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Tilt-Up Wall Panel |
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Tilt-Up Wall Panel |
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This program provides design investigation for a one foot wide strip of concrete wall panel subjected to axial and lateral loads due to wind or seismic forces. Six different design methods may be specified which cover the typical design philosophies for tilt-up wall panels. These methods combine vertical and lateral loads to calculate wall moments and deflections.
The differences in the design methods center around the moment of inertia used to calculate wall deflections, and exactly how the maximum wall deflection is obtained. The methods include:
| • | Analysis according to section 2614(i) of the Uniform Building Code. This method is based upon tests performed by a committee of the Structural Engineers Association of Southern California. |
| • | Analysis using ACI equation 9-7 to calculate moment of inertia. This simplified equation yields a conservative moment of inertia. Analysis using this moment of inertia can either iterate wall deflections to convergence, or directly calculate wall deflection at the maximum moment capacity. |
| • | Analysis using ICRACKED for the full height of the wall, and is very conservative. Analysis using this moment of inertia can either iterate wall deflections to convergence, or directly calculate wall deflection at the moment capacity of the wall. |
Along with these different analysis methods, you can include the effects of fixity at the base of the wall (for dock-high walls) and wind or seismic load on a projecting parapet.
In addition to eccentric roof dead and live loads, you can apply axial loads to the top of the wall, simulating loads due to a wall section above. The program also allows point and distributed loads to be applied laterally to the panel strip, giving you the capability to design narrow jambs beside openings.
Each time the program is recalculated, both seismic and wind loads are used to determine service and factored moments and deflections. Results include moment capacity, applied moments at mid-height and at top of wall, actual and allowable axial stress, reinforcement ratio, height/deflection ratio, and height/thickness ratio.
Basic Usage
| • | Wall Data defines the overall wall geometry. Clear Height is the distance the wall panel strip spans from points of lateral support, typically between floor and roof diaphragm. Parapet Height is actually used as a cantilever, applying additional vertical loads and moments to the top of the wall. Wall thickness and rebar size and spacing control the strength of the wall, and are the items you can easily change to achieve a satisfactory design. |
| • | Concrete Weight is used to generate lateral and vertical loads due to the walls own weight. Maximum Deflection ratio is typically a code specified limit on the clear span/deflection allowable. |
| • | Design Data allows you to define the items that specify the load combinations and factors used. Phi is entered to reflect the actual construction quality, and not a calculated value (this procedure is typical of many codes, with Phi being set to 0.72 for uninspected and 0.90 for inspected construction). The Seismic Factors for both wall and parapet can be entered to create the lateral seismic loads to a wall panel strip. If you choose to Include the Parapet in the analysis, the lateral wind and seismic loads acting on the parapet will counteract the lateral loads below. |
| • | Lateral Loads can be applied to the wall in addition to the automatically generated seismic loads. Wind Load analysis is always performed with each recalculation. Point and Uniform Lateral Loads can be applied to the panel strip to represent lateral load contributed from the concrete area above an adjacent opening (e.g: a lintel), and should be entered as unfactored loads (but with seismic factor already used to reduce the actual wall weight). |
| • | Vertical Loads from a roof or floor can be applied to the wall, either concentrically or eccentrically as from a ledger. |
| • | You can Choose Design Methods according to your own personal design theory preference. The methods basically allow you to vary the moment of inertia used to calculate deflections, and the method used to obtain maximum deflections. These choices are based on the design theories the SEAOSC Yellow and Green book methods, the UBC section 2614(i) procedure, and adaptation of ACI equation 9-7 to P-Delta analysis. |
| • | For each method, both wind and seismic load analysis are performed. Applied and generated vertical and lateral loads are factored and used to generate moment diagrams at 250 span increments along the clear height. Depending on the design method chosen, the deflections will then be iterated using P-Delta moments until deflection convergence occurs. |
| • | Because the program: |
| • | Allows fixity at the base of the wall. |
| • | Allows the parapet moments to reduce bending between supports, and |
| • | Allows added lateral point and uniform loads, |
| • | the standard methods of calculating moments at mid-height are not used. Instead, full deflection iteration is performed and all 250 span increments searched for maximum deflection and bending values. Enough detail is provided for the user to review all section analysis values, service load level deflection calculations, and factored load ultimate moment calculations. |
| • | By repeatedly modifying wall thickness and rebar size and spacing, you can quickly generate an economical wall panel strip design to conform to deflection limits, strength capacity, allowable axial stress, and acceptable reinforcing percentages. |
| • | When your design is complete, Print or Save the data from your calculation, Reset the calcsheet to begin another wall design, or use the Access Menu to use another program. |
Unique Features
| • | By supplying six different design methods, virtually all recognized design methods are available for use. |
| • | The actual moment and deflection of the wall is calculated by going through a series of iterations as the wall increasingly deflects laterally. The analysis is performed for 250 points along the wall's span. |
| • | Both wind load and seismic loads are evaluated side by side for quick determination of governing cases. |
| • | User may specify Phi factor to represent different special inspection conditions. |
| • | Program computes both service load deflection and factored moments. |
| • | Assumptions & Limitations |
| • | For lateral design of jamb strips or piers between openings, the user can determine the pro-rated lateral load on the strip of wall by multiplying the seismic factor by the ratio:(Tributary Load/Actual Load) * Code Specified Seismic Factor |
Example
The data entry for this example is shown in the screen captures that accompany the Data Entry Tabs and Results & Graphics Tabs sections to follow.
Data Entry Tabs
This set of tabs provides entries for all input in this calculation. While you are entering data and switching between these tabs you can view the desired resulting information on the tabs on the right-hand side of the screen (calculated values, sketches, diagrams, etc.). A recalculation is performed after any entry data is changed. After each data entry you can view the results on the right-hand set of tabs.
General Tab
Clear Height
Enter the distance between lateral supports for the wall. This is typically between the floor slab and attached floor and/or roof diaphragm.
Parapet Height
This height is an extension of the wall above the top support, and will be treated as a cantilever when lateral seismic and wind loads are applied. This will tend to reduce the moment and deflection between supports by applying an opposite concentrated moment at the top support.
Thickness
Wall thickness to be used in design analysis. This thickness will be used to calculate wall weight for vertical and lateral loads. When there are recessed reveals in the wall for architectural treatment, enter the gross thickness here and modify the reinforcing depth to center the rebar in the net panel thickness.
Bar Size
Enter the rebar size for vertical bars.
Bar Spacing
This indicates the horizontal spacing of the vertical reinforcement entered above.
Bar Depth
Enter the depth to the reinforcing steel. This depth will be used to determine moment capacity and moment of inertia.
Analysis Method
In this section, the user specifies one of six design methods to be used throughout the calculation.
| • | 1989 UBC 2614(i) Exact, Non-Iterated This selection follows the UBC section 2614(i) method almost exactly for calculating deflections and moments. The method is non-iterative; the wall deflection used for P-Delta is calculated as the maximum deflection of the wall when it reaches failure. When we say follows almost exactly, we mean that the code does not mention that the maximum moment is never at the wall mid-height , doesn't consider partial length, moment, or point lateral loads, nor does it consider base fixity. This method is the formal code adaptation of the Green Book published by the Structural Engineers Association of Southern California, and was the result of an extensive testing program. This method goes beyond the UBC simplifications to include partial length lateral loads, lateral point loads, and any degree of base fixity. |
| • | b This method is the same as above EXCEPT that deflections are iterated to calculate maximum wall deflections and moments. This is the most common of the six methods used. |
| • | ACI Eq. 9-7 Iterate This method uses ACI equation 9-7 to calculate the moment of inertia for the entire wall. Starting with a deflection due only to lateral wind or seismic on the wall, deflections are repeatedly iterated and the increased moment due to P-Delta effects added to create still greater moments. |
| • | ACI Eq. 9-7 Mx. Defl. This method uses ACI equation 9-7 to calculate moment of inertia, but uses a deflection that would result if the wall were about to fail from applied uniform loads. This yields the maximum possible deflection that could ever occur in the wall, which is then used to calculate a P-Delta moment. |
| • | Using ICR Full Height Iterate This method is very conservative, using only ICRACKED for deflection calculations. Starting with a deflection due only to lateral wind or seismic on the wall, deflections are repeatedly iterated and the increased moment due to P-Delta effects added to create still greater moments. |
| • | Using ICR Full Height Max. Defl. This method uses ICRACKED for the entire wall and uses a deflection that would result if the wall were about to fail from applied uniform loads. This yields the maximum possible deflection that could ever occur in the wall. This is the most conservative method of the five, and results in highly reinforced walls. |
Adjust Moment when Thickness/2 <> Bar Depth
This flag tells the software whether to decrease the moment capacity of the wall section by the internal moment produced when the rebar is not at the center of the wall. This is not common but some engineers do prefer to take this into consideration.
Normally the allowable moment would be calculated as:
Mn= As:eff Fy(d-a/2)
When this flag is checked then:
Mn= As:eff Fy(d-a/2) - Pu (WallThk/2-Bar Depth)
f'c
Enter the 28 day compressive strength of concrete to be used.
Fy
Enter the allowable yield stress of the reinforcing to be used.
Phi
The user can enter a value for Phi (capacity reduction factor) for design. Typically .9 is used for inspected construction, 0.72 for uninspected. Most codes now do not allow uninspected values.
Concrete Weight
Enter the concrete density to be used for calculation of vertical and seismic loads.
Minimum Vertical Steel Percentage
Specify the minimum allowable percentage of vertical reinforcing for the wall. This will be used to determine the Maximum Vertical Spacing.
Minimum Horizontal Steel Percentage
Specify the minimum allowable percentage of horizontal reinforcing for the wall. This will be used to determine the Maximum Vertical Spacing.
Strip Width Used for Analysis
This does an analysis using a vertical "Strip" of wall that is used to carry the vertical and lateral loads. By default this strip is 12" wide. If you have a larger width of wall, perhaps next to a door opening that is 18" wide, you can enter that dimension in here. The program will divided the applied point vertical and lateral loads over this distance.
Minimum Deflection Ratio
This is the minimum allowable ratio of Clear Height/Service Load Deflection.
Loads / Vertical Loads Tab
Uniform Loads
This represents the vertical load applied to the wall in addition to wall weight, and will be applied at the eccentricity from the wall centerline as specified. When using an eccentricity it will always be additive to the moment between supports.
Concentric Loads
This represents the vertical load applied to the wall in addition to wall weight. The program will apply it at the wall centerline, assuming no eccentricity. This load input is supplied in cases where significant load is being supported by the wall.
Combine Live Load with Short Term
The designer must specify whether the applied live load should be combined with the dead load when evaluating the design. Typically when wind load governs it should be included.
Moment of Inertia Magnifiers
These items are rarely used. To explain their purpose picture a tilt-up wall panel with a tall large opening. The jamb width is 24" for 3/4 of the walls height BUT the top 1/4 will be stiffened by the large concrete area above the opening.
By examination it is obvious that the jamb strip will be slightly stiffer because of this effect. When you would like to see the effect a higher moment of inertia (stiffer) jamb strip would have on the calculated P-Delta moments you can enter a value here to be applied DIRECTLY to the calculated effective moment of inertia of the wall strip being used.
Loads / Lateral Loads Tab
Wall Seismic Factor
Enter the seismic factor to be applied to the wall weight for lateral loading. If you have calculated a seismic factor from the 1997 UBC or IBC that is an "Ultimate" value divide it by 1.4 before entering it here to get it to a service load level.
Parapet Seismic Factor
Enter the seismic factor to be applied to the parapet weight for lateral loading. If you have calculated a seismic factor from the 1997 UBC or IBC that is an "Ultimate" value divide it by 1.4 before entering it here to get it to a service load level.
Wind Load
Enter the wind load in PSF that should be applied to the wall.
Point lateral Load
This load is applied to the 12" wide strip of wall in addition to the lateral load due to wind or seismic forces. It should be entered AFTER APPLYING A SEISMIC FACTOR. This additional lateral load is intended to enable the user to model a section of wall or jamb strip when additional loads are applied to it.
For example, due to an adjacent lintel cast integrally with the wall which spans vertically between roof and a horizontal bond beam at the head of the opening.
This load is factored using ACI factoring for wind and seismic loads, depending upon your entry for Type: Wind/Seismic.
....height
Enter the distance from the bottom of the wall to the point of application of the concentrated point load.
....load type : Seismic/Wind
This specifies whether this added load is due to seismic or wind forces. It is needed so that the ACI load factors can include the additional 1.1" factor for seismic forces.
Uniform Lateral Load
This load Is applied to the analysis of wall in addition to the lateral load due to wind or seismic forces. It should be entered AFTER APPLYING A SEISMIC FACTOR, if this is the case. This additional lateral load is intended to enable the user to model a section of wall or jamb strip when additional loads are applied to it, for example due to a horizontally spanning lintel cast integrally with the wall.
Distance to Top
Enter the distance from the bottom of the wall to the upper end of the uniform lateral load. Please be sure to limit this input to a maximum of Clear Height, as the program cannot apply this load above the top support.
Distance to Bottom
Enter the distance from the bottom of the wall to the start of the uniform lateral load.
...Load Type : Seismic/Wind
This specifies whether this added partial length uniform load is due to seismic or wind forces, needed so that the ACI load factors can include the additional 1.1 needed for seismic forces.
Use Lateral Parapet Weight ?
This YES/NO flag specifies whether the parapet lateral wind and seismic load should be used. Answering YES will generate moments at the top of the wall that will decrease the maximum moments between supports.
ACI Factors
This tab specifies the load factors to be used by the program when calculation the factored dead, live, and short term loads to be used in the internal load combinations for determining Mu for the wall.
Results & Graphics Tabs
This set of tabs provides the calculated values resulting from your input on the "Data Entry Tabs". Because a recalculation is performed with each data entry, the information on these tabs always reflects the accurate and current results, problem sketch, or stress/deflection diagram.
Results / Summary Tab
Factored Load Bending Analysis
The results here are the maximum governing moments in the wall panel strip after an iterated P-Delta calculation is performed to include the effect of additional moments induced from the lateral bending of the wall.
Maximum Iterated Moment
Using the design method specified, the factored loads are applied to the wall and deflections used to calculate maximum moments due to bending from the seismic or wind loads, added lateral loads, and P-Delta moments. This value is the Maximum Moment from P-Delta Analysis
Moment Capacity : Mn * Phi
This wall capacity is calculated using wall thickness, reinforcing, and includes the effect of axial load to increase the effective area of tension reinforcement. Since axial load can vary between seismic and live load conditions, the ultimate moment capacity must be calculated for both cases.
Service Load Deflection Analysis
The results here use service loads applied to the wall in an iterative P-Delta analysis until deflection convergence is reached where the moment is no longer increasing.
Maximum Iterated Deflection
This is the maximum calculated wall panel deflection due to service loads for the design method specified. A method that calculates deflections at the moment capacity of the wall will give far greater deflections than for an iterated solution.
Deflection Limit
This is the maximum allowable wall panel deflection calculated by entering the user defined "Max. Defl. Ratio" times the clear span of the wall.
Mn * Phi : Moment Capacity
The capacity of the wall for seismic and wind conditions is shown. These values are different because of the different components of vertical loads that contribute to design strength.
Applied Mu @ Mid-Span & Top of Wall
This is a breakdown of the four calculated ultimate moments in the wall panel. Moments are calculated at the top of the wall due to eccentric vertical loads and lateral parapet loads and also at the mid-span for both wind and seismic loadings.
Fa:Actual
This stress equals the vertical dead and live loads above mid-height. These loads are divided by Wall Thickness * 12 inches. For the UBC method, this stress should be limited to 0.04f'c.
Fa:Allowable
For the UBC method, the allowable axial stress is limited to 0.04f'c. This value will not apply when the other methods are being used.
Actual As %
When the UBC method is used, the maximum allowable steel percentage is limited to 0.6 times the balanced percentage.
Results / Wall Analysis Tab
This tab lists the results for the factored load moment analysis and the service load deflection analysis.
Basic Defl. & Deflection w/o P-Delta
This is the calculation of wall deflections and moments without any moment magnification from P-Delta effects. Only lateral seismic load, applied lateral load, and moments due to axial load eccentricity are applied in using a standard beam analysis.
Moment in excess of Mcr
This value is the moment in excess of Mcracked (which is the moment capacity of the wall when cracking in the tension region starts). This excess value is used in the calculation of the added deflections.
Max P-Delta Deflection & P-Delta Moment
This is the maximum calculated deflection of the wall after iterating P-Delta effects until there is no further increase in moment.
Maximum Allowable Bar Spacing
These spacing values are the result of applying the "Min. Steel %" entered on the "General" tab to the wall thickness.
Parapet Bar Spacing
This is the maximum required spacing of the bar size you specified for the wall when examining the moment at the top of the wall due to wind or seismic loads on the parapet.
Results / Analysis Data Tab
This tab shows various calculated values that are used in the wall analysis.
E
The modulus of elasticity for concrete is calculated as:
Ec = 57,000 * f'c½
n
This is the ratio of Steel/Concrete elastic modulus. See later in this section for formula used to calculate "E".
Ht / Thickness Ratio
This calculated value is a commonly referenced value that designers use to establish a panel's thickness. It is equal to the Clear Height/Wall Thickness.
S-gross
Gross section modulus for 12" of wall width:
12" * (Wall Thickness)2 / 6
Fr
The modulus of rupture is calculated by: Fr = 5 * f'c½
Mcr
The moment capacity of the gross wall section equals the gross section modulus times the modulus of rupture.
Rho Balanced
This represents the balanced steel area required for simultaneous steel yield and 0.003 in concrete strain. This value will be used to calculate the maximum allowable steel percentage by the UBC method.
As (eff)
The effective area of steel used to calculate moment capacity and section properties is listed here. The area of steel reinforcing is increased to take into account the effect of compression on the section.
a
This is the typical ACI equation for determining the depth of the equivalent compressive stress block used for analysis.
c
This is the true compressive stress block depth calculated from the strain compatibility equations, letting concrete strain = .003 in and steel strain equals yield strain.
I-gross
Gross moment of inertia for 12" of wall width:
12" * (Wall Thickness)3 / 12
I-cracked
The moment of inertia for 12" of wall width, considering a Cracked Section is taken as :
Icr = n * As(eff) * (d-c)2 + (4 * c3)
I-effective (Used for ACI methods only)
By using ACI equation 9-7 and the unfactored simple span and P-Delta applied moment, the effective moment of inertia to be used in calculating the wall deflections is obtained. When iteration is specified, this moment of inertia will converge closer to ICRACKED as the wall increasingly deflects outward. When deflection at moment strength is specified, Mn is used to calculate IEFFECTIVE.
Phi
This capacity reduction factor is applied to the calculated moment capacity to take into account such factors as quality control, use, and design/analysis assumptions. This value is a restatement of the Phi value entered under the sub-section Design Data.
Mn
This is the calculated maximum moment capacity of the section whose values for allowable stresses, reinforcing size and spacing, and effective area of steel.
Results / Additional Values Tab
Sketch Tab
This tab provides a sketch of the beam with loads and resulting values shown. Using the [Print Sketch] button will print the sketch in large scale on a single sheet of paper.
Printing Tab
This tab allows you to control which areas of the calculation to print. Checking a box will signal that the information described by the item will be printed. However, if there is no information in for a particular selection it will not be printed. So these checkboxes are best described as "If this particular area of the calculations contains data then print it".
Sample Printout
