Examination of ACI between and indicates that the main source of inconsistency in determining slenderness effects is the approximation of member stiffness, EI. At that point, the degree of cracking varies along its length. Thus, the stiffness of the member is somewhere between its gross and fully-cracked moment of inertia multiplied by the modulus of elasticity.
Fairly accurate methods exist to estimate the value of EI for a single member, but they are arbitrary for the design of a typical frame when considering the high degree of variability associated with multiple members of varying size, strength, and reinforcement. Therefore, ACI provides the following four equations for approximating member stiffness. Equations 1 and 2 are permitted for use with elastic second order and sway frame moment magnification analysis. Whereas, Equations 3 and 4 are used solely for the moment magnification procedure.
Rather, different values are implicitly included within the provisions. In Equation 1 , the value of 0. Mirza derived this value based on a reliability study. Depending on the method of analysis, ACI uses different values and expressions to estimate the stiffness of a column immediately prior to failure.
Again, the value of 0. That is, it implicitly assumes the cracked moment of inertia, I eff , to be equal to 0. The researchers derived this value based on lateral deflections measured in laboratory test frames Figure 2. Khuntia and Ghosh developed this expression analytically and verified it experimentally. The EI eff used in Equations 3 and 4 is contained in the numerator of each expression.
Committee recommended these expressions as lower end approximations of member stiffness. They were developed using a combination of theoretical load-moment-curvature diagrams, analysis of test frames, and computer simulations. The additional deflections resulting from creep must be accounted for because they will increase second order moments. In both cases, the loads should be from the same load combination.
For all equations, when sustained lateral loads exist e. This point is a major discrepancy and point of confusion amongst designers because it often results in significant differences between procedures.
Since the minimum value of k 1 and k 2 is 0. Let us take k 2 as 1. Thank you for reading We love you, and we will keep working hard for you. Like our Facebook page on www. Would like to ask From chart , why As.
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Lateral load effects on the building are governed by wind forces. Compare the calculated results with the values presented in the Reference and with exact values from spColumn engineering software program from StructurePoint. Factored Axial Loads and Bending Moments Service loads Load Combinations — Factored Loads Determine Slenderness Effects Moment Magnification at Ends of Compression Member Moment Magnification along Length of Compression Member Column Design Forces in the concrete and steel Column Interaction Diagram - spColumn Software Summary and Comparison of Design Results Factored Axial Loads and Bending Moments 1.
Load Combination Reference kip ft-kip ft-kip ft-kip ft-kip Top Bottom 2. ACI 6. Ag 4. Moment Magnification at Ends of Compression Member A detailed calculation for load combinations 2 and 6 is shown below to illustrate the slender column moment magnification procedure.
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