Mathcad - Beam Capacity with A prime s_Rev03

JOB # Customer: Subject: Engineer: Date: 1/17/2012 Page 1

SHEET NO._________ OF _________ 

Concrete Beam Capacity f'c := 5⋅ksi

cover := 4⋅ in

h := 24⋅ in

f y := 60⋅ ksi

db := 0.75⋅ in

 

 

β1 := if f'c ≤ 4⋅ ksi , 0.85 , if f'c ≥ 8 ⋅ksi , 0.65 , 0.85 − β1 = 0.8

ϕ := 0.9

d := h − cover −

db 2

ksi

 

⋅ 0.05

b := 18in

= 19.625⋅ in

2

( f'c − 4⋅ksi)

d' := cover +

db 2

= 4.375⋅ in

2

A's := 0.60⋅ in ⋅ 3

A's = 1.8⋅ in

2

2

As := 0.60⋅ in ⋅ 3

As = 1.8⋅ in

Concrete Beam Capacity per ACI 318 a :=

As⋅ f y

a = 1.41 1.412 2⋅ in

0.85⋅ f'c⋅ b

ϕMn := ϕ⋅ As⋅ f y⋅  d −

 

a 

ϕMn = 153.245⋅ ft⋅ k 

2 

Concrete Beam Capacity per ACI 318 including A's SEED VALUES VALUES FOR SOLVE SOLVE BLOCK C := 1 Given 0.85⋅ f'c⋅ β1 ⋅ b ⋅ C

2

87⋅ ksi

+

ksi⋅ in

Find C

k 

  s  

⋅ A' ⋅ C −

d'  in 

−

0.85⋅ f'c⋅ ( A's⋅ C) k 

As⋅ f y

−

2

⋅C

=0

ksi⋅ in

ANS := Find( C) C := ANS

C = 3.028

Cc := 0.85⋅ f'c⋅ β1 ⋅ C⋅ b ⋅ in

Cs :=

Cc = 185.313⋅ k 

 87⋅ksi⋅  C − d'    in  A's⋅ C 

T := As⋅ f y

 − 0.85⋅ f'

Concrete Shear Capacity per ACI 318 Cs = −77.313⋅ k 

c



ϕv := 0.75

T = 108⋅ k   a := β1 ⋅ C

Cs + Cc = 108⋅ k 

ϕMn := ϕ⋅ Cc⋅  d −



 

a⋅ in  2

Beam Capacity with A prime s_Rev03.xmcd

a = 2.422

 

+ C ⋅ ( d − C⋅ in)

s

ϕMn = 159.687⋅ ft⋅ k 

Vc := 2 ⋅

f'c psi

⋅ b ⋅ d ⋅ psi = 49.957⋅ k 

ϕv⋅ Vc = 37.468⋅ k 

JOB # Customer: Subject: Engineer: Date: 1/17/2012 Page 2

Beam Capacity with A prime s_Rev03.xmcd

SHEET NO._________ OF _________