1 1 PLANE STRUCTURES FRAMES – is a rigid structure which is made up of members at least one of which is not a two-force member. To simply put it, in order to solve for the unknown forces in the frame, you need to draw the FBD of the frame and individual members in the right sequence. 2 The compound beam shown below is pinned connected at B. Determine the reactions at its supports. Neglect its weight and thickness. EXAMPLE 6-15 2 m 2 m 2 m 10 kN 4 kN/m Dismember the beam into 2 segments A B C 3 4 Entire Beam Bar AB Bar BC 3 i. Dismember the beam into 2 segments: (For Bar AB) 10 kN 3 4 A x A y M A B x B y 2 m 4 m For bar BC Entire Beam Back given problem 4 B x B y 8 kN 1 m 2 m i. Dismember the beam into 2 segments: (For Bar BC) C y For bar AB Entire Beam (Summary) Back given problem 5 10 kN 3 4 A x A y M A B x B y 2 m 4 m B x B y 8 kN 1 m 2 m C y For bar BC For bar AB i. Dismember the beam into 2 segments: Compute for the reactions Segment BC Segment AB 6 10 kN 3 4 A x A y M A B x B y 2 m 4 m 0 ) 5 3 )( 10 ( = + − x x B kN A ; 0 = ↑ + ∑ y F → ; 0 = ∑ + x F 0 ) 5 4 )( 10 ( = − − y y B kN A 0 ) 4 ( ) 2 )( 5 4 )( 10 ( = − − m B kN M y A ; 0 = ∑ A M ii. Equations of Equilibrium (For segment AB) Segment BC Back
Transcript
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PLANE STRUCTURES FRAMES – is a rigid structure which is made up of members at least one of which is not a two-force member.
q To simply put it, in order to solve for the unknown forces in the frame, you need to draw the FBD of the frame and individual members in the right sequence.
2
The compound beam shown below is pinned connected at B. Determine the reactions at its supports. Neglect its weight and thickness.
EXAMPLE 6-15
2 m 2 m 2 m
10 kN 4 kN/m
Dismember the beam into 2 segments
A B
C 3
4
Entire Beam Bar AB
Bar BC
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i. Dismember the beam into 2 segments: (For Bar AB)
10 kN
3 4
Ax
Ay MA Bx
By 2 m
4 m
For bar BC
Entire Beam
Back given problem 4
Bx
By
8 kN
1 m
2 m
i. Dismember the beam into 2 segments: (For Bar BC)
Cy
For bar AB
Entire Beam (Summary)
Back given problem
5
10 kN
3 4
Ax
Ay MA Bx
By 2 m
4 m
Bx
By
8 kN
1 m
2 m
Cy
For bar BC For bar AB
i. Dismember the beam into 2 segments:
Compute for the reactions
Segment BC Segment AB
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10 kN
3 4
Ax
Ay MA Bx
By 2 m
4 m
0)53)(10( =+− xx BkNA
;0=↑+ ∑ yF
→ ;0=∑+xF
0)54)(10( =−− yy BkNA
0)4()2)(54)(10( =−− mBkNM yA
;0=∑ AM
ii. Equations of Equilibrium (For segment AB)
Segment BC Back
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7
Bx
By
8 kN
1 m
2 m
Cy
0=xB
;0=↑+ ∑ yF
→ ;0=∑+xF
08 =+− yy CkNB
0)2()1(8 =+− mCmkN y
;0=∑ BM
ii. Equations of Equilibrium (For segment BC)
Final Answer Back
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iii. Solving these equations, we obtain:
0)53)(10( =+− xx BkNA
0)54)(10( =−− yy BkNA
0)4()2)(54)(10( =−− mBkNM yA
0=xB
08 =+− yy CkNB
0)2()1(8 =+− mCmkN y
kNAx 6=
0=xB
kNCy 4=
kNAy 6=
kNBy 4=
kNmMA 32=
Review Problem Back
Next Problem
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EXAMPLE 6-16
Determine the horizontal and vertical components of force which the pin at C on member ABCD of the frame.
0.8 m 100 kg
1.6 m
0.4 m
1.6 m 0.4 m
F E C
B
A
D Draw the FBD of the frame
See the FBD
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i. FBD of the frame ABCD:
2 m
2.8 m
Dx
Ax
Ay
A
D
Dismember the beam into 3 segments Bar CF
Bar AD
Bar BE
Equation of Equilibrium for Entire Frame
F=981 N
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07.700 =− NAx
;0=↑+ ∑ yF
→ ;0=∑+xF
0)8.2()2(981 =+− mDmN x
;0=∑ AM
ii. Equations of Equilibrium (Entire Frame)
0981 =− NAy
2 m
2.8 m
Dx
Ax
Ay
A
D
Dismember the beam into 3 segments
Bar CF Bar AD Bar BE
F=981 N
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F
981 N
ii. Equations of Equilibrium (For Bar CEF)
0)45cos2.1734( =°−−− NCx
;0=↑+ ∑ yF
→ ;0=∑+xF
0)6.1)(45sin()2(981 =°−− mFmN B
;0=+ ∑ CMccw
0)45sin2.1734( =°−− NCy
C Cx
Cy
E
FB
45º
1.6 m 0.4 m
Bar ACD
Bar BE
Entire Frame
NCy 245−=
NCx 1230=
3
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Dx
Ax
Ay
A
D
FB
Cx
Cy
0.8 m
1.6 m
0.4 m
FBD of bar ACD
Back Bar BE Entire Frame
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FBD of bar BE
45º
FB
FB
Bar ACD
Entire Frame
Bar CEF
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Dx
Ax
Ay
A
D
C Cx
Cy
E F
981 N FB
45º
45º
FB
FB
FB Cx
Cy
0.8 m
1.6 m
0.4 m
1.6 m 0.4 m
Review
Final Answer
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NCy 245−=
ii. Final Answers for Problem 6-16
NCx 1230=
Review Next Problem
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EXAMPLE 6-17
The smooth disk shown below is pinned connected at D and has a weight of 20 lbs. Neglect the weights of the other members, determine the horizontal and vertical components of reaction at pins B and D.
