Column with Axial Load and Bending Moment

Program first computes stresses due to applied load and moments based on gross section properties. After computing the individual stress, the program computes total stress at extreme fibers of each section. It then tries to classify the section as cracked or non cracked.

There are several possible scenarios. In the first scenario, the entire section is in compression. In this case, the section is classified as U (Uncracked). In the second scenario, if there is tension at one of the faces/corner of the section, program compares the stress at the tensile face/corner of the tensile stress limit as specified by the user in the analysis/design parameter. If stress is less than the maximum allowed for tension the section is classified as uncracked. If the total tensile stress is more than the maximum allowed for tension, the section is classified as Cracked.

When a section is classified as class cracked, program computes the crack depth and then recomputes the cracked section properties and total stresses in the cracked section. In this scenario, the program assumes the concrete in a cracked section does not take any tension. Its tension contribution is ignored. In the computed service stresses reports, program reports stresses based on gross transformed area if the maximum tensile stress is less than allowable tension stress. If maximum tensile stress exceeds allowable tension stress, program computes the stresses using the iterative algorithm. Due to the combination of moments about both axes of column cross-section, the cracking line will be rotated at an angle for most biaxial bending cases. Rotation and position of cracking line (zero stress line or neutral axis, NA) can be interpolated from column corner stress. Cracking of column will be stabilizing at an equilibrium position. Cracking algorithm re-computes the position of the crack and subsequent section properties of cracked section.

Cracking algorithm proceeds with assuming the position of crack line and crack depth until it overlaps precisely with the stress line recomputed from column corner stress. Overlapping of assumed NA and re-computed NA, represents the condition of equilibrium of external applied forces and internal forces that are evaluated through a stress calculation. Stress is computed with the general stress formula. Transformed cracked section properties, external forces and moments are considered:

It then reports the computed compressive stress along with hypothetical tensile stress at the tensile face. This tensile stress however, should be ignored as in actual the section has cracked at that point. User has choice to perform stress check using only gross concrete section and /or transformed rebar section properties. User can select this choice in the analysis and design parameter.

Stress at a point of coordinates (x, z) = (P / A) - {[(Mz*Ix + Mx*Ixz) / (Iz*Ix-I²xz)] * x} + {[(Mx*Iz + Mz*Ixz) / (Iz*Ix-I²xz)] * z} If computed compressive stress at equilibrium is greater than allowable compressive stress a flag (asterisk) is issued for that location. Increased deflection associated with cracked section properties will be considered in a p-delta analysis.

Reinforcement Details

Program checks the provided reinforcement against the minimum and maximum reinforcement as per IS 456, 206.5.3.1. The minimum reinforcement is considered as 0.8% of gross concrete area and maximum reinforcement is as 6% of gross concrete sectional area. User can overwrite this minimum reinforcement requirement on the column design tab. In addition to reinforcement area checks, program checks spacing criteria as per clause 304.5.1 from IRC 21-2000. The minimum horizontal distance between bars allowed is the diameter of the largest rebar used. The minimum vertical distance is greater of 12 mm or diameter of the largest diameter. Maximum spacing along the peripheral is 300 mm.