Struktur Rabgka Bangunan Bangunan Baja _13776666.ppt
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This document provides an overview of the design of columns including: 1. It describes different types of columns and their reinforcement including tied and spiral columns. 2. It discusses the behavior and strength of short columns and how an elastic analysis is not suitable due to creep and shrinkage of concrete over time. 3. It outlines the nominal capacity, reinforcement requirements, and design procedure for columns under concentric axial loads including load combinations, strength requirements, and expressions to calculate the required reinforcement.
Struktur Rabgka Bangunan Bangunan Baja _13776666.ppt
- 1. Lecture - Design of Columns CEN 347
- 3. Introduction
- 16. Types of Column
- 19. Types of Column
- 20. Types of Column
- 22. Strength of short or Slender Columns
- 23. Strength of short or Slender Columns
- 24. Strength of short or Slender Columns
- 51. 0.70 0.65
- 56. Analysis and Design of “Short” Columns General Information Vertical Structural members Transmits axial compressive loads with or without moment transmit loads from the floor & roof to the foundation Column:
- 57. Analysis and Design of “Short” Columns General Information Column:
- 58. Analysis and Design of “Short” Columns Tie spacing h (except for seismic) tie support long bars (reduce buckling) ties provide negligible restraint to lateral expose of core Tie Columns - 95% of all columns in buildings are tied ?
- 59. Analysis and Design of “Short” Columns Pitch = 1.375 in. to 3.375 in. spiral restrains lateral (Poisson’s effect) axial load delays failure (ductile) Spiral Columns
- 60. Analysis and Design of “Short” Columns Elastic Behavior Concrete creeps and shrinks, therefore we can not calculate the stresses in the steel and concrete due to “acting” loads using an elastic analysis.
- 61. Analysis and Design of “Short” Columns Elastic Behavior An elastic analysis using the transformed section method would be: st c c nA A P f ? ? For concentrated load, P uniform stress over section c s nf f ? area steel area concrete / s c c s ? ? ? A A E E n
- 62. Analysis and Design of “Short” Columns Elastic Behavior An elastic analysis does not work because creep and shrinkage affect the acting concrete compression strain as follows:
- 63. Analysis and Design of “Short” Columns Elastic Behavior The change in concrete strain with respect to time will effect the concrete and steel stresses as follows: Concrete stress Steel stress
- 64. Analysis and Design of “Short” Columns Elastic Behavior Therefore, we are not able to calculate the real stresses in the reinforced concrete column under acting loads over time. As a result, an “allowable stress” design procedure using an elastic analysis was found to be unacceptable. Reinforced concrete columns have been designed by a “strength” method since the 1940’s. Creep and shrinkage do not affect the strength of the member. Note:
- 65. Behavior, Nominal Capacity and Design under concentric Axial loads Initial Behavior up to Nominal Load - Tied and spiral columns. 1.
- 66. Behavior, Nominal Capacity and Design under concentric Axial loads ? ? st y st g c 0 * 85 . 0 A f A A f P ? ? ? Factor due to less than ideal consolidation and curing conditions for column as compared to a cylinder. It is not related to Whitney’s stress block. Let Ag = Gross Area = b*h Ast = area of long steel fc =concrete compressive strength fy = steel yield strength
- 67. Behavior, Nominal Capacity and Design under concentric Axial loads Maximum Nominal Capacity for Design Pn (max) 2. ? ? ? 0 max n rP P ? r = Reduction factor to account for accidents/bending r = 0.80 ( tied ) r = 0.85 ( spiral )
- 68. Behavior, Nominal Capacity and Design under concentric Axial loads Reinforcement Requirements (Longitudinal Steel Ast) 3. g st g A A ? ? - ACI Code 10.9.1 requires Let 08 . 0 01 . 0 g ? ? ?
- 69. Behavior, Nominal Capacity and Design under concentric Axial loads 3. - Minimum # of Bars ACI Code 10.9.2 min. of 6 bars in circular arrangement w/min. spiral reinforcement. min. of 4 bars in rectangular arrangement Reinforcement Requirements (Longitudinal Steel Ast)
- 70. Behavior, Nominal Capacity and Design under concentric Axial loads 3. ACI Code 7.10.5 ? ? ? Reinforcement Requirements (Lateral Ties) # 3 bar if longitudinal bar # 10 bar # 4 bar if longitudinal bar # 11 bar # 4 bar if longitudinal bars are bundled ? ? size
- 71. Behavior, Nominal Capacity and Design under concentric Axial loads 3. Reinforcement Requirements (Lateral Ties) 16 db ( db for longitudinal bars ) 48 db ( db for tie bar ) least lateral dimension of column ? Vertical spacing: ? ? s s s
- 72. Behavior, Nominal Capacity and Design under concentric Axial loads 3. Reinforcement Requirements (Lateral Ties) Vertical spacing: Arrangement, At least every other longitudinal bar shall have lateral support from the corner of a tie with an included angle 135o. No longitudinal bar shall be more than 6 in. clear on either side from “support” bar. 1.) 2.) ?
- 73. Behavior, Nominal Capacity and Design under concentric Axial loads Examples of lateral ties.
- 74. Behavior, Nominal Capacity and Design under concentric Axial loads ACI Code 7.10.4 ? Reinforcement Requirements (Spirals ) 3/8 “ f (3/8” f smooth bar, #3 bar dll or wll wire) - size - clear spacing: ? 1 in. 3 in. ?
- 75. Behavior, Nominal Capacity and Design under concentric Axial loads Reinforcement Requirements (Spiral) s D A c sp s 4 Core of Volume Spiral of Volume ? ? ? Spiral Reinforcement Ratio, ?s ? ? ? ? ? ? ? ? ? s D D A 4 1 : from 2 c c sp s ? ? ?
- 76. Behavior, Nominal Capacity and Design under concentric Axial loads Reinforcement Requirements (Spiral) ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? y c c g s * 1 f f A A ? ACI Eqn. 10-6 ? ? psi 60,000 steel spiral of strength yield center) (center to steel spiral of tch spacing(pi spiral of edge outside to edge outside : diameter core 4 area core ent reinforcem spiral of area sectional - cross y c 2 c c sp ? ? ? ? ? ? ? f s D D A A ? where
- 77. Behavior, Nominal Capacity and Design under concentric Axial loads 4. Design for Concentric Axial Loads (a) Load Combination ? ? w DL u w LL DL u LL DL u 3 . 1 9 . 0 7 . 1 7 . 1 4 . 1 * 75 . 0 7 . 1 4 . 1 P P P P P P P P P P ? ? ? ? ? ? ? Gravity: Gravity + Wind: and Etc.
- 78. Behavior, Nominal Capacity and Design under concentric Axial loads 4. Design for Concentric Axial Loads (b) General Strength Requirement u n P P ? f f = 0.7 for tied columns f = 0.75 for spiral columns where,
- 79. Behavior, Nominal Capacity and Design under concentric Axial loads 4. Design for Concentric Axial Loads (c) Expression for Design ? ? 08 . 0 0.01 Code ACI g g st g ? ? ? ? ? A A defined:
- 80. Behavior, Nominal Capacity and Design under concentric Axial loads ? ? ? ? u c y st c g n steel 85 . 0 concrete 85 . 0 P f f A f A r P ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? f f or ? ? ? ? u c y g c g n 85 . 0 85 . 0 P f f f A r P ? ? ? ? ? f f
- 81. Behavior, Nominal Capacity and Design under concentric Axial loads ? ? ? ? 85 . 0 85 . 0 c y g c u g f f f r P A ? ? ? ? f * when ?g is known or assumed: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? c g u c y st 85 . 0 85 . 0 1 f A r P f f A f * when Ag is known or assumed:
- 82. Example: Design tied Column for concentric Axial Load Design tied column for concentric axial load Pdl = 150 k; Pll =300 k; Pw = 50 k fc =4500 psi fy = 60 ksi Design a square column aim for ?g =0.03. Select longitudinal transverse reinforcement.
- 83. Behavior under Combined Bending and Axial Loads Usually moment is represented by axial load times eccentricity, i.e.
- 86. Behavior under Combined Bending and Axial Loads Resultant Forces action at Centroid ( h/2 in this case ) s2 positive is n compressio c s1 n T C C P ? ? ? ? ? ? ? ? Moment about geometric center ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 2 * 2 2 * 2 * 2 s2 c 1 s1 n h d T a h C d h C M
- 90. Behavior under Combined Bending and Axial Loads Interaction Diagram Between Axial Load and Moment ( Failure Envelope ) Concrete crushes before steel yields Steel yields before concrete crushes Note: Any combination of P and M outside the envelope will cause failure.
- 91. Behavior under Combined Bending and Axial Loads Axial Load and Moment Interaction Diagram -General
- 92. Example: Axial Load vs. Moment Interaction Diagram