WEEK 9 COLUMN
Learning out comes At the end of this week the student should be able to:
Classify the type of column.(CO1) Calculate the axial load and moment induced in the column.(CO1) Design the column.(CO2) Draw the detailing of the column.(CO2)
Out line of this week presentation Introduction Definition, short and slender column Braced and un-braced column Effective height \End condition of column Analysis Design and detailing.
Introduction ď Ž
ď Ž
. A structural members that carry loads in compression along its length. Most frequently, as in a building, the column is in a vertical position transmitting gravity loads from its top down to its base. Columns are present in other structures as well, such as in bridges, towers, and cranes. Other terms used by both engineers and lay persons to identify a column are pillar, post, and strut.
Definition ď Ž
Any Element can be say as column when the greatest dimension doest not exceed four (4) times the smaller dimension (i.e h ≤ 4 b)
Circular
Rectangular
Square
Definition ď Ž
The size of a column and the position of the reinforcement in it may be affected by the requirements for durability and fire resistance, and these should be considered before the design is commenced
Short columns ď Ž
A short column is one whose length is relatively short in comparison to its cross-sectional dimensions and, when loaded to its extreme, fails by reaching the compressive strength of its material. This is called failure in axial compression.
Slender columns ď Ž
A slender column is one whose length is large in comparison to its cross-sectional dimensions and, when loaded to its extreme, fails by buckling (abruptly bending) out of its straight-line shape and suddenly collapsing before reaching the compressive strength of its material.
Column Classification
Effective height of a column
Effective height of a column
Effective height of a column
Column Classification
Column Classification
Column Classification
Example: Column Classification
Example: Column Classification
Example: Column Classification
ANALYSIS –AXIAL LOAD W2
N
W1
L1
L2
W4 Z L4
X
L3 Y
N = W1L1/2 + W2L2/2 + W3L3/2 + W4L4/2
W3
ANALYSIS –MOMENT BRACED COLUMN
ANALYSIS – MOMENT BRACED COLUMN MIDDLE COLUMN FEM FOR BEAM AB = 163.5 kNm BEAM BC = 55.2 kNm THE BALANCE MOMENT
= 163.5 -55.2 = 108.3 kNm MOMENT FOR TOP OF COLUMN = (4.57/(4.0 + 4.57 + 3.75 +3.75) ) x 108.3 = 30.8 kNm MOMENT FOR BOTTOM OF COLUMN = (4.00/(4.0 + 4.57 + 3.75 +3.75) ) x 108.3 = 27.0 kNm
ANALYSIS MOMENT UNBRACED COLUMN M2 1.5 m
M1 2.0 m
2.0 m
2.5 m
3.0 m
Additional moments induced by deflection at ULS M add = N a
M add = N x(1/2000) x(le/b’)2
Braced
Un-braced
Columns where le/h exceeds 20, bent about their major axis In these cases the section should be designed as biaxially bent, with zero initial moment about the minor axis
Columns bent about their major axis Where the ratio of the longer to the shorter side equals three or more,(h/b=>3) the section should be designed as biaxially bent with zero initial moment about the minor axis
Slender columns bent about a single axis (major or minor)
Provided the ratio of the length of the longer side to that of the shorter side is less than three (h/b<3) and that, for columns bent about their major axis, le/h does not exceed 20,
Slender columns bent about both axes ď Ž
Where the bending is significant about both axes, additional moments are calculated from equations 32 to 35 for both directions of bending. For each direction, bâ&#x20AC;&#x2122; in Table 3.21 should be taken as h, the dimension of the column in the plane of bending considered. These additional moments are then combined with the appropriate initial moments to obtain total design moments in the two directions. The critical section is then designed to withstand the design ultimate axial load, N, plus the total design moments in the two directions.
Design of column section for ULS Design charts for symmetricallyreinforced columns Design charts for symmetricallyreinforced columns are given in BS 8110-3.
ď Ž
Biaxial bending
Reinforcement in column The longitudinal reinforcement should not exceed the following amounts, calculated as percentages of the gross crosssectional area of the concrete: a) vertically-cast columns: 6 %; b) horizontally-cast columns: 8 %; c) laps in vertically- or horizontally-cast columns: 10 %.
Links for containment of beam or column compression reinforcement. When part or all of the main reinforcement is required to resist compression, links or ties, at least onequarter the size of the largest compression bar or 6 mm, whichever is the greater, should be provided at a maximum spacing of 12 times the size of the smallest compression bar.
Arrangement of links for containment of beam or column compression reinforcement
Example on the column