Beams
Rectangle
Analysis
Cracking Moment
Where:
Mcr= Moment
fr=7.5
Ig= Moment of Inertia
Yt=distance from centroid to tensile
fiber
Elastic Stresses Concrete Cracked
T-Beams
Design
Dimensions:
Minimum thickness
from ACI Table 9.5a
Width= thickness
Weight:
w=
Design
Find:
beff=1/4 beam span
8*slab thickness + bw
Clear distance
Check:
beff=1/4 beam span
8*hf + bw
Clear distance
As min
Find:
Assume large of:
Calculate:
N.A
Where:
n=modular ratio
E=modulus of elasticity
(assuming =0.9)
Compare with As min
Transformed Area
Select
Reinforcement:
Where:
b=base
d=distance from center of steel to top
compressive fiber
x=distance from top compressive fiber
to neutral axis
As=Area of Steel
Moment of Inertia
Analysis
If N.A. is in flange:
Trial Steel Area:
New Z
Check:
For Slabs:
Shrink & Temp. Steel
If N.A. is not in flange:
Bending Stresses
Doubly Reinforced Beams
Analysis
Find:
Design
Until As is consistent then compare
with As min
Find:
Ultimate Flexural Moments
Find:
Strength Analysis
If sy:
Check Safety Factor:
If sy:
Solve for c
Then find:
If s0.00207 fs =fy otherwise fs =s Es
If bars are different sizes:
Solve for c
If not strong enough use smaller
compressive steel.
Development Lengths
Where:
cb=Center of tension bar to nearest
concrete surface or center to
center spacing
Ktr=0 (ACIU 12.2.3)
If Bundled Bars:
Imaginary bar centroid is used
Development +20% for 3 bars
+40% for 4 bars
For Hooks:
Shear
Is reinforcement needed:
Calculate Vu at distance d from
support
Calculate:
If
stirrups are needed
Calculate:
Theoretical stirrup spacing-
Where
Maximum spacing for min area
Max Spacing:
Length after turn:
90 degree = 12db
180 degree = 4db
For Compression:
Columns
Axially Loaded:
Find Area of Concrete (Ag):
Assuming Ast=0.02Ag
Then Find Ast with selected Ag
Ties- =0.65
Spacing of ties = lesser of
16*longitudinal bar diameter or
48*tie diameter (#3bar ties for
#10 or smaller long. Bars, #4 for
larger)
Spiral-=0.75
Find Ac (area of core inside the
spiral)
Solve for spacing (s)
Where
Check V at different distances for
spacing changes.
Simple Beam Deflections
Instantaneous dead load-
Footings
WallAssume 12 in h with d=8.5in
Eccentricly Loaded:
Plastic Centroid-
Find Required Depth
Where bw =base width (assumed 1ft for wall
footing)
If d is metWhere a is the column width
Find steel as usual
Find Development Length
Longitudinal Temp & Shrinkage steel
Rectangular footings-
Reduction Factor:
DesignSplices
Compresssion:
for 60kpsi or less
for 60kpsi
Tension:
Find Transformed area &
moment of inertia as on the
front.
Depth Required for 2 way (punch)
If MaMcr Ma=Mcr
,
,
Find g on Interaction diagram
Calculate:
Depth Required for 1 way shear
Otherwise:
Crack Width (Gergely-Lutz)
Where:
h=ratio of distance to NA from
extreme tensile concrete to
extreme tensile steel
fs=0.6fy
dc=Outermost cover to centroid of
bar
A=tension area of concretecentroid of bars to outer layer
divided by the number of bars
Properties
Span Formulas
Inst. Dead + Live:
As with dead only
Simple-
If all depths are ok-
Fixed-
Combined footing:
Find Center of gravity-
Cantilever-
Footing length =2x+distance to property line
Footing Width = x
Create sheer & Moment diagrams solve as
Rectangular footing.
Inst. Live
Long Term
Where:
=Time factor (2 for 5+yrs, 1.4
for 1 yr, 1.2 for 0.5yr, 1 for 3
months)
=compression steel
