When we design columns in RCDC some times upper level columns have more reinforcement perhaps due to higher moments in upper storey . How to design columns so that lower storeys have equal or more reinforcement than upper level columns?
Principle used in RCDC for column design is to check the capacity of a section of given size with given reinforcement arrangement against the design-demand. Thus, for a given size of column with specific arrangement of reinforcement (in terms of location and diameter), for given grades of concrete and reinforcement, the P-M curves are generated as 'section capacity' curves. Then for all design load combinations, values of Pu, Mux and Muy (from analysis) are used and after due process for checking of minimum eccentricity, slenderness and other relevant checks, final design values are worked out as Pu-d, Mux-d and Muy-d. Now each value of this Pu-d, Mux-d and Muy-d is checked against capacity available as per the P-M curve envelope.
As mentioned that RCDC uses forces from STAAD analysis, but i observed that RCDC design for the less forces when compare to STAAD analysis results. Generally, we modelled with idealized node, which tends to give higher BM/SF compare to location forces on member between the floor. (1) I would like to understand that how RCDC extract forces from STAAD model w.r.t member length? (2) Do we have to model only in physical modeler to use RCDC? (3) Does crack width check consider diagonal Acr for both between bar & at corner location? (4) Is Acr calculated from longitudinal rebar face? and for circular column does it consider radial clear spacing for Acr derivation?
Please find below our pointwise reply to your queries;
(1) I would like to understand that how RCDC extract forces from STAAD model w.r.t member length?
RCDC reads the Beam end forces from the STAAD file for each of the member and considers the force at the Upper and Lower level. Refer below snip for clarification.
(2) Do we have to model only in physical modeler to use RCDC?
No, a regular Analytical model is read in RCDC and all the elements can be designed in RCDC.
(3) Does crack width check consider diagonal Acr for both between bar & at corner location?
Yes, it does. Refer below explanation on how RCDC on how RCDC computes the equilibrium location of Neutral Axis:
Please refer to adjacent figure, column is of size (B x D), with vertical reinforcement.
The column is subjected to following forces –
P = Axial Force
M-major = Moment about major axis = M @ LX
M-minor = Moment about minor axis = M @ LY
Eccentricity of force along both the axis can be calculated as:
Ex = M-minor/ P
Ey = M-major/ P
For equilibrium of forces acting on the cross-section,it is essential to understand the location of Neutral-axis. From vector forces, it can be easilyfound that effective moment acts at an angle ‘Alpha’ with LX axis.
Tan (Alpha) = M-major/ M-minor
Hence, NA (neutral axis) is perpendicular to this angle.
Neutral axis location is calculated iteratively, based on the principles of equilibrium as below –
Fc (concrete) + Fc (Steel) + Ft (Steel) = P
Mc (concrete) + Mc (Steel) + Mt (Steel) = P * N
The software works on an iterative algorithm, which calculates equilibrium position of neutral axis and establishes the force equilibrium. While performing calculations, stress is assumed to vary linearly from C1 to C2.
For NA-1 condition, stress at C1 is tensile and minimum. For NA-2 condition, stress at C1 is compressive and maximum.
Following are the principles for calculation of section forces –
There are three possible locations of NA -
From above conditions, it is clear that for NA-3, section is un-cracked. For NA-1 and NA-2, following checks are performed before calculating crack-width –
After finding the NA position, and confirming that stresses at C1 and for bar near C2 are within permissible limit, following calculations are performed for calculating crack-width and defining the adequacy –
(4) Is Acr calculated from longitudinal rebar face? and for circular column does it consider radial clear spacing for Acr derivation?
Yes. For circular column, Acr is calculated from the longitudinal rebar face. So acr = cover that is mentioned for the column design as cover in RCDC is the cover to Main reinforcement.