The following worked examples are in a PDF file format. Please note that the publications use table values and rounding while the program answers are based on formulas and are therefore exact, so the publication answers will be close, but may not match exactly. Please note that the publications use rounding while the program answers are based on formulas and are therefore exact, so the publication answers will be close, but may not match exactly. Please note that the publication uses rounding while the program answers are based on formulas and are therefore exact, so the publication answers will be close, but may not match exactly. Also the publication properties and forces are based on per foot of wall while the program is based on the design strip width 24" in the example , so you need to multiple the publication's results by 2. The program can perform 4 calculations side by side.
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Minimum Vertical Reinforcement Tilt-Up Wall Structural Analysis Applied loads Maximum wall forces Tension-controlled verification Analysis and Design of the Section between the Design Strips Horizontal Reinforcement Design Results Comparison and Conclusions Comparison of Wall Modeling Methods Tilt-up Wall Stiffness Reduction Comparison of Load Type Effects Cracked Moment of Inertia Calculation Methods Note: reference example started with a thickness of 6.
Assumed vertical reinforcement: 7 6 single layer for the left leg design strip 7 6 single layer for the right leg design strip Solution The effect of openings on out-of-plane bending in tilt-up panels can be approximated in hand calculations by a simple, one-dimensional strip analysis that provides accuracy and economy for most designs.
Where openings occur, the entire lateral and axial load, including self-weight above the critical section, is distributed to supporting legs or design strips at each side of the opening sometimes referred to as wall piers.
ACI This limit is not mandated by ACI , but is included as a practical guideline where the opening width is less than one-half the clear vertical span. In most cases the tributary width for loads can be taken as the width of the strip plus one-half the width of adjacent openings. Tilt-up design strips should have constant properties for the full height and the reinforcement should not be cut off just above or below the opening. Thickened vertical or horizontal sections can be introduced within the panel where openings are large or where there are deep recesses on the exterior face.
Some conditions may require ties around all vertical reinforcement bars in a vertical pilaster for the full height of the tilt-up panel. Minimum Vertical Reinforcement Av ,vertical 3. ACI 7. The same provisions are presented in ACI but reorganized in different chapters and in slightly revised terminology.
Tilt-Up Wall Structural Analysis 3. Applied loads The tributary width for loads can be taken as the width of the strip plus one-half the width of adjacent openings. Maximum wall forces The calculation of maximum factored wall forces in accordance with Tension-controlled verification ACI ACI Eq.
Tilt-Up Wall Shear Stress Check In-plane shear is not evaluated since in-plane shear forces are not applied in this example. Out-of-plane shear due to lateral load should be checked against the shear capacity of the wall.
By inspection of the maximum shear forces f, it can be determined that the maximum shear force is under 5 kip. The wall left leg the weakest section has a shear capacity approximately 50 kip and no detailed calculations are required by engineering judgement. See figure 6 for detailed shear force diagram 8. Additional reinforcement requirements are outlined in ACI It uses a graphical interface that enables the user to easily generate complex wall models.
The wall is idealized as a mesh of rectangular plate elements and straight line stiffener elements. Walls of irregular geometry are idealized to conform to geometry with rectangular boundaries.
Plate and stiffener properties can vary from one element to another but are assumed by the program to be uniform within each element. Six degrees of freedom exist at each node: three translations and three rotations relating to the three Cartesian axes. An external load can exist in the direction of each of the degrees of freedom. Sufficient number of nodal degrees of freedom should be restrained in order to achieve stability of the model.
The program assembles the global stiffness matrix and load vectors for the finite element model. Then, it solves the equilibrium equations to obtain deflections and rotations at each node. Finally, the program calculates the internal forces and internal moments in each element. In spWall, the required flexural reinforcement is computed based on the selected design standard ACI is used in this example , and the user can specify one or two layers of wall reinforcement.
In stiffeners and boundary elements, spWall calculates the required shear and torsion steel reinforcement. Wall concrete strength in-plane and out-of-plane is calculated for the applied loads and compared with the code permissible shear capacity.
For illustration and comparison purposes, the following figures provide a sample of the input modules and results obtained from an spWall model created for the reinforced concrete wall in this example. Design Results Comparison and Conclusions The model shown above was created in spWall taking into account the ACI provisions alternative design method and ACI recommendations regarding the analysis and design of tilt-up wall panels with openings in order to match the results presented in the reference.
In this model the left and right design strips are modeled such that the entire lateral and axial load, including self-weight above the critical section, are distributed to the two strips at each side of the opening. The tributary width for loads was taken as the width of the strip plus one-half the width of the opening. The following table shows the comparison between hand and reference results with spWall model results. Dz,ultimate in. Comparison of Wall Modeling Methods ACI provides the alternative design method as a simple and accurate option for analysis and design of simple walls meeting the method conditions.
Other methods such as finite element analysis can be used to address panels not meeting the numerous limitations of the alternative design method cantilevered walls, variable thickness and width, walls with openings, non-standard boundary conditions, walls with high compressive loads, in-plane lateral loads, non-standard concentrated load position from attachments of piping, racking etc.
The exact wall geometry and applied loads were modeled using spWall engineering software to investigate the differences between the simplified approximate method and the finite element method. For illustration and comparison purposes, the following figures provide a sample of the results obtained from an spWall model created for the reinforced concrete wall in this example using exact wall geometry and applied loads. It is very important to consider the wind load applied to the door opening and how it must be considered and applied in the model based on the door boundary condition.
In this example, the door support reactions are assumed along the left and right side of the door opening. Load is modeled as an equivalent uniform line load applied along the right edge of the left leg and the left side of the right leg. The complete model, as shown in the following figure, displays a complete view of the torsional moment distribution indicating areas of torsional stress concentration at opening edges.
This corresponds to the additional reinforcement requirements outlined in ACI Tilt-up Wall Stiffness Reduction In column and wall analysis, section properties shall be determined by taking into account the influence of axial loads, the presence of cracked regions along the length of the member, and the effect of load duration creep effects.
ACI permits the use of reduced moment of inertia values of 0. Cracking coefficients for out-of- plane bending and torsion and in-plane axial and shear stiffness can be entered for plate elements. Because the values of the cracking coefficients can have a large effect on the analysis and design results, the user must take care in selecting values that best represent the state of cracking at the particular loading stage. Cracking coefficients are greater than 0 and less than 1.
At ultimate loads, a wall is normally in a highly cracked state. A factor 0. It is intended to account for variations in material properties and workmanship.
This reduction factor in bending stiffness should be incorporated by all other alternate design methods to comply with the requirements of ACI as ACI committee stated. At service loads, a wall may or may not be in a highly cracked state.
Based on the previous discussion, the ratio between Icr and Ig including the reduction factor 0. In this example, Icr and Ig were found to be equal to in. Thus, the out-of-plane cracking coefficient for ultimate load combinations for the left leg can be found as follows: 0.
That means the left leg section is uncracked and the cracking coefficient can be taken equal to 1. Comparison of Load Type Effects During the process of analyzing the tilt-up wall panels, the effect of load type on the wall behavior at the critical section was investigated in terms of out-of-plane deflection at service and ultimate level, required axial capacity, and required out-of-plane moment capacity. However, modeling point loads to reflect actual behavior and stress distribution is beneficial in cases where there are openings, variable thicknesses, changes in geometry, intermediate supports, and other variations from a simply supported wall with constant width and thickness.
Cracked Moment of Inertia Calculation Methods The cracked moment of inertia for tilt-up wall panels can be calculated using different ACI provisions. The following shows the commonly used provisions to calculate the cracked moment of inertia: 1. Using the moment magnification procedure for nonsway frames: 0. This is intended to best match the reference approach using the alternative design method to analyze and design the tilt-up wall panels. The variation in the magnitude of Icr has a significant effect on the analysis results and specifically the wall moments and displacement.
In the following table a comparison of the resulting values based on variation of the I cr is summarized for information. The Dz,ultimate, values are calculated however are not used in any calculations and the deflection limits are given for Dz,service only. The range of the cracking coefficient and the cracked moment of inertia values vary widely based on the equation used.
In this example the spWall model utilized the value of the cracked moment of inertia using the alternative design method equation Eq. Tilt-Up Wall Reinforcement and Cracking Coefficient Optimization In the previous models, the cracking coefficients were selected based on the area of steel used by the reference and equation with the reduction factor to best match the reference.
The reinforcement selected in the reference is conservative and results in a higher cracking moment of inertia leading to lower values of reinforcement to be obtained by spWall.
To explore this topic in further details, the left leg design strip model results will be used.
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A publication of the Tilt-Up Concrete Association. In part, that is intentional. It allows ample time for review, dissenting opinions, and for resolution of differences. It is also due to the fact that committees meet but twice a year and the industry experts staffing those committees are volunteers with regular full-time jobs. The brand new, first-ever, ACI