The Structural Toolbox - ACI Corbel

Corbel - Inputs:

V_uc		kips	Vertical Load on Corbel
N_uc		kips	Direct Horizontal Load on Corbel
H_c		in	Total Corbel Height
B_c		in	Total Corbel Width
a_v		in	Distance from face of column to load application point.
L_c		in	Distance from face of column to edge of corbel.
S_c		in	Column/wall width.
cover		in	clear cover to exterior face of reinforcement.
Main Corbel Bar:
d_b	0.375	in	bar diameter
A_s	0.11	in²	bar area
Corbel Tie Bars:
d_b	0.375	in	bar diameter
A_s	0.11	in²	bar area
λ
f'_c		psi	Specified 28-day compressive strength of concrete.
β₁	0.85		[Table 22.2.2.4.3]
f_y		psi	Yield strength of bar to be developed.
μ:			Coefficient of friction for shear friction

Corbel - Results:

Section 16.5 applicable :
Section dimensions satisfy 16.5.2.4:
A_f ≤ A_f,limit:
A_sc,req :		in²
		in²
A_h,req :		in²
		in²

ACI 318-14 - Section 16.5 - Brackets and Corbels

Preliminary Computations
$d = H_{c} - (C o v e r + \frac{d_{b}}{2})$	22.313	in	Depth from bottom of corbel at face of support to center of primary reinforcement.
Φ_corbel	0.75		[Table 21.2.1 - Strength reduction factors Φ]
N_uc,design	5.000	kips	[16.5.3.5 - N_uc,design shall be at least 0.2V_uc]
$M_{u} = V_{u c} a_{v} + N_{u c, d e s i g n} (H_{c} - d) \frac{1 ft}{12 in}$	5.703	ft-kips	[16.5.3.1]

16.5.1.1 -- Verification that 16.5 is applicable
$\frac{a_{v}}{d}$
$N_{u c} \leq V_{u c}$

16.5.2.4 -- Verification that dimensions satisfy max shear friction
$0.2 F_{c}^{'} b_{w} d$
$(480 + 0.08 F_{c}^{'}) b_{w} d$
$1600 b_{w} d$

16.5.4 -- Design Strength
16.5.4.3 -- A_n for Tensile Strength
$A_{n} = \frac{N_{u c, d e s i g n}}{ϕ F_{y}}$		in²
16.5.4.4 -- A_vf for Shear Friction
$A_{v f} = \frac{V_{u c}}{ϕ μ λ F_{y}}$		in²
16.5.4.5 -- A_f for Flexure
$M_{u c} = ϕ A_{f} f_{y} (d - \frac{a}{2}),where a = \frac{A_{f} f_{y}}{0.85 f_{c}^{'} B_{c}}$
$\frac{- 1 ϕ 10 f_{y}^{2}}{17 f_{c}^{'} B_{c}} A_{f}^{2} + ϕ f_{y} d A_{f} - M_{u c, d e s i g n} = 0$		in²
$ϵ_{t} = (\frac{\frac{a}{β_{1}} - d}{\frac{a}{β_{1}}}) 0.003,limit ϵ_{t} = 0.004$
$A_{f, l i m i t} = \frac{51 B_{c} β_{1} d f_{c}^{'}}{140 f_{y}}$		in²

16.5.5 -- Reinforcement limits
16.5.5.1 -- A_sc, Area of primary tension reinforcement
$max [\begin{matrix} A_{f} + A_{n} \\ (\frac{2}{3}) A_{v f} + A_{n} \\ 0.04 (\frac{f_{c}^{'}}{f_{y}}) (B_{c} d) \end{matrix}]$	0	in²
16.5.5.2 -- A_h, Area of closed stirrups or ties parallel to A_sc
$A_{h} = 0.5 (A_{s c} - A_{n})$	0	in²