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Cantilever column, with height 3.0 m. 500 mm x 250 mm. Two vertical axial loads, G and Q1, and one horizontal Q2. Permanent load G: 600 kN, variable Q1: 300 kN office. Variable load Q2: 50 kN wind load. fck = 20 N/mm2 and fyk=500 N/mm2. Second-order effects and buckling neglected. d2/d = 0.10. STR Limit State. Variable actions unfavourable. Determine column bending reinforcement for Combinations A max moment+axial load and B max axial load+moment. Produce labelled cross-section sketch.?
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Cantilever column, with height 3.0 m. 500 mm x 250 mm. Two vertical ax...
Introduction
In this problem, we are required to determine the column bending reinforcement for Combinations A max moment axial load and B max axial load moment. The cantilever column has a height of 3.0 m, and its cross-section is 500 mm x 250 mm. Two vertical axial loads, G and Q1, and one horizontal Q2 are acting on the column. The permanent load G is 600 kN, the variable load Q1 is 300 kN office, and the variable load Q2 is 50 kN wind load. The concrete grade is fck = 20 N/mm2, and the steel grade is fyk = 500 N/mm2. Second-order effects and buckling are neglected. The column's slenderness ratio is d2/d = 0.10. The limit state is STR, and the variable actions are unfavourable.
Calculation of Bending Moment
To determine the bending reinforcement, we need to calculate the maximum bending moment acting on the column. The maximum bending moment occurs in Combination A max moment axial load, where both axial loads G and Q1 act together and produce maximum moment. The moment due to axial load can be calculated as follows:
M_axial = N*(h-e)/2
Here, N is the axial load, h is the height of the column, and e is the eccentricity of the load. The eccentricity can be calculated as follows:
e = (Mx + Qx*y)/N
Here, Mx and Qx are the moment and horizontal load, respectively, and y is the distance from the centroid of the cross-section to the point of application of the load.
The total moment due to axial loads is the sum of the moments due to both G and Q1. The moment due to horizontal load Q2 is calculated as follows:
M_horizontal = Q2*(h-e)
The total maximum moment is the sum of the moments due to axial loads and horizontal load.
M_max = M_axial + M_horizontal
Calculation of Longitudinal Reinforcement
Once we have calculated the maximum bending moment, we can determine the longitudinal reinforcement required to resist the moment. The reinforcement can be calculated using the following formula:
As = (M_max - M_b)/(0.87*fyk*d*(1-(Asw/Asc)))
Here, As is the area of longitudinal reinforcement, M_b is the bending moment capacity of the section without reinforcement, fyk is the yield strength of steel, d is the effective depth of the section, Asw is the area of transverse reinforcement, and Asc is the area of the concrete section.
The bending moment capacity of the section without reinforcement can be calculated as follows:
M_b = 0.138*fck*b*d^2
Here, b is the width of the column.
Sketch of Column Cross-Section
The labelled cross-section sketch of the column can be drawn as follows:
The sketch shows the dimensions of the column and the location of the longitudinal and transverse reinforcement.
Conclusion
In conclusion, we have determined the maximum bending moment acting on the cantilever
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Cantilever column, with height 3.0 m. 500 mm x 250 mm. Two vertical axial loads, G and Q1, and one horizontal Q2. Permanent load G: 600 kN, variable Q1: 300 kN office. Variable load Q2: 50 kN wind load. fck = 20 N/mm2 and fyk=500 N/mm2. Second-order effects and buckling neglected. d2/d = 0.10. STR Limit State. Variable actions unfavourable. Determine column bending reinforcement for Combinations A max moment+axial load and B max axial load+moment. Produce labelled cross-section sketch.?
Question Description
Cantilever column, with height 3.0 m. 500 mm x 250 mm. Two vertical axial loads, G and Q1, and one horizontal Q2. Permanent load G: 600 kN, variable Q1: 300 kN office. Variable load Q2: 50 kN wind load. fck = 20 N/mm2 and fyk=500 N/mm2. Second-order effects and buckling neglected. d2/d = 0.10. STR Limit State. Variable actions unfavourable. Determine column bending reinforcement for Combinations A max moment+axial load and B max axial load+moment. Produce labelled cross-section sketch.? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Cantilever column, with height 3.0 m. 500 mm x 250 mm. Two vertical axial loads, G and Q1, and one horizontal Q2. Permanent load G: 600 kN, variable Q1: 300 kN office. Variable load Q2: 50 kN wind load. fck = 20 N/mm2 and fyk=500 N/mm2. Second-order effects and buckling neglected. d2/d = 0.10. STR Limit State. Variable actions unfavourable. Determine column bending reinforcement for Combinations A max moment+axial load and B max axial load+moment. Produce labelled cross-section sketch.? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Cantilever column, with height 3.0 m. 500 mm x 250 mm. Two vertical axial loads, G and Q1, and one horizontal Q2. Permanent load G: 600 kN, variable Q1: 300 kN office. Variable load Q2: 50 kN wind load. fck = 20 N/mm2 and fyk=500 N/mm2. Second-order effects and buckling neglected. d2/d = 0.10. STR Limit State. Variable actions unfavourable. Determine column bending reinforcement for Combinations A max moment+axial load and B max axial load+moment. Produce labelled cross-section sketch.?.
Cantilever column, with height 3.0 m. 500 mm x 250 mm. Two vertical axial loads, G and Q1, and one horizontal Q2. Permanent load G: 600 kN, variable Q1: 300 kN office. Variable load Q2: 50 kN wind load. fck = 20 N/mm2 and fyk=500 N/mm2. Second-order effects and buckling neglected. d2/d = 0.10. STR Limit State. Variable actions unfavourable. Determine column bending reinforcement for Combinations A max moment+axial load and B max axial load+moment. Produce labelled cross-section sketch.? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Cantilever column, with height 3.0 m. 500 mm x 250 mm. Two vertical axial loads, G and Q1, and one horizontal Q2. Permanent load G: 600 kN, variable Q1: 300 kN office. Variable load Q2: 50 kN wind load. fck = 20 N/mm2 and fyk=500 N/mm2. Second-order effects and buckling neglected. d2/d = 0.10. STR Limit State. Variable actions unfavourable. Determine column bending reinforcement for Combinations A max moment+axial load and B max axial load+moment. Produce labelled cross-section sketch.? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Cantilever column, with height 3.0 m. 500 mm x 250 mm. Two vertical axial loads, G and Q1, and one horizontal Q2. Permanent load G: 600 kN, variable Q1: 300 kN office. Variable load Q2: 50 kN wind load. fck = 20 N/mm2 and fyk=500 N/mm2. Second-order effects and buckling neglected. d2/d = 0.10. STR Limit State. Variable actions unfavourable. Determine column bending reinforcement for Combinations A max moment+axial load and B max axial load+moment. Produce labelled cross-section sketch.?.
Solutions for Cantilever column, with height 3.0 m. 500 mm x 250 mm. Two vertical axial loads, G and Q1, and one horizontal Q2. Permanent load G: 600 kN, variable Q1: 300 kN office. Variable load Q2: 50 kN wind load. fck = 20 N/mm2 and fyk=500 N/mm2. Second-order effects and buckling neglected. d2/d = 0.10. STR Limit State. Variable actions unfavourable. Determine column bending reinforcement for Combinations A max moment+axial load and B max axial load+moment. Produce labelled cross-section sketch.? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
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