The I.C.E. Block™ system is a concrete forming system which produces a continuous insulated monolithic concrete wall requiring no stripping and ready to receive finish materials. The system is presently available in two types of form. The original expanded polystyrene form, 48 inches wide by 16 inches high produces a waffle shaped concrete wall with vertical columns 12 inches on center and horizontal beams 16 inches on center with a continuous 2 inch web of concrete joining all the beams and columns. This creates a monolithic reinforced concrete wall. The form may be cut to provide a minimum web of 3 5/8 inch for increased fire rating. A solid wall expanded polystyrene form is also available which produces a uniform thickness of wall, usually a full 6 inch or 8 inch thick solid continuous wall, the same as other removable forming systems. The solid wall form is 48 inches long by 12 inches high with sheet metal plate ties at 8 inches on center and the expanded polystyrene insulation is 2-1/2 inch thick on both sides.

This forming system optimizes the use of concrete and insulating materials to produce the finished wall. Because of the unique shape of the resulting concrete wall, the requirements for minimum reinforcing steel must be met. This is necessary to maintain the structural integrity of the system throughout its useful life. If the wall is to be subjected to design loads or longer spans than those required for minimum reinforcement, structural calculations must be performed by qualified personnel to determine the required steel reinforcing for the design conditions.

This concrete system, if properly designed and reinforced, will perform adequately for walls with axial and lateral loads; columns to carry concentrated loads, especially on the sides of openings; and shear walls to resist in-plane shear loads from shear diaphragms or other shear elements. This Manual will provide you with the design information and assist you in the design methods for the proper design of an I.C.E. Block™ wall system.

MINIMUM REINFORCEMENT REQUIREMENTS

I.C.E. Block™ recommends the use of reinforcing to meet the requirements of the American Concrete Institute's Building Code Requirements for Reinforced Concrete (ACI 318). At the time of preparation of this Manual, the current Code was 1995. The following recommendations conform the requirements of this model Code with the exception Section 14.3.5 which requires a maximum spacing of reinforcing of 18 inches in both the horizontal and vertical directions. This criteria is usually not required to be met in most residential, light commercial, and light industrial applications. If this minimum requirement is to be met, the I.C.E. Block™ system can easily achieve the requirements with reinforcing spacing at 12 inches vertically and 16 inches horizontally in the waffle form, or any desired spacing in the solid form.

Minimum reinforcing for the I.C.E. Block™ waffle system is one #4 (1/2 inch) bar placed in every other vertical core (24 inch centers) and one #4 bar placed in every third horizontal core (48 inch centers). Every opening less than 4 feet wide must have a reinforced lintel over the door of at least 8 inch of depth of concrete with two #4 bars, each with 3/4 inch clear concrete cover on the bar top and bottom of the lintel; and two vertical #4 bars on each side of the opening. ACI 318 Section 14.3.7 requires at least two #5 bars on each side of the opening.

Included in this Manual are tables of common load applications for the waffle form. The inclusion of a table for backfill for an equivalent fluid pressure of 30 psf/ft. of depth is included as this value is sometimes used for local practice. However, this lower value of equivalent fluid pressure is generally associated with retaining walls whose top is free to deflect and mobilize the shear strength of the soil, generally referred to as "active" pressure. For basement walls, the top is restrained from moving and "at rest" pressure should be used. Included is a table for 40 psf/ft. of depth, which is the minimum for well drained uncompacted granular material placed next to the wall.

LOAD CAPACITIES - Waffle Wall Form

With a minimum of 2500 psi concrete and Grade 40 reinforcing, these minimum reinforcing requirements will carry the following service loads:

6 INCH WALL

1. Wall axial loads up to 4,500 pounds per lineal foot (plf) for a 10 foot height with no lateral loads (ACI Equation 14-1).
2. Lateral Wind Loads to 25 pounds per square foot for walls up to 10 feet high.
3. Backfill up to 4.5 feet on walls 8 feet high with an equivalent fluid pressure of 40 pounds per cubic foot.

8 INCH WALL

1. Wall axial loads up to 9,500 pounds per lineal foot (plf) for a 12 foot height with no lateral loads (ACI Equation 14-1).
2. Lateral Wind Loads to 30 pounds per square foot for walls up to 12 feet high.
3. Backfill up to 5.5 feet on walls 8 feet high for an equivalent fluid pressure of 40 pounds per cubic foot.
4. Cantilever retaining walls up to 5 feet for an equivalent fluid pressure of 40 pounds per cubic foot.

To compare the maximum capacity of the I.C.E. Block™ wall, with 4000 psi concrete and Grade 60 reinforcing with #6 @ 12 inches in the 6 inch wall, and #7 @ 12 inches in the 8 inch wall (set to 3/4 inch from the side of the form opposite the side the load is applied to), the system has the capacity to carry the following service loads:

6 INCH WALL

1. Wall axial loads up to 14,500 pounds per lineal foot (plf) for a 12 foot height with no lateral loads.
2. Lateral loads to 200 pounds per square foot for walls up to 12 feet high.
3. Backfill up to 9 feet on walls 9 feet high with an equivalent fluid pressure of 55 pound per cubic foot.

8 INCH WALL

1. Wall axial loads up to 45,000 pounds per lineal foot (plf) for a 12 foot height with no lateral loads.
2. Lateral loads to 350 pounds per square foot for walls up to 12 feet high.
3. Backfill up to 12 feet on walls 12 feet high with an equivalent fluid pressure of 55 pounds per cubic foot.
4. Cantilever retaining walls up to 10 feet with an equivalent fluid pressure of 55 pounds per cubic foot.

The above listed range of load capacities indicates the I.C.E. Block™ system has wide application in residential, commercial and industrial construction. The range of capacities also indicates the need for detailed structural calculations to determine the optimum use of concrete and steel reinforcing materials. Loads in excess of the minimum capacities require engineering design. Load capacity of the solid wall form are the same as with removable forming systems, greater than those listed above.

CALCULATION METHODS

Standard engineering methods are used to determine the structural capacities of the concrete wall system. Load combinations and load factors conforming to the ACI 318-95 Building Code or 1991 UBC Chapter 26 (1994 Chapter 19) requirements are used to determine the design requirements of the wall. The UBC requirements are identical to the ACI requirements except for additional provisions in 2614(i) Alternate Design Slender Walls, (1997 Section 1914.8) usually defined as the Slender Wall Method.

The following pages include drawings of the equivalent cross sections of the wall used for structural analysis, a sample calculation worksheet, design tables to aid in the calculation procedure, and uniaxial interaction curves for combinations of axial and moment loads.

A thorough application of the following steps will result in the safe and economical design of an I.C.E. Block™ wall. Although this may seem a lengthy procedure, several steps will be an obvious necessity, no matter what system is used, and after a couple applications, it can be accomplished relatively easily and quickly. I.C.E. Block™ is presently developing computer software to perform the more tedious calculation, and many of these have been reduced to design charts and diagrams presented in this Manual. The references are to the Building Code Requirements for Reinforced Concrete, ACI 318-95.

1. Determine the structural system which will bear on and/or support the wall. This would include floor and roof members.
2. Identify the spans which will bear on walls and which walls will be non bearing. Also identify shear walls which will provide reactions to floors and roof diaphragms to resist lateral loads.
3. Determine the design loads for the floors and roof members bearing on the walls, and lateral loads on the walls due to wind, seismic, or soil backfill pressures. Use the local building code requirements for minimum values.
4. Sketch attachment details for connection of floor and roof members to the I.C.E. Block™ wall system. This will identify off center eccentricities for connections which are necessary for a correct analysis of the loads transferred to the wall. Typically this would include ledger systems for floors attached to the side of the I.C.E. Block™ wall system. For example, a wood ledger bolted to an 8 inch concrete wall supports floor joists set in metal joist hangers nailed on the ledger. If a 2x is used for the ledger and standard joist hangers with a bearing length of approximately 1.5 inch, the resulting eccentricity for the floor load would be 1.5 inches/2 + 1.5 inches + 7 inches/2 = 5.75 inches. This will introduce a moment into the wall which must be designed for. This condition must be compared to other loads which also produce moments in the wall. Often this condition will produce counterbalancing moments to soil backfill pressures or wind pressure because the floor eccentricity will produce a moment in the opposite direction of the soil or wind pressure. Wind suction and seismic load generally will combine with floor eccentric loads to produce additive moments.
5. Determine the design load for the wall from the floor, roof, and lateral loads identified above. This is usually the multiplication of contributory span lengths times the unit load on the floor or roof member. This must be separated into dead load, live load, and short term load because of the ACI 318 required load combinations (Section 9.2, Equations 9-1, 9-2, and 9-3). These loads must be multiplied by their respective eccentricities to determine design moments on the wall. Be careful of sign convention to make sure correct moments are added or subtracted. Include the weight of the wall , calculated using 56 psf for the 6 inch wall , and 76 psf for the 8 inch wall.
6. Determine the lateral design loads for the wall. This would generally include wind, seismic, and soil backfill pressure. Be sure to include any lateral pressures from a surcharge on the backfill such as a parking lot next to the wall. Typically wind and seismic loads are modeled as uniform loads and soil pressures are modeled as triangular or trapezoidal loads. Trapezoidal varying loads may be broken into combination of triangular and uniform loads.
7. Determine the shear and moments induced in the wall from the lateral loads. Again, the different live , dead, and short term components should be kept separated for differing combinations and load factors.
8. Multiply the various loads by the appropriate load factors and add together in the following ultimate load combinations, U:
9. U = 1.4D + 1.7L (9-1)
10. U = .76(1.4D + 1.7L + 1.7W) (9-2)
11. U = .9D + 1.3W (9-3)
12. where: U = ultimate design load, axial, moment and shear
13. D = dead load
14. L = live load
15. W = wind load (substitute 1.1E for seismic load)
16. The combinations above must be checked for both: 1) maximum axial load with the corresponding moment for the same load case; and 2) the maximum moment with the corresponding axial load. Along with each of the values for axial load and moment, the corresponding maximum shear values should be determined.
17. We suggest a check of the wall thickness for shear at this point. The wall may be capable of being reinforced to resist flexural and axial load but may be inadequate to resist the shear induced by the lateral loads. The nominal shear capacity of the wall is determined by Equation 11-3 of the ACI Code, Section 11.3:
18. 
19. This Equation and Equation 11-1 result in the following table (f = .85):

20. 		6" Wall Waffle	8" Wall Waffle	6" Wall Solid	8" Wall Solid
    	psi	kips	kips	kips	kips
    Reinforcing in the center of the wall,	3,000	1.454	2.281	3.352	4.469
    d = 2.5" for 6", 3.5" for 8" waffle	3,500	1.571	2.464	3.621	4.828
    d = 3.0" for 6", 4.0" for 8" solid	4,000	1.68	2.634	3.871	5.161
    Reinforcing with 3/4" cover at edge of wall,	3,000	2.328	3.91	5.587	7.821
    d = 4.0" for 6", 6.0" for 8"	3,500	2.514	4.224	6.034	8.448
    d = 5.0" for 6", 7.0" for 8" solid	4,000	2.58	4.516	6.451	9.031

21. The shear capacity is per cell or per 1 foot section of solid wall which has vertical reinforcing in it.
22. The capacities can be increased by applying Equation 11-4 to account for the increase in shear capacity due to axial load, however the increase for most applications is so small it does not justify the extra calculation effort.
23. At this stage in the calculations, a check should be made for conformance to ACI Section 10.12.3.2 for minimum eccentricities. Although this Code provision is intended for columns and not required for walls, a conservative design would consider minimum eccentricities, especially under high axial loads. Eccentricity is the distance off the centroid of the section that the axial load is applied. The Code specifies a minimum eccentricity of (.6 + 0.03h) inches. For the I.C.E. Block™ system this is .75 inches for the 6 inch waffle wall, .78 inches for the 6 inch solid wall, .81 inches for the 8 inch waffle wall and .84 for the 8 inch solid wall. Compute M_u /P_u being careful to use consistent units. This will give you the equivalent eccentricity to be compared to the Code minimum. If the design eccentricities are less than the Code minimums, use design moments of .75P_u for the 6 inch waffle wall, 78P_u for the 6 inch solid wall, .81P_u for the 8 inch wall, and .84P_u for the 8 inch solid wall (units of inch-kips or inch-pounds). Determine the two load cases to be checked:
24. (1) Maximum P_u and the corresponding M_u
25. (2) Maximum M_u and the corresponding P_u.
26. If the axial loads are relatively light with the resultant of all factored loads located within the middle-third of the wall (maximum eccentricity = 0.833 inch for the 6 inch waffle, 1 inch for the 6 inch solid, 1.667 inch for the 8 inch waffle, and 2 inch for the 8 inch solid wall), ACI Section 14.5. Empirical design method applies and Equation 14-1 may be used:
27. 
28. Moment Magnifier Method
29. A check for slenderness is generally necessary because of the shape of the waffle wall system. Refer to the following pages for the Equivalent Core sketches to calculate structural properties. In our calculations, we use for the waffle wall rather than the Code allowed r = 0.30h because it results in a more conservative value. This results in a radius of gyration, r = 1.44 inches for the 6 inch wall, and r = 2.02 inches for the 8 inch wall. Another conservative assumption made is that the walls are designed as simple spans vertically with no end moments. Requirements of section 10.12.2 of the ACI Code then reduces to considering the slenderness only when kl_u / r is greater than 34 because the end moments M_1b and M_2b are assumed zero.

1. Determine the amount of reinforcing steel necessary to resist the two design load cases for axial load and moment. Note that each load case will have a different moment magnifier.
2. Generally, if the reinforcing is selected on the basis of the maximum magnified moment, the corresponding axial load capacity is adequate for the typical application of the ICE Block^TM wall system. There are three basic ways to determine the required reinforcing steel. If the amount of reinforcing is selected on the basis of the design moment, the load case should be checked by plotting on the interaction diagram for the selected wall thickness and steel reinforcing size and position. The three methods are :
   1. Substitute the maximum ultimate design moment M_c in the following equation to determine the coefficient of resistance, R_u:
   2. 
   3. where b = 6.25" for 6" waffle walls, and 7.0" for 8" waffle walls, and 12" for solid walls of any thickness.
   4. where d = 2.5" for 6" waffle walls, 3.0" for 6" solid walls, 3.5" for 8" waffle walls and 4.0" for 8" solid walls (centered)
   5. or: d = 6.0" for 8" waffle walls, 5.0" for 6" solid walls, 7.0" for 8" solid walls (at edge) where f = .9
   6. Substitute the value for R_u in the following equation for the required % of steel:
   7. 
   8. where
   9. where f'_c = concrete strength;
   10. and f_y = yield strength of reinforcing steel (40 ksi for Grade 40 and 60 ksi for Grade 60) then the required area of steel is:
   11. 
   12. Select Moment-Axial load Interaction Diagram for the closest selected area of steel, plot on the two load cases to make sure the combination of axial load and moment fall within the curve.
   13. Choose a reinforcing bar size, determine the flexural capacity, and then compare to see if it exceeds the load induced design moment, revising and recalculating if necessary. The nominal section capacity equation is:
   14. 
   15. where = height of compressive stress block, f = 0.9 and other variables as defined in A. above.
   16. Select Moment-Axial load Interaction Diagram for the selected area of steel, plot on the two load cases to make sure the combination of axial load and moment fall within the curve. Make sure this capacity is the same as the load on each cell or per foot of wall as the reinforcing spacing (24 inch spacing carries the load for 2 foot of wall, not just per foot).
   17. Select Moment-Axial Interaction diagram in which both load cases plot inside of the interaction curve. Use concrete strength and reinforcing as specified for the curve.

Included in this Manual are Moment-Axial Interaction diagrams for the I.C.E. Block™ waffle wall system for some typical concrete strengths and reinforcing bar placement. These were produced using the Portland Cement Association's computer program PCACOL. Other geometry and material properties are available upon request. The Manual does not include tables for reinforcing off center for the 6 inch wall. If the application has enough lateral load that cannot be resisted by reinforcing centered in the 6 inch wall, we normally recommend using an 8 inch wall. Only load diagrams for waffle walls are included in this Manual.

Note the limit of application of the Moment Magnifier method is to a slenderness ratio kl_u/r is limited to 100 (ACI 10.11.5). Along with this slenderness ratio, the Code effectively limits the maximum ultimate axial load to 70% of the critical buckling load P_c as you get a negative Moment Magnifier. Stability is critical when the axial load exceeds 50% of P_c because the Moment Magnifier increases rapidly. Stability failure occurs at 70% of P_c because the Moment Magnifier gets very large as it approaches 70% and then goes negative.

Slender Wall Method

The UBC allows an alternative procedure to steps 11. and 12. above. The Slender Wall method limits the maximum axial stress and eliminates the stability problem of the Moment Magnifier method, but also does not allow near the axial load capacity of the Moment Magnifier method, but allows taller thinner lightly loaded walls.

If the slenderness ratio is greater than 100, you must use the UBC procedure. However this method also has limitations outlined in 1191 UBC 2614(i)1 (1997 Section 1914.8). These limitations are:

1.  
2. Vertical service load stress at the location of maximum moment does not exceed .04 f'c. This guarantees that flexural tension controls, a required criteria for this Method
3.  
4. The reinforcement ratio r does not exceed .6r_b.
5.  
6. Nominal moment capacity times phi, fM_n must be greater than M_cr.
7.  
8. Distribution of concentration loads does not exceed the width of bearing plus a width increasing at a slope of 2 vertical to 1 horizontal down to the design flexural section.
9.  
10. Secondary moments based on the maximum potential deflection, D_n, which is a function of reinforcing and I_cr.
11.  
12. Service load deflection cannot exceed l/150.

Because of the UBC limitations, the allowable interaction diagram is a small rectangle, limited by fM_n on the x-axis and .04 f'c (service load) on the y-axis. The interaction diagram has little meaning with these limitations, so the applied loads are checked against these limits and no interaction diagram is necessary.

Note the secondary moments are not based on service load deflections, but rather on a maximum potential deflection, D_n. Also note the maximum deflection under which the service load applies, and the minimum reinforcement moment capacity times phi, fM_n must be greater than the cracking moment. To calculate these deflections and relevant variables, the UBC included the following equations and definitions in the Code:

		;		;		;
For		;
For		;		;

Where:

vertical distance between supports

nominal moment capacity as defined in Step 12 above.

maximum moment in the wall resulting from unfactored load combinations

gross moment of inertia of uncracked section, neglecting reinforcing

distance from centroidal axis of the gross section, neglecting reinforcement, to extreme fiber in tension

In order to evaluate a proposed design, reinforcing bar selection must be made first and the relevant properties calculated. The provision for ductility must also be checked using Equation 8-1 of the ACI Code (1991 UBC Section 2608(e) or 1194 1908.4.3):

where b ₁ = .85 for f’_c up to 4000 psi, reduced .05 for each 1000 psi greater than 4000 psi to a minimum of .65.

Service moments should first be calculated due to lateral loads, applicable load factors applied, and both ultimate moments and axial loads calculated. A reinforcement should then be selected and the nominal moment capacity calculated. The maximum potential deflection, D_n, calculated and secondary moments, P_u *D_n added to the ultimate moments due to lateral loads, similar to step 11 E. above. This total design moment must then be compared to the nominal moment capacity times the strength reduction factor, fM_n > M_u. The service load deflection must then be calculated and compared to the maximum allowable wall deflection, l/150.

I.C.E. Block™ LINTELS

Lintels over openings are easily formed with the I.C.E. Block™ wall system. The design of lintels is the same as for any other reinforced concrete beam. Most lintels over openings in walls are placed monolithically with the wall on either side of the opening with the horizontal reinforcing of the lintel continuing into the wall. This normally results in construction which can be modeled as a beam with fixed ends, or conservatively fixed one end and simply supported on the other. Moments and shears are determined using standard engineering methods, and multiplied by the Code required load factors. Lintels should have the horizontal beam section of the forming system as the top of the lintel. This is to make sure there is adequate concrete on top to form the compression flange of the beam. The bottom needs to be cut out for a depth of 3 inch x the core width of the form for adequate cover around the bottom reinforcing. The solid wall form may be treated as any other rectangular concrete beam design except for a reduction in the effective depth of concrete for shear carrying capacity of the concrete.

Flexural reinforcement to resist design moments should be proportioned as described in step 12 above for the design of the wall system, except there are no considerations for axial loads, magnified moments or interaction diagrams although you can pick out the steel from the interaction diagram with P_u = 0. The compressive stress block height, a, must be checked to determine adequate capacity of the section to develop without a compression failure. If the bottom of the beam is not at the horizontal beam section of the forms, check the compression block at the ends of the beam for the fixed end moment. If the ends are overstressed, design the bottom reinforcing in the center for a simple span moment. If this is not desirable, a doubly reinforced beam analysis could be performed at the ends of the beam to determine actual compression stresses. Typical lintels, however, normally do not require this extensive of an analysis.

The only special consideration for the I.C.E. Block™ waffle wall system is the checking of the beam shear for the nominal 2 inch web. The metal plates with holes which form the "wall ties" of the system form a plane of weakness and a reduction of shear capacity if not reinforced. We recommend the addition of 1 #3 bar horizontally through each hole of the ties to contain the concrete through the hole and provide aggregate interlock for shear strength. In addition the 2 inch web must be checked for adequate strength according to ACI Section 11.1. When the ultimate design shear V_u exceeds one half of the nominal capacity of the concrete, ACI Equation 11-3,

then shear reinforcement must be added, proportioned to meet ACI Equations 11-17 and 11-2 with f = .85. Minimum shear reinforcing must meet the requirements of Section 11.5.5.3 and Equation 11-13. The solid wall section has a similar plane of weakness constraint at the metal wall ties, which are spaced at 8 inch on center. The nominal shear capacity of the concrete may be calculated by using the full wall thickness for b_W and a reduced value for the effective depth, d. This effective depth may conservatively be calculated by using the full height of the lintel section, subtracting 3 inch to the centroid of the bottom bars (tied to the metal ties), and also subtracting 6 inch for each 12 inch high course of I.C.E. Block™. For example, a 24 inch high lintel in an 8 inch wall would have 8 for the value for b_W, and 9 for the effective depth (24 inch – 3 inch - (2x6 inch)). The remaining shear capacity would be made up by steel reinforcing for shear.

Shear reinforcement for the waffle wall may be either #3 bar bent into an "S" shape and hooked around the top and bottom reinforcing, a "U" shape in which the bottom of the U crosses the bottom reinforcing in the lintel and the top ends of the U terminate in hooks over the top reinforcing, or welded wire fabric bent into an "S" shape hooked under and over the bottom and top reinforcing with a cross rod of the wire mesh at each end to help develop the vertical rods of the mesh. Another method is the placement of the shear reinforcing at a 45 degree angle with the top of the bar at the support end and angling downward toward the center of the lintel. See the included detail for bar placement. Using this method, the minimum stirrup placement may be increased according to ACI 11.5.4.2.

Shear reinforcement for the solid wall system may be formed as for normally reinforced concrete beams. This is normally a continuous closed stirrup, terminating in 135 degree hooks in one corner. However, for the I.C.E. Block™ system, this could present a placement difficulty bcause the top horizontal bars in a lintel would have to be threaded above the form ties and below the closed stirrup. An alternative method for stirrup placement is to use two "U" shaped bars to form a closed stirrup, one right side up, the other upside down, with the vertical legs overlapping the entire vertical height of the lintel (minus concrete cover over the bars). This would allow a much easier sequence of bottom horizontal bars, rightside up "U" bars, I.C.E. Block™ forms, horizontal top bars and finally the upside down "U" bars slipped down alongside the rightside up "U" bars and tied to them.

Shear reinforcement for the solid wall system must be spaced with no more than 1 inch between the stirrup and the form ties, which are spaced 8 inch on center. This will provide reinforcing for a shear crack which may jump to the tie and may crack between stirrups if placed too far from the tie. For a standard practice in placing lintels, we suggest using a Grade 40 or better #3 stirrup placed 8 inch on center throughout the length of any lintel less than 12 inches high or over 3’–6" in span. This will increase the lintel shear capacity substantially.

The shear capacity of a 12 inch lintel without reinforcing would be at least 1,530 pounds (6 inch wall, 2500 psi concrete). The Code requires reinforcement when the shear load exceeds one-half of this capacity. For a 3'-6" span this is at least 500 pounds per lineal foot, (shear at d from the face of support). It would be rare in most I.C.E. Block™ applications where this load would be exceeded. When a Grade 40 #3 closed stirrup spaced 8 inch on center is added to a 12 inch lintel, the shear capacity increases by 8,800 pounds for a total capacity of 10,330 pounds. For example, a 16 foot span 12 inch high lintel, this means a shear capacity of at least 1,200 pounds per lineal foot when reinforced with #3 shear stirrups at 8 inch on center.

SHEAR WALLS

Analysis of walls acting as shear walls to provide reactions to diaphragms or perpendicular walls by providing shear resistance in the plane of wall shall be designed in accordance with ACI Section 11.10. An overall stability analysis of the entire structure must be performed first to determine the forces acting on each individual wall. This analysis must include identifying which walls will act as shear walls, distributing the proper shear force to each wall through the diaphragm using code specified procedure, in proportion to the wall's stiffness and torsional characteristics of an unsymmetrical shear wall system. Be sure to correct analysis as torsional effects are not allowed for flexible diaphragms. This type of analysis is beyond the scope of this Manual.

After the shear forces to each wall are identified, each wall should be checked for overall stability in an overturning analysis. This should also include investigation of footing soil pressures. If the wall is of insufficient weight to resist overturning (Code required Factor of Safety of 1.5 against overturning) then alternate methods must be used to increase stability. Once the overall stability has been checked, the internal strength capacity must be investigated.

Shear walls are normally modeled as cantilevered beams with a concentrated shear force at the top, and often overturning moments carried from stories above. In most applications, the shear wall will have nominal capacity far in excess of that required to carry the load.

According to ACI Section 11.10.4, the flexural capacity may be checked using a value of d equal to .8 times the length of the wall. Vertical reinforcing at the end of the wall to resist the overturning moment can be proportioned by:

A_s = M_u /(.8L_w f_y)

Don't forget to subtract off the wall weight in computing M_u. Since many design lateral loads occur in any direction, normally this amount of reinforcing is applied to each end of the wall. The nominal shear capacity of the wall can conservatively be calculated as:

A more refined calculation may be made utilizing Equations 11-31 and 11-32 of the Code if the required strength is close to the above calculation for V_c. If the design shear V_c is more than one half the nominal shear capacity, V_c shear reinforcing is required to meet the requirements of Section 11.10.9. If reinforcing steel is required for the shear wall capacity, the Code requires conformance to Chapter 14 requirements for walls, including maximum spacing of the horizontal reinforcing to be 18 inches. This requires the ICE BlockTM system to have one bar every horizontal beam at 16 inches. The minimum reinforcing is one #4 bar in every horizontal beam at 16 inches on center. Equation 11-34 is:

The resulting shear capacity for minimum reinforcing is quite high. For example, if a shear wall constructed of the waffle form and 3000 psi concrete is 10 feet long, d = 96 inches, V_c = 21 kips, V_s = 144 kips, and .85(V_c + V_s) = 140 kips. This nominal capacity normally would exceed any shear wall requirement in the general application of the ICE Block^TM wall system. The shear wall capacities of the solid form are substantially higher. The b_W term is the wall thickness, and the d term does not have to be reduced for the form ties because the load is applied perpendicular to the ties. With the required minimum reinforcing for a shear wall, the resulting nominal capacity normally would exceed any shear wall requirement in the general application of the I.C.E. Block™ wall system.

CALCULATION WORKSHEET

The following pages entitled "I.C.E. Block™ WALL ANALYSIS" are worksheets to calculate the required reinforcing to resist design lateral loads placed on the wall in combination with the applied axial loads. Two methods are presented. The first determines the moment magnifier and combines the design axial loads with moments from lateral loads to identify the maximum load cases to compare to the interaction diagrams. The second is a slender wall analysis as provided in the Uniform Building Code for the procedure of calculating secondary effects due to deflection of a slender wall. An explanation of the worksheets serves as sample calculations. The boxed in areas are variable inputs, the other values are derived from the input. Refer to Figure 2 for additional explanation of the application of loads.

The top section of the worksheets, titled "VERTICAL SERVICE LOADS" is a calculation of the vertical loads applied to the wall. Two load cases for vertical dead load and live load may be input. This allows two different spans and eccentricities to be placed on the wall such as the inclusion of roof and floor loads of two differing spans. Two or more floors may be input by adding the total dead load and live load for the two floors together and averaging the contributory span to the wall. Typically floors bearing on one wall are the same span and design loads, so only one input can be generally used to cover more than one floor if necessary. Also one load case for short term load may be used, either wind or 1.1 times seismic loads, (vertical axial loads only). The wall weight may be input for any height, typically for the height of the wall above the location of the maximum moment. Conservatively the total height of the wall may be used as this value is used in computing the total load for the design section of the wall.

The vertical unit loads are multiplied by the contributory span to the wall. Typically the contributory span to a wall is one half the total span for simple span conditions, 1.25 times the span for a two span continuous condition where the wall is the center support, or .375 times the span for the end span of a two span continuous support. Eccentricities for each load condition may be input. The wall eccentricities will be added to or subtracted from the moments due to the lateral loads on the wall. Technically this is not correct as the moment due to eccentricity may vary with the wall height, or may be distributed in a two story wall application, but the simple addition of moments should be a conservative result in most cases.

The next section of the worksheets, titled "LATERAL SERVICE LOADS" is set up to determine shear and moment in the wall due to lateral loads on the wall. Several load types may be combined, including a triangular distribution typically for soil pressure on backfill; two uniform loads, typically for a surcharge on backfill or wind, or a partial loading of both for a partially exposed wall; and a point load which may be used to model other conditions if necessary. These loading conditions are analyzed to indicated shear and moment at tenth points along the wall height. The values under the loads are service values, but the total column at the end is a summation of all the service shears and moments times their respective load factors.

Axial loads from the unit loads and spans are computed and multiplied by load factors.

The next section of the worksheets is a calculation of the structural properties of the wall. The values of b and h are taken from the equivalent core sketches for either a 6 inch or an 8 inch wall. The value for d is assumed one half of h for reinforcing centered in the wall or the wall thickness minus 3/4 inch cover for reinforcing placed on one side of the cell. The total gross cross-sectional area, moment of inertia, and radius of gyration are computed. As stated previously, r is actually computed instead of using .3h as allowed by the Code as this value is more conservative. The height is taken form the vertical span input under the lateral load section, and the slenderness calculated. A maximum slenderness of 100 is used as the upper limit for wall heights using the Moment Magnifier Method as this is the limiting value for which this analysis is allowed. More slender sections must be evaluated by a special analysis (ACI 10.10.1), which according to the UBC, the Slender Wall Method complies with (1991 UBC 2614(i) or 1997 UBC 1914.8.1) when flexure tension controls the design of the wall.

The equivalent stiffness EI and critical buckling load P_c are calculated. These values are then used with the axial dead and total loads identified in the top section of the worksheet to determine the moment magnifier. A moment magnifier, the maximum design values for axial load, magnified moments, and shears are evaluated for the design load cases. A check for maximum % of steel for ductility is left to the designer as this seldom occurs for most applications of the I.C.E. Block™ wall system.

A summary of the wall geometry, loads, and induced forces are tabulated. These are compared to wall capacity calculations to verify adequacy of the design. Finally, the axial load moment combinations are plotted on an interaction diagram to graphically verify the design adequacy.

The procedure for the Slender Wall Analysis would be similar, except there would be no interaction diagram to check because the axial load is limited to guarantee that flexural tension controls the design. A sample calculation for the Slender Wall Method follows the Moment Magnifier worksheet. It follows the same format as the Moment Magnifier Method up to the structural properties of the wall. Other properties required for slenderness effects are calculated, including a ductility check for the more restrictive requirements of the Slender Wall Method, and an axial stress check to determine the suitability of the method. Deflections and corresponding second order moments are calculated and checked for Code compliance with deflection limitation and moment capacity. A summary of the design is presented on the final page of the calculations.

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While ICE Block™ and Foam Block of Texas have taken every precaution to utilize the existing state of the art and to assure the correctness of the analytical solutions and design techniques used in this Manual, it is possible that there may be errors, both of omission and commission and the responsibilities for modeling the structure to develop input data, applying engineering judgment to evaluate the output, and implementing engineering drawings remain with the structural engineer of record. Accordingly ICE Block™ and Foam Block of Texas does and must disclaim any and all responsibility for defects or failures in structures in connection with which this information is used.

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