SME
Reinforced Concrete Design · Problem type
Minimum steel
Use this for “What is the least steel area for a beam 14 in wide with d = 24 in, f′c = 5000 psi and fᵧ = 60,000 psi?”
Diagram
h drawn as d plus half a bar, the stirrup and the cover.
This is an example. Type your own values to start a new problem.
f′c
Concrete strength
example
fᵧ
Steel yield stress
example
b
Beam width
example · in
d
Depth to the bars
example · in
As,min
Minimum steel area
calculated · in²
Formulas
As,min
=
200
×
b
×
d
fᵧ
0.8
=
200
×
12
×
20
60,000
Assumptions
•
ACI 318-19 minimum flexural steel for a beam; f′c and fᵧ go into the formula in psi.
•
Up to f′c = 4,444 psi the 200 psi floor governs; above it 3√f′c does.
•
With less steel than this, the beam can fail suddenly as soon as the concrete cracks.
Step-by-step
WE KNOW
f′c = 4,000 psi, fᵧ = 60,000 psi, b = 12 in, d = 20 in
FIND
minimum steel area (As,min)
Step 1 · Find minimum steel area (As,min)
Use As,min = 200 × b × d ÷ fᵧ
First
3
×
√
4
,000
=
189.7
psi
≤
200
psi,
so
the
200
psi
floor
governs.
That
stress
times
the
area
bd,
over
fᵧ.
3
×
√
4
,000
≤
200:
200
psi
governs
As,min
=
200
×
12
×
20
60,000
As,min
=
2,400
×
20
60,000
As,min
=
48,000
60,000
As,min = 0.8 in²
Check
Put the numbers back in. Both sides should match.
0.8
=
200
×
12
×
20
60,000
✓
Topic check
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