structural design report for corbel...

Structural Design Report

for Corbel Template

Table of Contents

1. Design Conditions

1) General Characteristics

(1) Project Name

(2) Design Code

(3) Unit

(4) Strength Reduction Factors

(5) Scope of Report

2) Materials

(1) Concrete

(2) Steel

3) Geometrical Shape

4) Loads and Load Combinations

(1) Loads

(2) Load Combinations

5) Reference

(1) Designer

(2) Date

(3) Note

2. Strut-Tie Model Design (Load Combination-1)

1) Construction of Strut-Tie Model

(1) ESO (Evolutionary Structural Optimization)

(2) Compressive Principal Stress Flow

(3) Constructed Strut-Tie Model

2) Analysis of Strut-Tie Model

(1) Loading Conditions

(2) Strut and Tie Types

(3) Strut and Tie Forces

3) Strength Verification and Required Rebars

(1) Strength under Bearing/Loading Plates

(2) Required Area of Rebars

(3) Available Widths of Struts and Nodal Zones

(4) Strength of Struts

(5) Strength of Nodal Zones

3. Summary

1) Dimensioned Shape

2) Required and Used Areas of Rebars

3) Placement of Rebars


1) General Characteristics

(1) Project Name : Corbel Template

(2) Design Code : ACI 318M-14

(3) Unit : KN.m

(4) Strength Reduction Factors

Strut : 0.75

Tie : 0.75

Node : 0.75

(5) Scope of Report

The purpose of this report is to design structural concrete member using strut-tie

model. The design is performed according to the ACI 318M-14 strut-tie model

provisions.

This report provides results of calculation for:

- check capacity of bearing plates

- design tie reinforcement

- check capacity of struts

- check capacity of nodal zones

2) Materials

(1) Concrete

- Mass : 2,350 kg/m³

- Weight : 23.5 kN/m³

- Poisson's ratio : 0.15

- Compressive Strength of Concrete, fck : 24.0 MPa

- Tensile Strength of Concrete, fct : 2.4 MPa

- Elastic modulus of concrete, Ec : 27,849 MPa

(2) Steel1

- Mass : 7,850 kg/m³

- Weight : 78.5 kN/m³

- Poisson's ratio : 0.15

- Yield strength of steel, fy : 400.0 MPa

- Elastic modulus of steel, Es : 200,000 MPa

Corbel Template


Pg. 3

HanGil ITTemplate1_01_Corbel_SI_ACI.stm

19/7/2017 PM 13:242) Materials

3) Geometrical Shape

- Thickness : 1.00 m

Corbel Template


Pg. 4


19/7/2017 PM 13:243) Geometrical Shape

4) Loads and Load Combinations

(1) Loads

D (Dead load)

L (Live load)

Corbel Template


Pg. 5


19/7/2017 PM 13:244) Loads and Load Combinations

(2) Load Combinations

1) LC01 : 1.30D + 2.15L

5) Reference

(1) Designer : Hangil IT

(2) Date : 2017-07-15

(3) Note : Design of Corbel using Template (ACI 318-14)

Corbel Template


Pg. 6


19/7/2017 PM 13:245) Reference


1) Construction of Strut-Tie Model

(1) ESO (Evolutionary Structural Optimization)

1. STAGE-01 (Initial shape)

2. STAGE-04 (Elimination ratio = 31%)

Corbel Template


Pg. 7


19/7/2017 PM 13:241) Construction of Strut-Tie Model



Corbel Template


Pg. 8




(2) Compressive Principal Stress Flow

Corbel Template


Pg. 9



(3) Constructed Strut-Tie Model

(A) Nodal Coordinates

Node

No.

X

coordi.

Z

coordi.

Node

No.

X

coordi.

Z

coordi.

1 -0.080 1.020 2 -0.666 1.020

3 -0.420 0.500 4 -0.420 0.080

5 -0.080 0.080 6 -0.080 0.500

7 -0.666 0.760 8 -0.420 0.760

(B) Element Connectivity

Element

No.

Start

Node

End

Node

Element

No.

Start

Node

End

Node

1 1 2 2 2 3

3 3 4 4 4 5

5 5 6 6 6 1

7 3 6 8 1 3

9 6 4 10 2 7

11 7 3 12 3 8

13 8 2 14 7 8

(C) Restraints

Corbel Template


Pg. 10



Node Ux Uy Uz Rx Ry Rz

4 - O O O - O

5 O O O O - O

2) Analysis of Strut-Tie Model

(1) Loading Conditions

(1) Dead load (D)

Corbel Template


Pg. 11


19/7/2017 PM 13:242) Analysis of Strut-Tie Model

(2) Live load (L)

Corbel Template


Pg. 12



(2) Strut and Tie Types

- Strut1 : Prismatic Strut

- Strut3 : Bottle Shape Strut (Not Satisfying ACI 318M-14 23.5.3)

- Tie1 : Tie for outer rebars

- Tie2 : Tie for inner rebars

- Tie3 : Tie for top rebars

- Tie4 : Tie for intermediate horizontal rebars

Corbel Template


Pg. 13



(3) Strut and Tie Forces

Elem.

No.

Force

(kN)

Elem.

No.

Force

(kN)

Elem.

No.

Force

(kN)

Elem.

No.

Force

(kN)

1 479.2 2 -631.3 3 -1444.9 4 142.4

5 908.8 6 732.9 7 142.4 8 -875.7

9 -226.3 10 -70.7 11 -97.3 12 -70.7

13 -97.3 14 66.9

Corbel Template


Pg. 14



3) Strength Verification and Required Rebars

(1) Strength under Bearing/Loading Plates

phi fce = phi·0.85·beta·fck < Fu / A

beta = 1.00 (for the nodal zone bounded by struts, bearing areas, or both)

0.80 (for the nodal zone anchoring one tie)

0.60 (for the nodal zone anchoring two or more ties)

A = Area of bearing plates ( = BxW )

Node beta fce(MPa)Fu

(kN)B (mm) W (mm)

Fu/A

(MPa)Note

2 0.80 12.24 712.0 1000.0 268.0 2.657 O.K

(2) Required Area of Rebars

1) Main Rebars

(A) Horizontal Rebars

As.req = Fu / phi·fy·cos theta < As.used

where,

Fu = member force of steel tie

phi = strength reduction factor of steel tie : 0.75

fy = yield strength of steel : 400.0 MPa

theta = angle of steel tie measured from positive horizontal axis

(+: counterclockwise)

Tie No. Types Fu (kN)theta

(deg.)Rebars

As.req

(mm²)

As.used

(mm²)Note

1 Top 479.23 0.0 4-#8 1597 2027 O.K

(B) Vertical Rebars

As.req = Fu / phi·fy·sin theta < As.used

where,







(deg.)Rebars

As.req

(mm²)

As.used

(mm²)Note

6 Outer 732.94 90.04-#8, 4-

#82443 4054 O.K

2) Transverse Rebars

Corbel Template


Pg. 15


19/7/2017 PM 13:243) Strength Verification and Required Rebars

(A) Horizontal Rebars

Tie No. Fu (kN)theta

(deg.)Rebars

Weff,tie

(mm)Sh (mm)

phi Fn

(kN)Note

4 142.40 0.0 3-#8 160.0 300.0 202.7 O.K

7 142.40 0.0 3-#8 260.0 300.0 329.4 O.K

14 66.88 0.0 3-#8 188.0 300.0 238.2 O.K

phi·Fn = phi·Avh ·fy ·Weff,tie · cos theta / Sh > Fu

where,






Sh = spacing of horizontal rebars

Weff,tie = effective width of tie

(3) Available Widths of Struts and Nodal Zones

1) Node without bearing plate

The available widths of a strut at both ends and nodal zone faces are determined by

taking the minimum ones from the values calculated below for case 1 and case 2.

2) Node with bearing plate

The available widths of a strut at both ends and nodal zone faces are determined by

taking the values calculated below for case 3.

Corbel Template


Pg. 16



Corbel Template


Pg. 17



The available widths of struts and ties determined by the methods introduced above

are shown below

Elem.

No.i-width j-width

Available

Width

Elem.

No.i-width j-width

Available

Width

2 302.0 111.2 111.2 3 160.0 160.0 160.0

8 191.2 142.3 142.3 9 205.9 205.9 205.9

10 268.0 123.0 123.0 11 117.0 178.7 117.0

12 160.0 123.0 123.0 13 117.0 290.9 117.0

(4) Strength of Struts

Wreq = Fu / phi·0.85·bata·fck·b < Wprov (See ACI 318M-14 Section 23.4)

beta = 1.00 (prismatic strut - uniform cross-sectional area along length)

0.75 (bottle-shaped strut satisfying ACI 318M-14 Section 23.5.3)

0.60 (bottle-shaped strut unsatisfying ACI 318M-14 Section 23.5.3)

0.40 (strut in tension zones)

0.60 (all other cases)

phi = strength reduction factor of concrete strut = 0.75

Strut

No.beta theta Fu (kN) b (mm) Wreq (mm)

Wprov

(mm)Note

2 0.60 64.7 631.3 1000.0 68.8 111.2 O.K

3 1.00 90.0 1444.9 1000.0 94.4 160.0 O.K

8 0.60 56.8 875.7 1000.0 95.4 142.3 O.K

10 0.60 90.0 70.7 1000.0 7.7 123.0 O.K

11 0.60 46.6 97.3 1000.0 10.6 117.0 O.K

12 0.60 90.0 70.7 1000.0 7.7 123.0 O.K

13 0.60 46.6 97.3 1000.0 10.6 117.0 O.K

(5) Strength of Nodal Zones

Corbel Template


Pg. 18



The verification of the nodal zone strength should be done through comparing the

available nodal zone area with that required. In this report, if the thickness of

the structural concrete is consistent, the verification will be done by comparing the

available nodal zone width, Wprov, with that required, Wreq

Wreq = Fu / phi·0.85·beta·fck·b < Wprov (See ACI 318M-14 Section 23.9)

beta = 1.00 (for the nodal zone bounded by struts, bearing areas, or both)

0.80 (for the nodal zone anchoring one tie)

0.60 (for the nodal zone anchoring two or more ties)

Node No. beta Type Element Fu (kN) Wreq (mm)Wprov

(mm)Note

1 0.60 CTT

T-1 479.2 52.2 520.0 O.K

T-6 732.9 79.8 160.0 O.K

C-8 875.7 95.4 191.2 O.K

2 0.80 CCT

V 712.0 58.2 268.0 O.K

T-1 479.2 39.2 140.0 O.K

C-2 631.3 51.6 302.1 O.K

C-10 70.7 5.8 268.0 O.K

C-13 97.3 7.9 290.9 O.K

3 0.80 CCT

C-2 631.3 51.6 111.2 O.K

C-3 1444.9 118.1 160.0 O.K

T-7 142.4 11.6 260.0 O.K

C-8 875.7 71.5 142.3 O.K

C-11 97.3 7.9 178.7 O.K

C-12 70.7 5.8 160.0 O.K

4 0.80 CCTC-3 1444.9 118.1 160.0 O.K

T-4 142.4 11.6 160.0 O.K

5 0.60 TTT T-4 142.4 15.5 160.0 O.K

6 0.60 CTTT-6 732.9 79.8 160.0 O.K

T-7 142.4 15.5 420.0 O.K

7 0.80 CCT

C-10 70.7 5.8 123.0 O.K

C-11 97.3 7.9 117.0 O.K

T-14 66.9 5.5 188.0 O.K

8 0.80 CCT

C-12 70.7 5.8 123.0 O.K

C-13 97.3 7.9 117.0 O.K

T-14 66.9 5.5 260.0 O.K

C: compression; T: tension; V: vertical force; H: horizontal force

Corbel Template


Pg. 19



3. Summary

1) Dimensioned Shape

1) Load Combination - 1

2) Required and Used Areas of Rebars

1) Load Combination - 1

(A) Main Rebars


(deg.)Rebars

As.req

(mm²)

As.used

(mm²)Note

1 Top 479.23 0.0 4-#8 1597 2027 O.K

Corbel Template

3. Summary

Pg. 20


19/7/2017 PM 13:242) Required and Used Areas of Rebars


(deg.)Rebars

As.req

(mm²)

As.used

(mm²)Note

6 Outer 732.94 90.04-#8, 4-

#82443 4054 O.K

(B) Transverse Rebars

Tie No. Fu (kN)theta

(deg.)Rebars

Weff,tie

(mm)Sh (mm)

phi Fn

(kN)Note

4 142.40 0.0 3-#8 160.0 300.0 202.7 O.K

7 142.40 0.0 3-#8 260.0 300.0 329.4 O.K

14 66.88 0.0 3-#8 188.0 300.0 238.2 O.K

Corbel Template

3. Summary

Pg. 21


19/7/2017 PM 13:242) Required and Used Areas of Rebars

structural design report for corbel...

Documents