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7/25/2019 3 Pinned Portal Frames
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PORTAL FRAME STRUCTURES
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PORTAL FRAME STRUCTURES
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PORTAL FRAME STRUCTURES - ANALYSIS
PINNED BASE
PORTAL FRAME
A
HAHE
B
E
D
VA VE
3 equations :
M=0, V=0 & H=0
BUT
4 UNKNOWNS :-
HA, VA, VE& HE !!!!
SOLUTION:- Introduce an INTERNAL PIN at, say, position C ......
Hence an extra equation is generated, MC= 0 (4 unknowns & 4 equations)
C
internal pin,
BM = 0
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PORTAL FRAME STRUCTURESSIGN CONVENTION FOR BENDING
MOMENT AND SHEAR FORCE
NEGATIVEBENDING MOMENT
AND
SHEAR FORCE
POSITIVE
BENDING MOMENTAND
SHEAR FORCE
A
B
E
DC
A
B
E
DC
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WORKED EXAMPLE3 PINNED FRAME (SUPPORT REACTIONS)
HE
VE
5 kN/m
15 kN/m
1m1m 2m2m
4m
25 kN
C
25 kN
AHA
B
E
D
VA
M@A, M = 0:-
(15 x 4 x 2) + (25 x 2) + (5 x 6 x 3)
+ (25 x 4)6VE= 0
360 = 6VE or VE= 60 kN ()
M@C (pin), for RHS of frame, MC=0 :-
(25 x 1) + (5 x 3 x 1.5) + 4HE3VE = 0
4HE= 18047.5 or HE= 33.1 kN ()
V = 0 :-
VA+ VE= 80 VA = 20 kN (
)
H = 0 :-
HA+ HE= (15 x 4) or HA = 26.9 kN ()
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NBD (33.1)
MBD= 12.4 (-ve BM)
SBD(20)
Beam BC - D
WORKED EXAMPLE3 PINNED FRAME ( COLUMN AB )
COLUMN A - B
15 kN/m
4m
A26.9 kN
20 kN
B
MBA
MBA= (26.9 x 4)(15 x 4 x 2) =12.4 kNm
SBA
SBA= 26.9 15 x 4 =33.1 kN
NBA
NBA= 20 kN
BM at mid-span AB
= (26.9 x 2)(15 x 2 x 1) = 23.8 kNm
SBA
MBA
NBA
Forces (shown +ve)
at top of column,
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WORKED EXAMPLE3 PINNED FRAME (BM DISTRIBUTION BEAM B - C - D)
M at x = 0m = - 12.4 kNm
M at x = 2m = - 12.4 + ( 20 x 2 )( 5 x 2 x 1 ) = 17.6 kNm
x
1m
NBD (33.1)
MBD= 12.4 (-ve BM)
SBD(20)
Beam BC - D
25 kN 25 kN
2m1m
2m
5 kN/m
M at C (pin) = - 12.4 + ( 20 x 3 )( 5 x 3 x 1.5 )( 25 x 1 ) = 0 kNm
(OK re pin)
M at x = 4m = - 12.4 + ( 20 x 4 )( 5 x 4 x 2 )( 25 x 2) = - 22.4 kNm
Actually =
0.1 but OK
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WORKED EXAMPLECOLUMN D - E
MDE= (33.1 x 4) = 132.4 kNm ( -ve sign)
MDB
Beam BC - D
MDE
COLUMN D - E
4m
E33.1 kN
60 kN
D
33.1 kN
(SDE)
MDB= 132.4 kNm ( -ve sign)
NDE = 60 kN
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3 PINNED FRAME (BENDING MOMENT DIAGRAM)
+
+--
C
B
E
D
A
23.8
12.4
17.6
132.4
132.4
2m
2m
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3 PINNED FRAME (SHEAR FORCE DIAGRAM)
+
+
+-
33.1 CB
E
D
A
20
26.9
33.110
15
25
50
60
33.1
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CLASS EXAMPLE/TUTORIAL3 PINNED FRAME
(SUPPORT REACTIONS)
(i) Calculate the values of the support reactions
(ii) Draw BMD and SFD
VE
HE
15 kN/m
6 kN/m
1m1m
6m
6m
C
26 kN
A
HA
B
E
D
VA
