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A detailed overview of reinforced concrete beam design, focusing on the calculation of moment capacity. It covers key concepts such as the location of the neutral axis (ina), modular ratio, and allowable stresses in both concrete and steel. Formulas and methods for determining the moment capacity of both cracked and uncracked concrete sections, as well as doubly reinforced concrete beams. It also addresses the calculation of cracking moment and the impact of tensile and compressive stresses on the overall design. Useful for students and professionals in civil and structural engineering seeking to understand the principles behind reinforced concrete design and analysis. (410 characters)
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ALD HOOSE
THE
max mum sare
unlpurm
luad Mcap uorrtMmax(
iF
cOtora
D3re yung N.A,
iF
dX
(rteel)
KN-M
INA
= 3 2 t nAs
fe INA
(
corcrete)
KN-n
b(x)()
+(x)(2)
(*)
Ratio
&
proportion (norizotal
dim @NA)
t4ttotwr Resirting Moment)
MA aoe
(Moments
*NASd-x)
tranpOm
ed
MA below
Arm)
To Find
x f
As
Nmm?
(
Area
oF
cteel
Actfs
nM(dx)
INA
trecr
Allouabe
McI INA
Mx 4700
fO Eeoncrete
ESteel 2x MPai
(
modular
ratio)
Selpwegnt.
24 kN
m (iF not given
cONCRETE
CRACKEO
LASTC STRESES
STAGE
smler
Positive
Mc
T
prl MPa,
ksi
for
Mbalance
:
KN/m
I.NA
always
Mor
bh
os,Ascam(
Yi)
dcheckng
cr-ckd
or
Abesn
t
or
AT (9) A1y A2Y
INA
t Ad
2
Eo 400
'c
fC
(
elacticity)
meric
fot <fr
turcr•ed)
fr
Erteei 200GPa
2xoS MPa
metic
ft LO
2P
ft<fr
UNCRACKEO
CONCRETE CHAPTER STAGE
2
(WSO
RCD DATE:
NO.:
pomuto)
abautNA)
Tensile
f
scel (Act)
Njmm?
moduls
oF
Englin)
modulur
of
rupture)
NO.: DATE:
AllboadeSreres(Actual)
X
MC (concrete)
2n(x-d)
(steelcompre«sicn) Mcap
2nM{x-d')
MAavve MAbelw
D(*)()(2Xx)%)+ (2n-1)A's (xa): nAS (d-x)
1 (2n-1)(A)(*d)t nAS (d-x)? INA 3 12
frFNA
MomentoFInertio
Rectargle semi-cirde
bh A-bh 3
Triangle
3TT bh A:on
|2 0-25 Ta`bt Ad
Circle
I: (^025) b A r + Ad
Ar
Spardrel Quartercirce
n
Xc 4
A
YC 4n+ 4r 3T A:
Tab
2
mcap
KNm
Mcap
|75-
51 KN
mcap
X
fc INA
IV-Dn
Concrete
On sttd
I NA
3O
xo mm
250a
2
X
=
02 mm
MAaove
MA beloo
(^250) I
75
2
mm
0
525 i
X
fO
250
ue fc:
lOMPa,
fr
146MP
,
n8,
As
PROBLEM
Determine
the
moment capacity^2800
mm"
cf ne
trapezcidal
bcam ecticn
shan
OFe b0th
concrete
ctodC
4 4B
9.5(
ConcreeMcap
fCTNA
n(d-x)
2n
(x-d')
fr IN
INA
NA *
(2n-1)
A't
AG(a-x)?
X 2):
(^44) mm A
fDO
I50 Ac
35omm
200(
x
(
X-12)
MAove
:
MAelDw
700|40D
2n-1= 2(7-5)
d' 75 mm
A's
»
(200mn
(^2) d 25 mm
fe l
MPa,fS
5 MPa
n7.
PROBLEM. Detemine
box-girder
(teet
comprerron)
fS INA
INA
3 +
(2n-1)(A)
(x-d)
nAs
(d-)
b(x) (2n-1)(As)
(*-d') inAs(d-
x) MAaove
AS
n
d
NA.
(2n-1)A
20
A's
fC
ir
reinForced
in dotn
tension
conprecslon
Doubly
Reintorcc
Concrete
kN-)
steeI Tensian
(2n-1)
A's
(x-a')=