1. تتتتت تتتتت
تتتتتتت
20132013
ALB
Dr. Eng. ALaa Ali Bashandy
Menufiya Unv.
Design of Reinforced ConcreteDesign of Reinforced Concrete
StructuresStructures
Design of R. C. Beams
Dr. ALaa Ali Bashandy
4. ALB Dr. Eng. ALaa Ali Bashandy
Members
of
Concrete
Construction
Members
of
Concrete
Construction
Slabs
Beams
Column
Footing
Shallow found.
Deep found.
Solid Slabs
Hollow Block Slabs
Flat Slabs
Paneled Beam system
Isolated Footing
Combined Footing
Strip Footing
Raft/ Mat found.
Friction Pile
Bearing Pile
Axially Loaded Col. Eccentric Loaded Col.or
Simple Beam Continuous Be. Cantilever Beamoror
Dropped Beam Inverted Beam Hidden Beamor or
Long Column Short Columnor
Rectangular Column Circular Columnor
Braced Column Unbraced Columnor
Structural
Sys.
Position ref.
to slab
Loads
Design
Section
Bracing
Design of R. C. Beams
6. ALB
Cross Sections of BeamsCross Sections of Beams
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
7. BeamsBeams
Referring to its position comparing to slabsReferring to its position comparing to slabs
ALB
Hidden BeamDropped Beam Inverted Beam
bb
slabslab
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
8. BeamsBeams
Referring to its position comparing to slabsReferring to its position comparing to slabs
BeamsBeams
Referring to its position comparing to slabsReferring to its position comparing to slabs
ALB
Hidden BeamHidden BeamDropped BeamDropped Beam Inverted BeamInverted Beam
Dr. Eng. ALaa Ali Bashandy
9. 21
Sec. 2Sec. 1
1 1 2 2
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
10. Sec. 2Sec. 1
T – Sec.((
211 1 2 2
R – Sec.((
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
11. 211 1 2 2
Sec. 2Sec. 1
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
12. Sec. 2Sec. 1
L – Sec.((
211 1 2 2
R – Sec.((
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
15. Different Cases for One-way SlabDifferent Cases for One-way Slab
Cantilever one-way slabCantilever one-way slab
2.0
L
L
S
≥
LLSS
LL
LLSS LLCC
Load DistributionLoad Distribution from one-way slabfrom one-way slab
One-way slabOne-way slab
One directionOne direction
22--sidessides
One directionOne direction
22--sidessides
One directionOne direction
11--sideside
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
17. Load DistributionLoad Distribution from two-way slabfrom two-way slab
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
Load from slab
L
B1
B2Ls
Two-way S.
Slab
2.00
L
L
s
<
L
Ls
B1
B2
18. Two-way S. Slab 2.00
L
L
s
<
L
Ls
B1
B2
L
B1
Wa
L
L
We
Equivalent load forEquivalent load for ShearShear (Wa or Wβ(
Equivalent load forEquivalent load for MomentMoment ( We or Wα(
Momentfor))L/L(
3
1
-1(Cα
Shearfor))L/L(
2
1
-1(Cβ
2
se
sa
==
==
for Trapezoidal Load only
t/m( )[ ]WallS O.WtO.Wtx1.4Cax
2
L
Wu B1
s
XB1Wa ++
=
t/m
Load DistributionLoad Distribution from two-way slabfrom two-way slab
( )[ ]WallS O.WtO.Wtx1.4Cex
2
L
Wu B1
s
xB1We ++
=
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
19. L
Ls
B1
B2
Wa
LS
LS
We
Equivalent load forEquivalent load for ShearShear (Wa or Wβ(
Equivalent load f orEquivalent load f or MomentMoment (We or Wα(
for Triangle Load only
t/m
t/m
B2
Ls
Momentfor32Cα
Shearfor21Cβ
e
a
==
==
( )[ ]WallS O.WtO.Wtx1.4Cax
2
L
Wu B2
s
x2BWa ++
=
( )[ ]WallS O.WtO.Wtx4.1Cex
2
L
Wu B2
s
x2BWe ++
=
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
20. 2
L
L1 >1.1.
L
L
L1
( )
++=
==
wall
W
B
O.Wtx1.4sx Wu
L
Area
ShearforLoadMomentforLoadWB
2
L
L1 <22..
L1 L1
LL
L1
L
Special Cases of LoadingSpecial Cases of Loading
L
L1
( )
++=
==
wall
W
B
O.Wtx1.4sx Wu
L
Area
ShearforLoadMomentforLoadW
1
B
oror
oror
WB
WB
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
29. WBeam (t/m’
) = (Wall Wt. + O. Wt.Beam ) x 1.4 + Wus (From slab)
1.Dead Load (D.L)
22
3
P.C
3
R.C
R.C
ConcreteR.Concrete
t/m0.15kg/m150C.FL.
t/m2.2γ&t/m2.5γ
γ*1.0x1.0xt
x γVW
)F.C(coverfloor-2
(O.Wt)slabofOwn weight-1
s
==
==
=
=
2.Live Load ( L .L)
3.Total Load ( T.L)
Load ValuesLoad Values
1.00m
ts
1.00m
From SlabFrom Slab
From BeamFrom Beam
R.CBConcreteR.Concrete
γxbxtxVW
)W(BeamofOwn weight-1
γWt.O
Wt.O
==B
B
From WallsFrom Walls
( )
cm2512b3t/m15001200
xhxbxtxVW
wWall
Wall
wwWallwallwall
γ
γγ
→=→
==
=
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
according to code
30. Live Load ValuesLive Load Values According to Egyptian CodeAccording to Egyptian Code
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
31. tB min = 40 cm
Cantilever Beam
Estimation of tEstimation of tBB
t B min = Leff / 16 Leff / 18 Leff / 21 Lc / 5
it is required to check deflection if the span < 10 m
for High Tensile Steel 400/600 (H.T.S)
t B min = previous values ÷ ( 0.4 + fy / 650)
for any other steel type fy / fu
Simple Slab
Continuous Slab
From tow side
Continuous Slab
From one side
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
32. but not less thanbut not less than 40 cm40 cm
Cantilever Beam
Value of tValue of tBB
t B = span / 10 span / 12 Lc / 5
GenerallyGenerally
Simple Slab
Continuous Slab
From tow side
Continuous Slab
From one side
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
33. LLSS
WWuu t/mt/m
/24WL2
/24WL2
/24LW
2
22
/24LW 2
11
/8WL2
/9WL2
/11LW
2
11 /11LW
2
22
/10WL2
/12LW
2
11 /16LW
2
22
/12WL2
/16LW
2
33
/24LW 2
11
minmin MM + ve+ ve==
8
LxuW 2
Moment ValuesMoment Values
Simply supportedSimply supported continuous two spanscontinuous two spans
continuous more than two spanscontinuous more than two spans
Empirical values for B.MEmpirical values for B.M (Max difference in(Max difference in loadload && spanspan ≤≤ 20%20% and D.L >L.L )and D.L >L.L )
Dr. Eng. ALaa Ali Bashandy
Design of R. C. Beams
34. MM supportsupport
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
)L'L'(8.5
L'WL'W
21
3
22
3
11
supportMLoadUniform
+
+
=
)L'L'(
L'PkL'Pk
21
2
222
2
111
supportMLoadedConcentrat
+
+
=
L1
m
W2
L2
m
W1
L1
m
L2
m
P1 P2
a1 a2
L m
L’ = L
L m
L’ = 0.8L
a1 / L1 & a2 / L2 0.3 0.4 0.5 0.6 0.7
K1 & k2 0.168 0.182 0.176 0.158 0.128
In case of:In case of: difference indifference in loadload oror spanspan ≥≥ 20%20%
35. Shear ValuesShear Values
Simply supported beamSimply supported beam
Continuous two spansContinuous two spans
Continuous more than two spansContinuous more than two spans
Dr. Eng. ALaa Ali Bashandy
Design of R. C. Beams
Lm
a b
0.5 W L
S.F.D
+
0.5 W L
-
L1
m
a
0.4 W1 L1
+
0.6 W1 L1
-
L2
m
C
0.6 W2 L2
S.F.D +
0.4 W2 L2
-
b
L1
m
a
0.4 W1 L1
+
0.6 W1 L1
-
L2
m
C
0.5 W2 L2
+
0.5 W2 L2
-
b
-
L3
m
0.5 W3 L3
S.F.D
+
36. Possible cases of bPossible cases of b
Estimation of bEstimation of b
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
Rectangular sectionRectangular section R-sec.R-sec.
T - sec. → internal beamT - sec. → internal beam
L - sec. → edge beamL - sec. → edge beam
R - sec.R - sec.
T - sec.T - sec. L - sec.L - sec.
::Values of bValues of b
16 t16 t ss + b+ b
LL22 / 5 + b/ 5 + b
CL. to CL.CL. to CL.
6 t6 t ss + b+ b
LL22 / 10 + b/ 10 + b
½½ CL. to CL.CL. to CL.
bb
LL22 = L= L LL22 = 0.8 L= 0.8 L LL22 = 0.7 L= 0.7 L LL22 = 2 L= 2 L
b.F
M
Cd
cu
u
1=
Least of :Least of :
37. Given : M u , t s , b =100 cm , Fcu , Fy
Req. : As
d = ts - c (cover) c = 20 - 50 mm(cover) c = 20 - 50 mm
AS min = 0.15 % Ac H.T.S 360/520
= 0.25 % Ac for Mild steel 240/350
.....J.....C
b.F
M
Cd 1
cu
u
1 ===
m′== /cm........
f.d.J
Mu
As 2
y
Ac = b x d
Design of SectionDesign of Section
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
AS max = 0.4 % Ac recommended
38. CC1 & J& J
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
39. ALB
Shear Behavior of BeamsShear Behavior of Beams
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
40. Choice of Shear ValuesChoice of Shear Values
Simply supported beamSimply supported beam
Continuous two spansContinuous two spans
Continuous more than two spansContinuous more than two spans
Dr. Eng. ALaa Ali Bashandy
Design of R. C. Beams
S.F.D
Chose the larger value of shear along the beam span - axisChose the larger value of shear along the beam span - axis Qmax
Lm
a b
0.5 W L
S.F.D
+
0.5 W L
-
Q1
Q2
L1
m
a
0.4 W1 L1
+
0.6 W1 L1
-
L2
m
C
0.6 W2 L2
S.F.D +
0.4 W2 L2
-
b
Q1
Q2
Q3
Q4
L1
m
a
0.4 W1 L1
+
0.6 W1 L1
-
L2
m
C
0.5 W2 L2
+
0.5 W2 L2
-
b
-
L3
m
0.5 W3 L3
+
Q5
Q4Q2
Q3
Q1
41. Critical Sections of ShearCritical Sections of Shear
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
42. Shear Limitations of BeamsShear Limitations of Beams
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
43. Check of ShearCheck of Shear
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
44. Cases of qCases of quu
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
45. Check of ShearCheck of Shear
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
46. Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
47. Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
48. Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
58. Using Straight RebarsUsing Straight Rebars
22--spans Beamspans Beam
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
59. Using Straight RebarsUsing Straight Rebars
More than 2-spans BeamMore than 2-spans Beam
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
60. Using Straight RebarsUsing Straight Rebars
Over hanging BeamOver hanging Beam
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
61. Using Straight RebarsUsing Straight Rebars
Cantilever BeamCantilever Beam
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
62. Using Bent RebarsUsing Bent Rebars
Simple BeamSimple Beam
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
63. Using Bent RebarsUsing Bent Rebars
22--spans Beamspans Beam
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
64. Using Bent RebarsUsing Bent Rebars
More than 2-spans BeamMore than 2-spans Beam
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
65. Using Bent RebarsUsing Bent Rebars
Cantilever BeamCantilever Beam
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
66. Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
67. ExampleExample::
For the given plan it is required to:
Calculate loads for slabs & Beams
Data:
FL.C = 150 kg/m2
L.L = 300 kg/m2
Steel Grade 360/520
SolutionSolution::
Slabs
D.L = (0.12 m * 2.5 t/m3
)+ 0.15 t/m2
= 0.45 t/m2
L.L = 0.3 t/m2
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
Wus = 1.4 x 0.45 t/m2
+ 1.6 x 0.3 t/m2
= 1.11 t/m2
To have slab thickness ts
S1 → ts = 400/40 = 10 cm
S2 → ts = 300/45 = 6.67 cm
S3 → ts = 500/45 = 11.1 cm
take ts = 12 cm
68. Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
1.5
4
6
r ==For S1
→trapezoidal Ca = 0.67 & Ce = 0.85
→triangle Ca = 1/2 & Ce = 2/3
1.33
3
4
r ==For S2
→trapezoidal Ca = 0.63 & Ce = 0.81
→triangle Ca = 1/2 & Ce = 2/3
1.2
5
6
r ==For S3
→trapezoidal Ca = 0.582 & Ce = 0.769
→triangle Ca = 1/2 & Ce = 2/3
1.67
3
5
r ==For S4
→trapezoidal Ca = 0.701 & Ce = 0.881
→triangle Ca = 1/2 & Ce = 2/3
69. Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
W4 ( Wa & We) t/m
6m
B1 B2
BeamsBeams
O. wt. of beam = 0.25 x 0.6 x 2.5 t/m3
= 0.375 t/m
( ) ( )
t/m'2.951.2x1.4t/m0.375x1.4
2
m1.5
xt/m1.11
x W4.1wt.O.x1.4
2
L
xWuWW
2
wall
s
s4e4a
=++
=
++
==
B4 tB = span / 10 = 600 / 10 = 60 cm
take tB = 60 cm
Wall weight = Wwall = 0.25 (width) x 2.7 (height) x 1.8 (γwall = 1.2 – 1.8 t/m3
) = 1.2 t/m
2.95 t/m
6m
13.275 m.t
8.85 t 8.85 t
B1 B2
B. M. D.
70. B1
( ) ( )
( ) ( ) t/m'3.2281.2x1.4t/m'0.3125x1.4
2
1
x
2
m4
xt/m1.11
x W1.4wtO.x1.4Cx
2
L
xWuW
2
walla
s
sa1
=++
=
++
=
( ) ( )
( ) ( ) t/m'3.6051.2x1.4t/m'0.3125x1.4
3
2
x
2
m4
xt/m1.11
x W1.4wtO.x1.4Cx
2
L
xWuW
2
walle
s
se1
=++
=
++
=
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
4 m 5 m 1.5 m
8.85 t
a b c
d
Part ab
Part bc
Part cd
t/m'2.11751.2x1.4t/m'0.3125x1.4WW e3a3 =+==
( ) ( )
( ) ( ) t/m'3.5051.2x1.4t/m'0.3125x1.4
2
1
x
2
m5
xt/m1.11
x W1.4wtO.x1.4Cx
2
L
xWuW
2
walla
s
sa1
=++
=
++
=
( ) ( )
( ) ( ) t/m3.9771.2x1.4t/m'0.3125x1.4
3
2
x
2
m5
xt/m1.11
x W1.4wtO.x1.4Cx
2
L
xWuW
2
walle
s
se1
=++
=
++
=
71. Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
3.228 t/m 3.505 t/m
4 m 5 m
Shear
G2G1 G3
B1
1.5 m
3.605 t/m 3.977 t/m
4 m 5 m
Moment
G2G1 G3
1.5 m
2.1175 t/m
8.85 t
8.85 t
Moment Values of B1
W2L2
2
/9
W1L1
2
/9
or
W1L1
2
/11 W2L2
2
/11
WcLc
2
/ 2
Msupp. = 9.514 m.t
6.214 m.t5.244 m.t
P x Lc + WcLc
2
/ 2 = 15.66 m.t
B. M. D.
72. O. wt. of beam = 0.25 x 0.5 x 2.5 t/m3
= 0.3125 t/m
( ) ( )
t/m'4.2761.2x1.4t/m'0.3125x1.40.63x
2
m3
xt/m1.11
2
1
x
2
m4
xt/m1.11
x W4.1wt.O.x1.4Cx
2
L
xWuW
22
walla
s
sa2
=++
+
=
++
=
( ) ( )
t/m'4.9541.2x1.4t/m'0.3125x1.40.81x
2
m3
xt/m1.11
3
2
x
2
m4
xt/m1.11
x W1.4O.wtx1.4Cx
2
Ls
xWuW
22
wallese2
=++
+
=
++
=
B2
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
tB = span / 12 = 500 / 12 = 41.67cm
take tB = 50 cm
Part ab
Part bc
t/m'4.4751.2x1.4t/m'0.3125x1.40.582x
2
m3
xt/m1.11
2
1
x
2
m5
xt/m1.11W 22
a2 =++
+
=
t/m'5.2571.2x1.4t/m'0.3125x1.40.769x
2
m3
xt/m1.11
3
2
x
2
m4
xt/m1.11W 22
e2 =++
+
=
4.275 t/m 4.475 t/m
2.1175 t/m
4 m 5 m 1.5 m
Shear
4.954 t/m 5.257 t/m
2.1175 t/m
4 m 5 m 1.5 m
Moment
Part cd
t/m'2.11751.2x1.4t/m0.3125x1.4WW e2a2 =+==
4 m 5 m 1.5 m
R B4
a b c
d
73. B2
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
4.954 t/m 5.257 t/m
4 m 5 m 1.5 m
8.85 t
2.1175 t/m
0.4x4.276x4 = 6.84 t
0.4x4.475x5 + 8.85 = 17.8 t
L1
m
a
0.4 W1 L1
+
0.6 W1 L1
-
L2
m
C
0.6 W2 L2
S.F.D +
0.4 W2 L2
-
b
Q1
Q2
Q3
Q4
0.6x4.276x4 = 10.26 t
0.6x4.475x5 = 13.43 t
Wc Lc
3.176 t
8.85 t
+ 8.85 t
4.275 t/m 4.475 t/m 2.1175 t/m
4 m 5 m
1.5 m
Shear
G2G1 G3
8.85 t
W2L2
2
/9
W1L1
2
/9
or
W1L1
2
/11 W2L2
2
/11
WcLc
2
/ 2
Moment Values of B2
10.67 m.t6.656 m.t
P x Lc + WcLc
2
/ 2 = 15.66 m.t
Msupp. = 12.734 m.t
B. M. D.
= 8.81 m.t
= 14.61 m.t
74. B3
( ) ( )
( ) ( ) ( ) t/m'4.2761.2x1.4t/m'0.3125x1.4m1xt/m1.110.63x
2
m3
xt/m1.11
x W1.4wtO.x1.4Cx
2
L
xWuW
22
walla
s
sSpanLefta3
=+++
=
++
=
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
( ) ( )
( ) ( ) ( ) t/m'4.3951.2x1.4t/m'0.3125x1.4m1xt/m1.110.701x
2
m3
xt/m1.11
x W1.4wtO.x1.4Cx
2
L
xWuW
22
walla
s
sSpanRighta3
=+++
=
++
=
Part ab
Part bc
( ) ( )
( ) ( ) ( ) t/m'4.5761.2x1.4t/m'0.3125x1.4m1xt/m1.110.81x
2
m3
xt/m1.11
x W1.4wtO.x1.4Cx
2
L
xWuW
22
walle
s
sSpanLefte3
=+++
=
++
=
( ) ( )
( ) ( ) ( ) t/m'4.6941.2x1.4t/m'0.3125x1.4m1xt/m1.110.881x
2
m3
xt/m1.11
x W1.4wtO.x1.4Cx
2
L
xWuW
22
walle
s
sSpanRighte3
=+++
=
++
=
a b c
75. Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
4.276 t/m 4.395 t/m
4 m 5 m
Shear
G2G1 G3
4.576 t/m 4.694 t/m
4 m 5 m
Moment
G2G1 G3
W2L2
2
/9
W1L1
2
/9
or
W1L1
2
/11 W2L2
2
/11
B3
Moment Values of B3
13.04 m.t
10.67 m.t6.656 m.t
B. M. D.
76. Main Beams (GirdersMain Beams (Girders))
6.842 t
6.0m 3.0m
G1
RB2 at point a = 0.4 x (4.267 t/m
x 4 m) = 6.842 t
WG1 (wa = we = 3.732 t/m(
( ) ( )
( ) ( ) t/m'3.7321.2x1.4t/m'0.5625x1.4
m9
m1.5xm3x
2
1
m2x
2
m6m2
xt/m1.11
x W1.4wtO.x1.4
Span
Area
WWW
2
wallG1eG1aG1
=++
+
+
=
++===
∑
RB2
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
O. wt. of main beam/ girder = 0.25 x 0.9 x 2.5 t/m3
= 0.5625 t/m
tG = span / 10 = 900 / 10 = 90 cm
take tG = 90 cm
77. 6.842 t
6.0m 3.0m
WG1 (wa = we = 3.732 t/m(
RB2
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
47.29 m.t
21.36 t19.075 t
Mmax = 48.75 m.t
Distance 5.11 m from left supp.
G1
B. M. D.
78. G2
WG2 (wa = we = 4.997 t/m
(
6.0m 3.0m
RB2
23.69t
RB2 at point b = Wa2 * L = 4.276 t/m
x 4 m + 4.475 t/m
x 5 m = 23.69 t
( ) ( )
( ) ( ) t/m'4.8841.2x1.4t/m'0.5625x1.4
m9
2xm1.5xm3x
2
1
m2.5x
2
m6m1
m2x
2
m6m2
xt/m1.11
x W1.4wtO.x1.4
Span
Area
WWW
2
wallG2eG2aG2a
=++
+
+
+
+
=
++===
∑
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
79. WG2 (wa = we = 4.997 t/m(
6.0m 3.0m
RB2
23.69t
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
91.33 m.t
37.77 t29.87 t
G2
B. M. D.
80. 20.455 t
G3
RB2 at point c = 0.4 x W L + P + M/L = 6.842 t
WG3 (wa = we = 4.38 t/m
(
( ) ( )
( ) ( )
t/m'4.38
1.2x1.4t/m'0.5625x1.4
m9
m6x
2
1.5
m1.5xm3x
2
1
m2.5x
2
m6m1
xt/m1.11
x W1.4wtO.x1.4
Span
Area
WWW
2
wallG3eG3aG3
=
++
+
+
+
=
++===
∑
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
RB2 at point c = 0.4 x 4.475 x 5 + 8.85 + (8.85x1.5 + (2.1175 x (Lc
2
/2))/5) = 20.455 t
81. Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
20.455 t
WG3 (wa = we = 4.38 t/m
(
80.34 m.t
G3
33.35 t26.53 t
B. M. D.
83. ALB
Design of R. C. Beams
Dr. Eng. ALaa Ali Bashandy
Dr. ALaa A. Bashandy
E-Mail : Eng_ ALB@yahoo.com
1.1.ECP 203-2007ECP 203-2007
2.2.2032007.
3.3.2032007.
4.4.Design of R. C. StructuresDesign of R. C. Structures– - Vol. 1, 2, 3Vol. 1, 2, 3