internal loading developed in structural...
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![Page 1: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/1.jpg)
Chapter 4Chapter 4
Internal Loading Developed in Structural Members
![Page 2: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/2.jpg)
Chapter 4
Internal Loading Developed in Structural
Members
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Internal loading at a specified Point
In General
• The loading for coplanar structure will
consist of a normal force N, shear force V,
and bending moment M.
• These loading actually represent the resultants
of the stress distribution acting over the member’s
cross-sectional are
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Sign Convention+ve Sign
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Procedure for analysis
• Support Reaction
• Free-Body Diagram
• Equation of Equilibrium
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Example 1Determine the internal shear and moment acting in the
cantilever beam shown in figure at sections passing through
points C & D
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mkNM
MM
kNV
V F
c
cC
C
Cy
.50
020)3(5)2(5)1(5 0
15
05550
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mkNM
MM
kNV
V F
D
DC
C
Dy
.50
020)3(5)2(5)1(5 0
20
055550
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Example 2
kNRR BA 9
mkNM
MM
kNV
V F
D
y
.12
0)2(9)1(6 0
3
0690
sectionat
6kN
Determine the internal shear and moment acting in section 1 in the
beam as shown in figure18kN
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Example 3Determine the internal shear and moment acting in the
cantilever beam shown in figure at sections passing through
points C
![Page 11: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/11.jpg)
ftkM
MM
kV
V F
D
c
Cy
.48
0)6(9)2(3 0
6
0390
c
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Shear and Moment functionProcedure for Analysis:
1- Support reaction
2- Shear & Moment Function
Specify separate coordinate x and associated origins, extending
into regions of the beam between concentrated forces and/or
couple moments or where there is a discontinuity of distributed
loading.
Section the beam at x distance and from the free body diagram
determine V from , M at section x
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Example 4Determine the internal shear and moment Function
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Example 5Determine the internal shear and moment Function
![Page 15: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/15.jpg)
151
302
xw
2
12
2
2
12
3
0 30 015
30 0.033
0 30( ) 600 015 3
600 30 0.011
y
S
xF V
V x
x xM M x
M x x
w 2
30x
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Example 6Determine the internal shear and moment Function
![Page 17: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/17.jpg)
2
11
211S
1
1
1
21081588
041081588 0
4108
041080
120
1
xxM
xxMM
xV
xV F
x
x
y
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130060
06481081588 0
60
0481080
2012
2
22S
2
xM
xxMM
V
V F
x
y
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Example 7Determine the internal shear and moment Function
![Page 20: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/20.jpg)
920
xw
12
2
12 2
2 3
0 75 10 (20) 09
75 10 1.11
0 75 10 (20) 09 3
75 5 0.370
y
xS
xF V x x
V x x
x xM M x x x
M x x x
w 20
9x
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Shear and Moment diagram for a Beam
![Page 22: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/22.jpg)
2O
)(
0)()( 0
)(
0)()(0
xxwxVM
MMxxxwMxVM
xxwV
VVxxwV Fy
dxxVMVdx
dM
dxxwVxwdx
dV
xfor
)(
)( )(
0
![Page 23: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/23.jpg)
When F acts downward on the beam, ∆𝑉 is negative so that the
shear diagram shows a “jump” downward.
Likewise, if F acts upward, the jump is upward.
Internal Shear due to concentrated Load
![Page 24: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/24.jpg)
If an external couple moment M’ is applied clockwise, ∆𝑀 is positive, so
that the moment diagram jumps downward,
and
when M’ acts counterclockwise, the jump must be upward.
Internal Moment due to concentrated moment
![Page 25: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/25.jpg)
Example 8Draw shear force
and Bending
moment Diagram
B.M.D
S.F.D
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Example 9Draw shear force
and Bending
moment Diagram
S.F.D
B.M.D
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Example 10Draw shear force
and Bending moment
Diagram
18 kN
Max. moment at x = L/2
then
8
2222
2
max
2
wLM
LwLwLM
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Example 11Draw shear force and Bending moment Diagram
![Page 29: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/29.jpg)
S.F.D
B.M.D
![Page 30: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/30.jpg)
Draw shear force
and Bending
moment Diagram
Example 12
49
)7(14)5.3(14
7
142
M
MM
x
x
S
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Example 13aDraw shear force
and Bending
moment Diagram
S.F.D
B.M.D
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Example 13bDraw shear force
and Bending
moment Diagram
S.F.D
B.M.D
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Example 13cDraw shear force
and Bending
moment Diagram
S.F.D
B.M.D
![Page 34: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/34.jpg)
Example 13dDraw shear force
and Bending
moment Diagram
![Page 35: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/35.jpg)
![Page 36: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/36.jpg)
![Page 37: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/37.jpg)
Draw shear force and Bending moment Diagram
Example 14
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32
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Draw shear force and Bending moment Diagram
Example 15
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V(kN)
![Page 41: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/41.jpg)
Example 16Draw shear force and Bending moment Diagram
![Page 42: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/42.jpg)
+
![Page 43: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/43.jpg)
Example 17Draw shear force
and Bending
moment Diagram
99
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Example 18Draw shear force and Bending moment Diagram
![Page 45: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/45.jpg)
![Page 46: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/46.jpg)
Sketch BMD
![Page 47: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/47.jpg)
Sketch BMD
![Page 48: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/48.jpg)
Sketch BMD
![Page 49: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/49.jpg)
Example 19Draw shear force and Bending moment Diagram
![Page 50: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/50.jpg)
++
+
+
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Problem 1
Draw shear force and Bending moment Diagram
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Example 20
Draw shear force and Bending moment Diagram
![Page 53: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/53.jpg)
486
30.5 23.5
+
+
-
-
![Page 54: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/54.jpg)
Example 21
Draw shear force and Bending moment Diagram
![Page 55: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/55.jpg)
kE
E
EF
kC
CM
kA
AM
y
y
xx
y
yE
y
yleftB
6
045420518 0F
0 0
45
060)32(4)27(20)16(5)6(18)12( 0
4
060)5(20100
y
Reaction Calculation
![Page 56: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/56.jpg)
![Page 57: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/57.jpg)
Frame Structures (Example 1)
Draw Bending moment Diagram
![Page 58: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/58.jpg)
Support reaction & Free Body diagram
![Page 59: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/59.jpg)
![Page 60: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/60.jpg)
_ _
S.F.D B.M.D
![Page 61: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/61.jpg)
+
-
S.F.D
B.M.D
![Page 62: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/62.jpg)
-
B.M.D
-
15k.ft
15+
-
S.F.D
3
1
-
N.F.D
3-
![Page 63: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/63.jpg)
Frames (Example 2)
Draw shear force and Bending moment Diagram
![Page 64: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/64.jpg)
![Page 65: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/65.jpg)
N.F.D
S.F.D
B.M.DN.F.D S.F.DB.M.D
N.F.D
+
+
+
_
+
+
-
-
![Page 66: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/66.jpg)
Frames (Example 3)
Draw shear force and Bending moment Diagram
![Page 67: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/67.jpg)
![Page 68: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/68.jpg)
B.M.DN.F.D S.F.D
-
--
![Page 69: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/69.jpg)
_
+
+
N.F.D
S.F.D
B.M.D
251.6
64
26
![Page 70: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/70.jpg)
B.M.D
N.F.D
S.F.D
168
![Page 71: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/71.jpg)
S.F.D
B.M.D
168
432 139.3
251.6
432
36
64
26
13.22
31.78
+
_
_
+
_
_
+
![Page 72: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/72.jpg)
Frames (Example 4)
Draw shear force and Bending moment Diagram
![Page 73: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/73.jpg)
![Page 74: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/74.jpg)
![Page 75: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/75.jpg)
+
+
S.F.D
B.M.D
![Page 76: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/76.jpg)
+
_ S.F.D
B.M.D
![Page 77: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/77.jpg)
Frames (Example 5)
Draw shear force and Bending moment Diagram
![Page 78: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/78.jpg)
![Page 79: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/79.jpg)
Frames (Example 6)
Draw shear force and Bending moment Diagram
![Page 80: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/80.jpg)
![Page 81: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/81.jpg)
_
_
_
N.F.D S.F.D B.M.D
![Page 82: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/82.jpg)
+
_
+
_
__
+
N.F.D
S.F.D
B.M.D
![Page 83: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/83.jpg)
_
+
_
N.F.DS.F.DB.M.D
![Page 84: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/84.jpg)
Problem 1
Draw Normal force, shear force and Bending moment Diagram
![Page 85: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/85.jpg)
Problem 2
Draw Normal force, shear force and Bending moment Diagram
![Page 86: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/86.jpg)
Problem 3
Draw Normal force, shear force and Bending moment Diagram
![Page 87: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/87.jpg)
Frames (Example 5)Draw Normal force, shear force and Bending moment Diagram
![Page 88: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/88.jpg)
10kN/m
60kN
26.56o
53.726.8
47.7
43.2
10.5
20.8
110
![Page 89: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/89.jpg)
N.F.D S.F.D B.M.D
S.F.D
B.M.D
![Page 90: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/90.jpg)
N.F.D
S.F.D
B.M.D
![Page 91: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/91.jpg)
B.M.D
![Page 92: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/92.jpg)
Moment diagram constructed by the
method of superposition
Example 1
![Page 93: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/93.jpg)
![Page 94: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/94.jpg)
![Page 95: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/95.jpg)
Example 2.a
![Page 96: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/96.jpg)
![Page 97: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/97.jpg)
Example 2.b
![Page 98: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/98.jpg)
![Page 99: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/99.jpg)
Problem 4
Draw Normal force, shear force and Bending moment Diagram
![Page 100: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/100.jpg)
Problem 5
Draw Normal force, shear force and Bending moment Diagram
![Page 101: Internal Loading Developed in Structural Memberssite.iugaza.edu.ps/marafa/files/Chapter-4-2019.pdfChapter 4 Internal Loading Developed in Structural Members Internal loading at a specified](https://reader033.vdocuments.mx/reader033/viewer/2022060405/5f0f260b7e708231d442ba4c/html5/thumbnails/101.jpg)
Problem 6
Draw Normal force, shear force and Bending moment Diagram