose largest cross-sectional dimension is 36 inches. Construction materials are 2 by 4s and 1-inch sheathing.
Step 1. Lay out materials available.
2 x 4s and 1-inch sheathing
Step 2. Determine column height.
Step 3. Determine the largest cross-sectional dimension.
Step 4 and Step 5. Determine the maximum yoke spacing, refer to Table 4-12. Starting from the base, the yokes are: 8, 8, 10, 11, 12, 15, 17, 17, and 10-inches. The spacing between the top two yokes are reduced due to the limits of the column height. Adjust the final spacing to be at the top of the column.
|David L. Heiserman, Editor||
Copyright © SweetHaven
Revised: June 06, 2015