Rc corbel example

1. DAR GROUP
Project
The Pearl
Job Ref.
Q09079
Section
PA
Sheet no./rev.
1
Calc. by
Eng.MS
Date
09-July-06
Chk'd by
Eng.AE
Date App'd by Date
RC SINGLE CORBEL DESIGN TO ACI 318-05
Vu
Nuc
a
d
h
Framing
bars
Main
tension
bars
Horizontal
bars
Steel angle
min d / 2
Shd
2
3
Sh
Sh
Corbel geometry
Width of corbel; b = 300 mm
Total thickness of corbel; h = 500 mm
Depth to main reinforcement; d = 450 mm
Material properties
Yield strength of reinforcement; f
y = 415
MPa
Compressive strength of concrete; f’
c = 35
MPa
Type of concrete; Normal weight
Unit weight of concrete;  = 1.00
Corbel construction; Monolithic
Coefficient of friction;  = 1.4   = 1.40
Design load data
Factored vertical load; V
u = 370.00
kN
Distance of vertical load from face of column; a = 100 mm
Horizontal force acting on corbel; N
uc = 75.00
kN
Strength reduction factor;  = 0.750
Vertical load capacity check
Nominal vertical load; V
n = Vu / = 493.33
kN
Nominal vertical load capacity; V
n_cap = min(0.2  f’ c  b  d, 5.5 MPa  b  d) = 742.50
kN
PASS - Nominal vertical load is less than the nominal vertical load capacity
Find shear friction reinforcement
Minimum horizontal force acting on corbel; N
uc_min = 0.2  V u = 74.00
kN
Horizontal force acting on corbel; N
uc_act = max(Nuc, Nuc_min) = 75.00
kN
For balanced condition; j = 0.85
Area for shear friction reinforcement; A vf = Vn / (fy ) = 849 mm
2
Af = [(Vu  a) + (Nuc_act  (h –d))] / (  f y  j  d) = 342 mm
2
Nominal area required; A n = Nuc_act / ( f y) = 241 mm
2

2. DAR GROUP
Project
The Pearl
Job Ref.
Q09079
Section
PA
Sheet no./rev.
2
Calc. by
Eng.MS
Date
09-July-06
Chk'd by
Eng.AE
Date App'd by Date
Main tension reinforcement check
Minimum area of tension reinforcement; A
sc_min = 0.04  f’ c  b  d / f y = 455
mm
2
Area of tension reinforcement required; A sc = max([(2  A vf) / 3] + An, Af + An) = 807 mm
2
Asc_req = max(Asc, Asc_min) = 807 mm
2
Main tension reinforcement; 3 No.6 bars
Diameter of tension bars; D tension = 19 mm
Number of tension bars; N
tension = 3Area of tension reinforcement provided; A sc_prov = Ntension    D tension
2 / 4 = 851
mm
2
PASS - Tension reinforcement is adequate
Horizontal reinforcement check
Minimum area of horizontal reinforcement; A
h_min = 0.5  (A sc_req - An) = 283
mm
2
Area of horizontal reinforcement required; A h = max(Avf / 3, Af / 2) = 283 mm
2
Ah_req = max(Ah, Ah_min) = 283 mm
2
Horizontal reinforcement; 3 No.3 bars
Diameter of horizontal bars; D horizontal = 9 mm
Number of horizontal bars; N
horizontal = 3Area of horizontal reinforcement provided; A h_prov = 2  N horizontal    D horizontal
2 / 4 = 382
mm
2
PASS - Horizontal reinforcement is adequate
Maximum spacing of horizontal bars; S h_max = 2  d / (3  N horizontal) = 100 mm
Actual spacing of horizontal bars; S
h = 100
mm
PASS - Horizontal bar spacing is adequate
Design Summary
Single corbel 300 mm wide by 500 mm deep with 35 MPa concrete and 415 MPa steel
Provide main tension reinforcement as 3 No. 6 bars
Provide horizontal reinforcement as 3 No. 3 link bars at maximum 100 mm centres