Column Design: Design Calculations

COLUMN DESIGN CALCULATIONS
Project Name	:	Unassigned
Client Name	:	Unassigned
Engineer Name	:	Unassigned
Design File	:	D:\Bentley\Common data\Bentley Communities\ACI\ACI_English_validation Sheet\2014_English\Column_regular\STAAD file\Sample Model_R0-Column-1.rcdx
Analysis File	:	D:\Bentley\Common data\Bentley Communities\ACI\ACI_English_validation Sheet\2014_English\Column_regular\STAAD file\Sample Model_R0.STD
Analysis Last Modified	:	2/21/2023 11:18:20 AM

Definitions Of Terms:

	All forces in units 'kip' and 'ft'
	All reinforcement details like area, spacing in 'in'
	Neutral axis angle for resultant design moment is with respect to local major axis.

1	βdns	=	Ratio to account for reduction of stiffness of columns due to sustained axial loads
2	δns	=	Moment magnification factor for frames not braced against sidesway
3	Δo	=	First-order relative deflection between the top and bottom of the story due to Vu in 'kip'
4	∑Pu	=	Total factored vertical load in 'kip'. (Clause 6.6.4.4)
5	δu	=	Design displacement in 'in'
6	λ	=	Modification factor reflecting the reduced mechanical properties Of concrete
7	ac	=	Coefficient defining the relative contribution Of concrete strength To nominal wall shear strength
8	Ach	=	Cross-sectional area of a structural member measured to the outside edges of transverse reinforcement in 'in²'
9	Acv	=	Gross area of concrete section bounded by web thickness And length of section in the direction Of shear force considered in 'in²'
10	Aj	=	Effective cross-sectional area within a joint In a plane parallel To plane Of reinforcement generating shear In the joint in 'in²'
11	As	=	Area Of non-prestressed longitudinal tension reinforcement in 'in²'
12	Avmin	=	Minimum area Of shear reinforcement within spacing 's' in 'in²'
13	B	=	Width of column/ wall in 'in'
14	beff	=	Effective Width of column/ wall in 'in'
15	bc1 and dc1	=	Cross-sectional dimension of member core measured to the outside edges of the transverse reinforcement composing area Ash in 'in'
16	c	=	Distance from extreme compression fiber to neutral axis in 'in'
17	Cc	=	Clear cover to longitudinal reinforcement in 'in'
18	Cm	=	Factor relating actual moment diagram to an equivalent uniform moment diagram
19	D	=	Depth / diameter of column in 'in'
20	deff	=	Effective Depth / diameter of column in 'in'
21	d	=	Distance from extreme compression fiber to centroid of longitudinal tension reinforcement in 'in'
22	d'	=	Distance from extreme compression fiber to centroid of longitudinal compression reinforcement,'in'
23	Ec	=	Modulus of elasticity of concrete in 'ksi'
24	EI	=	Flexural stiffness of compression member in 'lbs-in²'
25	f'c	=	Specified compressive strength of concrete cylinder in 'ksi'
26	fy	=	Specified yield strength of reinforcement in 'ksi'
27	fyt	=	Specified yield strength fy of transverse reinforcement in 'ksi'
28	hw	=	Height of entire wall from base to top of wall segment considered in 'in'
29	Icr	=	Moment of Inertia of concrete crack section
30	k	=	Effective length factor for compression member
31	lc	=	Length of compression member in a frame, measured center-to-center of the joints in the frame in 'in'
32	lg	=	Moment of inertia of gross concrete section about centroidal axis neglecting reinforcement in 'in⁴'
33	lw	=	Length of entire wall in 'in'
34	lux	=	Un-supported length for compression member along D in 'in'
35	luy	=	Un-supported length for compression member along B in 'in'
36	MCap	=	Moment capacity of section for a given NA angle at design Pu in 'kip-ft '
37	Mcr	=	Cracking Moment
38	MRes	=	Resultant design moment at a given load angle to local major axis in 'kip-ft '
39	Mc	=	Factored moment amplified for the effects of member curvature used for design of compression member in 'kip-ft'
40	Mm	=	Factored moment modified to account for effect of axial compression in 'kip-ft'
41	Mmx	=	Factored moment along D of column modified to account for effect of axial compression in 'kip-ft'
42	Mmy	=	Factored moment along D of column modified to account for effect of axial compression in 'kip-ft'
43	Mur	=	Sqrt (Mmy^2 + Mmx^2) for circular column in 'kip-ft'
44	Mux	=	Factored moment acting on a section along D in 'kip-ft' from Analysis (Momemt About Major Axis)
45	Muy	=	Factored moment acting on a section along B in 'kip-ft' from Analysis (Momemt About Minor Axis)
46	M1	=	Smaller factored end moment on a compression member in 'kip-ft'
47	M1ns	=	Factored end moment on a compression member at the end at which M1 acts, due to loads that cause no appreciable sidesway in 'kip-ft'
48	M1s	=	Factored end moment on compression member at the end at which M1 acts, due to loads that cause appreciable sidesway in 'kip-ft'
49	M1sldr	=	Smaller factored end moment on a compression member due to slenderness effect in 'kip-ft'
50	M2	=	Larger factored end moment on compression member in 'kip-ft'
51	M2min	=	Minimum value of moment M2 as per minimum eccentricity of column
52	M2ns	=	Factored end moment on compression member at the end at which M2 acts, due to loads that cause no appreciable sidesway in 'kip-ft'
53	M2s	=	Factored end moment on compression member at the end at which M2 acts, due to loads that cause appreciable sidesway in 'kip-ft'
54	M2sldr	=	Largest factored end moment on a compression member due to slenderness effect in 'kip-ft'
55	Mnb	=	Flexure Capacity for Beam
56	Mnc	=	Flexure Capacity for Column
57	Mnty	=	Nominal Flexure strength of column at top along depth in 'kip-ft'
58	Mnby	=	Nominal Flexure strength of column at bottom along depth in 'kip-ft'
59	Mntx	=	Nominal Flexure strength of column at top along width in 'kip-ft'
60	Mnbx	=	Nominal Flexure strength of column at bottom along width in 'kip-ft'
61	Nu	=	Factored axial force normal to cross section occurring simultaneously with Vu in 'kip'
62	Pc	=	Critical buckling load in 'kip'
63	pt	=	Ratio of area of distributed transverse reinforcement to gross concrete area perpendicular to that reinforcement
64	Pω	=	Ratio of As to B x d
65	Q	=	Stability index for storey
66	r	=	Radius of gyration of cross section of a compression member in 'in'
67	Vc	=	Nominal shear strength provided by concrete in 'kip'
68	Vj	=	Shear Force acting at the joint in 'kip'
69	Vn	=	Nominal shear strength in 'kip'
70	Vn'	=	Nominal shear strength at joint in 'kip'
71	Vs	=	nominal shear strength provided by shear reinforcement in 'kip'
72	Vs permissible	=	Maximum nominal shear strength provided by shear reinforcement in 'kip'
73	Vur	=	Factored resultant shear force acting on the column in 'kip'
74	Vus	=	Factored horizontal shear in a storey in 'kip'
75	Vux	=	Factored shear at section along B in 'kip' (From Analysis)
76	Vux1	=	Shear induced due to column flexural capacity along width,'kip'
77	Vux2	=	Shear due to enhanced earthquake factor along width, 'kip'
78	Vuy	=	Factored shear at section along D in 'kip' (From Analysis)
79	Vuy1	=	Shear induced due to column flexural capacity along depth, 'kip'
80	Vuy2	=	Shear due to enhanced earthquake factor along depth, 'kip'
81	y	=	Neutral axis depth.
82	β	=	It is a Neutral Axis angle corresponding to load angle to find out MCap
83	So	=	Center to center spacing of transverse reinforcement within the length lo in 'in'
84	lo	=	Length, measured from joint face along axis of member, over which special transverse reinforcement must be provided in 'in'

Code References:

ACI 318 - 14

Sr.No	Element		Clause / table
1	Minimum area of longitudinal reinforcement for column	:	18.7.4
2	Maximum area of longitudinal reinforcement for column	:	18.7.4
3	Minimum longitudinal and transverse reinforcement for wall	:	18.10.2.1
4	Minimum diameter of transverse ties	:	25.7.2
5	Minimum spacing of transverse ties	:	25.7.2
6	Maximum spacing of longitudinal and transverse reinforcement for wall	:	18.10.2.1
7	Applicability of boundary element	:	18.10.6
8	Area and spacing of special confining reinforcement	:	18.7.5
9	Slenderness Moments	:	6.2.5
10	Shear Strength provided by concrete for column	:	22.5.5
11	Design of shear for non-ductile wall	:	11.5.4
12	Design of shear for ductile wall	:	18.10.4.1
13	Minimum Flexural Strength of Columns	:	18.7.3
14	Shear Check at Column Joint	:	18.8.4.1
15	Shear Strength of Column	:	18.3.3, 18.4 & 18.6.5
16	fs,perm	:	10.6.4
17	fc,perm	:	10.2.7.1
18	Wcr	:	Eq 4.2(a)

Sway Calculation (Stability Index)

For Global-X Direction

Level	Load Combination Analysis	Storey Height (ft)	Gravity Load P (kip)	Relative Displacements (in)	Storey Shear (kip)	Stability Index (Q)	Sway Condition
Level	Load Combination Analysis	A	B	C	D	B x C / (A x D)	Sway Condition
0 ft to 16 ft	12	16	3070.46	0.78	240.1	0.052	Sway
16 ft to 32 ft	10	16	1499.22	0.47	120.05	0.031	Non Sway

For Global-Y Direction

Level	Load Combination Analysis	Storey Height (ft)	Gravity Load P (kip)	Relative Displacements (in)	Storey Shear (kip)	Stability Index (Q)	Sway Condition
Level	Load Combination Analysis	A	B	C	D	B x C / (A x D)	Sway Condition
0 ft to 16 ft	11	16	3070.46	0.35	240.1	0.023	Non Sway
16 ft to 32 ft	13	16	1499.22	0.27	120.05	0.017	Non Sway

General Data
Column No.	:	C1
Level	:	16 ft To 32 ft
Frame Type	=	Non-Ductile
Response Modification Coefficient	=	3
Design Code	=	ACI 318 - 14
Grade Of Concrete (f'c)	=	C3.5	ksi
Grade Of Steel (Main)	=	Fy60	ksi
Grade Of Steel (Shear)	=	Fy60	ksi
Grade Of Steel - Flexural Design	=	Fy60	ksi
Grade Of Steel - Shear Design	=	Fy60	ksi
Consider Ductile	=	No
Column B	=	15	in
Column D	=	24	in
Clear Cover, Cc	=	2	in
Clear Floor Height @ lux	=	162	in
Clear Floor Height @ luy	=	162	in
No Of Floors	=	1
No Of Columns In Group	=	1

Flexural Design (Analysis Forces)
Analysis Reference No.	=	41
Critical Analysis Load Combination	:	12
Load Combination	=	[8] : 1.2 (LOAD 1: LOAD CASE 1) +0.5 (LOAD 2: LOAD CASE 2) -(LOAD 3: LOAD CASE 3)
Critical Location	=	Top Joint
Put	=	109.91	kip
Muxt	=	56.62	kip-ft
Muyt	=	157.25	kip-ft
Vuxt	=	-18.29	kip
Vuyt	=	6.55	kip
Pub	=	117.11	kip
Muxb	=	-48.1	kip-ft
Muyb	=	-135.35	kip-ft
Vuxb	=	-18.29	kip
Vuyb	=	6.55	kip

Effective Length Calculation

Calculation Along Major Axis Of Column

Joint	Column Stiffness	Beam Sizes		Beam Stiffness		ψ
Joint	Column Stiffness	Beam 1 (Length x Width x Depth)	Beam 2 (Length x Width x Depth)	Beam 1	Beam 2	ψ
	lbs-ft x 10^6	in	in	lbs-ft x 10^6	lbs-ft x 10^6
Bottom	100.46	No Beam	156 x 15 x 30	-	241.48	0.832
Top	100.46	No Beam	156 x 15 x 30	-	241.48	0.416

User Defined Effective Length Factor

1.2

Calculation Along Minor Axis Of Column

Joint	Column Stiffness	Beam Sizes		Beam Stiffness		ψ
Joint	Column Stiffness	Beam 1 (Length x Width x Depth)	Beam 2 (Length x Width x Depth)	Beam 1	Beam 2	ψ
	lbs-ft x 10^6	in	in	lbs-ft x 10^6	lbs-ft x 10^6
Bottom	39.24	228 x 15 x 30	No Beam	165.22	-	0.475
Top	39.24	228 x 15 x 30	No Beam	165.22	-	0.237

User Defined Effective Length Factor

1.2

Check For Stability Index
Along D
Q	=	0.017
	0.017< 0.05, Column shall be designed as non-sway frame (Braced)

Along B
Q	=	0.031
	0.031< 0.05, Column shall be designed as non-sway frame (Braced)

Slenderness Check
Column Is Braced Along D
Slenderness Check along D
k	=	1.2
r	=	6.93	in
Kluy /r	=	28.06
M1	=	-48.1	kip-ft
M2	=	56.62	kip-ft
Min (40, 34 - 12 x (M1/M2))	=	40
	28.06 < 40, Column not slender along D
Column Is Braced Along B
Slenderness Check along B
k	=	1.2
r	=	4.33	in
Klux /r	=	44.89
M1	=	-135.35	kip-ft
M2	=	157.25	kip-ft
Min (40, 34 - 12 x (M1/M2))	=	40
	44.89 > 40, Column slender along B

Moment Magnification:
For Non-sway frame:

Along B
βdns	=	0.6
Ec	=	3372.05	ksi
Ig ( x 10 ⁶)	=	0.01	in⁴
EI ( x 10 ⁶)	=	6570.63	lbs-in²
M2min	=	10.24	kip-ft
Cm	=	0.26
Pc	=	1715.99	kip
δns	=	1
Mc1	=	-135.35	kip-ft
1.4 MuyB	=	-189.49	kip-ft
Mc1	=	Min (-135.35, -189.49)	kip-ft
	=	-135.35	kip-ft
Mc2	=	157.25	kip-ft
1.4 MuyT	=	220.15	kip-ft
Mc2	=	Min (157.25, 220.15)	kip-ft
	=	157.25	kip-ft

Calculation of Design Moment

Direction	Manalysis	Msldr or Mc	Mdesign-final
	A	B	C
Major Axis Mux (top)	56.62	-	56.62
Major Axis Mux (bottom)	-48.1	-	-48.1
Minor Axis Muy (top)	157.25	157.25	157.25
Minor Axis Muy (bottom)	-135.35	-135.35	-135.35

Where
A	=	Moments from analysis
B	=	Moment due to slenderness effect
C	=	Final design Moment = Maximum of (Manalysis, Maximum of (Msldr or Mc))

Final Critical Design Forces

Critical Case - Axial Load & BiAxial Bending
Pu	=	109.91	kip
Mux	=	56.62	kip-ft
Muy	=	157.25	kip-ft

Φ Pn, Max Check

Critical Analysis Load Combination	=	6
Load Combination	=	[2] : 1.2 (LOAD 1: LOAD CASE 1) +1.6 (LOAD 2: LOAD CASE 2)
Critical Location	=	Bottom Joint
Pu	=	156.37	kip
Mux	=	-69.22	kip-ft
Muy	=	-91.24	kip-ft
Pt Calculated	=	1.4
φ Pn, Max	=	706.83	kip
		Pu < φ Pn, Max	Hence, OK

Minimum Ast Calculation

Critical Analysis Load Combination	=	6
Load Combination	=	[2] : 1.2 (LOAD 1: LOAD CASE 1) +1.6 (LOAD 2: LOAD CASE 2)
Pu-max from all Combinations	=	156.37	kip
Pt required for Pu-max	=	0	%
Pt min (User Defined)	=	1	%
Minimum Pt required	=	1	%

Resultant Moment (Combined Action)
Moment Capacity Check
Pt Calculated	=	1.4
Reinforcement Provided	=	10-#6 + 2-#5

Load Angle	=	Tan^-1(Muy/Mux)
	=	70.2	deg
MRes	=	167.13	kip-ft
( φ ) MCap	=	169.08	kip-ft
Capacity Ratio	=	MRes/ MCap
	=	0.988 < 1

Shear Calculation (Analysis Forces)	Along D	Along B
lu (in)	162	162
Column Dimension (D , B) (in)	24	15
Check	lu > 5 x D	lu > 5 x B
Shear from Moment Capacity
Critical Analysis Load Combination	13	12
Critical Load Combination	[9] : 1.2 (LOAD 1: LOAD CASE 1) +0.5 (LOAD 2: LOAD CASE 2) -(LOAD 4: LOAD CASE 4)	[8] : 1.2 (LOAD 1: LOAD CASE 1) +0.5 (LOAD 2: LOAD CASE 2) -(LOAD 3: LOAD CASE 3)
Nu (kip)	114.1	109.91
Mu (kip-ft)	147.48	157.25
Vu3 (kip)	16.4	-18.29
λ	1	1
φ	0.75	0.75
Deff (in)	21.62	12.62
ρw (50% of As provided)	0.008	0.008
Mm (kip-ft)	59.09	103.01
φVc (kip)	29.72	26.43
Check	Vu < φVc	Vu < φVc
Link For Shear Design	Not Required	Not Required

Design Of Links
Links in the zone where special confining links are not required
Normal Links
fyt	=	60	ksi
Along D
Av/s min-1	=	0.75 x Sqrt(f'c) x B x 12 / fyt
	=	0.13	in²/ft
Av/s min-2		50 x B x 12 / fyt
	=	0.15	in²/ft
Av/s min	=	Max ( Av/s min-1, Av/s min-2)
	=	0.15	in²/ft

Along B
Av/s min-1	=	0.75 x Sqrt(f'c) x D x 12 / fyt
	=	0.21	in²/ft
Av/s min-2		50 x B x 12 / fyt
	=	0.24	in²/ft
Av/s min	=	Max ( Av/s min-1, Av/s min-2)
	=	0.24	in²/ft
Maximum Longitudinal Diameter	=	Dia Of Rebar
Rebar Number of bundled bar, D1	=	6
Diameter of bundled bar, D1	=	0.75	in
Bundled Rebar	=	No
Minimum diameter of link	>=	0.37	in
Provided Link Rebar Number	=	3
Provided Diameter of link	=	0.37	in

Criterion for spacing of normal links
Min. Longitudinal Bar dia X 16	=	10	in
48 x diameter of links	=	18	in
Min. Dimension of column	=	15	in

Provided spacing	=	10	in


Numbers of legs provided along D	=	3
Av/s provided along D	=	0.4	in²/ft
Numbers of legs provided along B	=	5
Av/s provided along B	=	0.66	in²/ft
		Hence, OK
Provided spacing	=	10	in

Table For Links

Note: Ductile Design of Links is Applicable Only For Boundary Elements

	Required			Provided
	Normal Design	Shear Design	Ductile Design	Normal Zone	Ductile Zone
Link Rebar Number	3	---	---	3	---
Spacing	10	---	---	10	---