Beam-Column Joint Design

DESIGN OF R.C. BEAM-COLUMN JOINT DESIGN - HK CoP 2013

1.0 INPUT DATA

Material Properties

f_cu = MPa Characteristic concrete cube strength

f_y = MPa Characteristic steel yield strength

Column Properties

b_c = mm Column dimension in X-direction

h_c = mm Column dimension in Y-direction

c_c = mm Concrete cover

N = kN Minimum axial load (compression +ve)

Figure 1: Typical Beam-Column Joint Configuration

2.0 BEAM PARAMETERS

Input "0" for all parameters if beam is NOT present on that side

For beam type: Input "1" = Wind/Seismic beam, "0" = Gravity only

Beam X1 (Left)

B_X1 = Beam type (1=W/S, 0=Gravity)

b_x1 = mm Breadth

h_x1 = mm Overall depth

d_x1 = mm Effective depth

A_st,x1 = mm² Top steel (hogging)

A_sb,x1 = mm² Bottom steel (sagging)

Beam X2 (Right)

B_X2 = Beam type (1=W/S, 0=Gravity)

b_x2 = mm Breadth

h_x2 = mm Overall depth

d_x2 = mm Effective depth

A_st,x2 = mm² Top steel (hogging)

A_sb,x2 = mm² Bottom steel (sagging)

Beam Y1

B_Y1 = Beam type (1=W/S, 0=Gravity)

b_y1 = mm Breadth

h_y1 = mm Overall depth

d_y1 = mm Effective depth

A_st,y1 = mm² Top steel (hogging)

A_sb,y1 = mm² Bottom steel (sagging)

Beam Y2

B_Y2 = Beam type (1=W/S, 0=Gravity)

b_y2 = mm Breadth

h_y2 = mm Overall depth

d_y2 = mm Effective depth

A_st,y2 = mm² Top steel (hogging)

A_sb,y2 = mm² Bottom steel (sagging)

3.0 DESIGN MOMENTS AT COLUMN FACE

X-Direction

M_h,x1 = kNm Hogging at X1

M_s,x1 = kNm Sagging at X1

M_h,x2 = kNm Hogging at X2

M_s,x2 = kNm Sagging at X2

Y-Direction

M_h,y1 = kNm Hogging at Y1

M_s,y1 = kNm Sagging at Y1

M_h,y2 = kNm Hogging at Y2

M_s,y2 = kNm Sagging at Y2

4.0 JOINT SHEAR REINFORCEMENT PARAMETERS

Horizontal Joint Shear Reinforcement

Horizontal joint shear reinforcement shall consist of links or hoops uniformly distributed between but not immediately adjacent to the innermost layers of the top and bottom beam reinforcement.

d_b,h = mm Diameter

S_h = mm Vertical spacing (≤ min[10d_b; 200mm])

Vertical Joint Shear Reinforcement

Vertical joint shear reinforcement should consist of vertical links or intermediate column bars adequately anchored in the column and placed between the corner bars and within the effective joint area. Each vertical face of the joint should be provided with at least one vertical joint shear bar.

d_b,v = mm Diameter

S_v = mm Horizontal spacing (≤ max[0.25X; 200mm])

* CALCULATIONS *

A_g = b_c × h_c

A_g = 875 × 250 = 218750 mm²

1. Determine Analysis Case

Case 1: Non sway / gravity frame | Case 2: Sway frame, gravity dominant | Case 3: Sway frame, lateral dominant

X-direction:

Case X = 3 : Sway frame, lateral dominant

Y-direction:

Case Y = 2 : Sway frame, gravity dominant

2. Lever Arms

X-direction:

z_x1 = min[(0.5 + √(0.25 - K_x1/0.9))·d_x1; 0.95·d_x1]

z_x1 = 688.00 mm

z_x2 = min[(0.5 + √(0.25 - K_x2/0.9))·d_x2; 0.95·d_x2]

z_x2 = 653.60 mm

Y-direction:

z_y1 = — mm (no beam)

z_y2 = 525.35 mm

3. Tension Forces in Beam Bars

X-direction:

T_x1 = 1295.00 kN

T_x2 = 1295.00 kN

Y-direction:

T_y1 = 0.00 kN

T_y2 = 934.47 kN

4. Horizontal Joint Shear Forces

V_jhx = 2590.00 kN

V_jhy = 934.47 kN

5. Shear Stress Check (Cl. 6.8.1.3)

v_limit = 0.2·f_cu

v_limit = 9.00 MPa

Effective joint widths:

b_jx = min(h_c; max(b_x1; b_x2) + 0.5·b_c)

b_jx = 250 mm

b_jy = min(b_c; max(b_y1; b_y2) + 0.5·h_c)

b_jy = 250 mm

Nominal shear stresses:

v_jhx = V_jhx·10³/(b_jx·b_c)

v_jhx = 11.82 MPa

FAIL (v_jhx = 11.82 > v_limit = 9.00 MPa)

v_jhy = V_jhy·10³/(b_jy·h_c)

v_jhy = 1.71 MPa

PASS (v_jhy = 1.71 ≤ v_limit = 9.00 MPa)

Figure 2: Typical Joint Shear Failure

6. Design Shear Reinforcement (Eqn 6.72)

X-direction:

A_jhx,req = (V_jhx·10³/0.87·f_y)·(0.5 − (C_jx·N·10³)/(0.8·A_g·f_cu))

A_jhx,req = 1132.18 mm²

Horizontal reinforcement provided:

H_x = max(h_x1; h_x2) = 750 mm

N_hx = ceil(H_x/S_h) − 1 = 7 sets

A_jvx,prov = N_hx × legs_hx × π·(d_b,h/2)²

A_jvx,prov = 7 × 4 × π × (16/2)² = 1407.43 mm²

PASS

Vertical reinforcement required (X-direction):

A_jvx,req = (0.4·max(h_x1; h_x2)/b_c·V_jhx·10³ − C_jx·N·10³)/(0.87·f_y)

A_jvx,req = — mm²

A_jvx,prov = 0 mm²

N/A

Y-direction:

A_jhy,req = (V_jhy·10³/0.87·f_y)·(0.5 − (C_jy·N·10³)/(0.8·A_g·f_cu))

A_jhy,req = 408.70 mm²

Horizontal reinforcement provided:

H_y = max(h_y1; h_y2) = 600 mm

N_hy = ceil(H_y/S_h) − 1 = 5 sets

A_jvy,prov = N_hy × legs_hy × π·(d_b,h/2)²

A_jvy,prov = 5 × 3 × π × (16/2)² = 603.19 mm²

PASS

Vertical reinforcement required (Y-direction):

A_jvy,req = 0 mm²

A_jvy,prov = 1256.64 mm²

PASS

* OUTPUT SUMMARY *

Design Summary

Gross area, A_g = 218750 mm²

Case X: 3 - Sway, Lateral Dominant

Case Y: 2 - Sway, Gravity Dominant

Joint shear forces:

V_jhx = 2590.00 kN

V_jhy = 934.47 kN

Nominal shear stresses:

v_jhx = 11.82 MPa

v_jhy = 1.71 MPa

v_limit = 9.00 MPa

Shear stress check X: FAIL

Shear stress check Y: PASS

X-direction reinforcement:

Horizontal: 7 sets T16-4legs = 1407.43 mm²

Vertical: — sets T20-—legs = 0 mm²

Y-direction reinforcement:

Horizontal: 5 sets T16-3legs = 603.19 mm²

Vertical: 8 sets T20-2legs = 1256.64 mm²

RESULTS

DESIGN CHECK - SHEAR STRESS IN X-DIRECTION EXCEEDS LIMIT

DESIGN OF R.C. CORBEL

DESIGN OF R.C. BEAM-COLUMN JOINT DESIGN - HK CoP 2013

1.0 INPUT DATA

2.0 BEAM PARAMETERS

3.0 DESIGN MOMENTS AT COLUMN FACE

4.0 JOINT SHEAR REINFORCEMENT PARAMETERS

* CALCULATIONS *

1. Determine Analysis Case

2. Lever Arms

3. Tension Forces in Beam Bars

4. Horizontal Joint Shear Forces

5. Shear Stress Check (Cl. 6.8.1.3)

6. Design Shear Reinforcement (Eqn 6.72)

* OUTPUT SUMMARY *

Design Summary

RESULTS

Other Tools

DESIGN OF R.C. BEAM-COLUMN JOINT DESIGN - HK CoP 2013

1.0 INPUT DATA

2.0 BEAM PARAMETERS

3.0 DESIGN MOMENTS AT COLUMN FACE

4.0 JOINT SHEAR REINFORCEMENT PARAMETERS

*** CALCULATIONS ***

1. Determine Analysis Case

2. Lever Arms

3. Tension Forces in Beam Bars

4. Horizontal Joint Shear Forces

5. Shear Stress Check (Cl. 6.8.1.3)

6. Design Shear Reinforcement (Eqn 6.72)

*** OUTPUT SUMMARY ***

Design Summary

RESULTS

Other Tools

* CALCULATIONS *

* OUTPUT SUMMARY *