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Problems on support reaction.pdf
1. Problems on
Q1. Calculate the support reactions for the beam shown in fig
ANS
:
Step 1: Consider
Step 2: Consider
Step 3: Consider
𝑅𝐴 +
Step 4: Consider
Prepared by: Prof. V.V. Nalawade
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Problems on Support Reactions
Calculate the support reactions for the beam shown in fig
: Consider FBD of beam
: Consider ƩFx
Ʃ𝐹 = 0
As there are no horizontal forces
: Consider ƩFy
Ʃ𝐹 = 0
3 + 4 + 5 − 𝑅𝐴 − 𝑅𝐵 = 0
𝑅𝐴 + 𝑅𝐵 = 3 + 4 + 5
+ 𝑅𝐵 = 12 𝐾𝑁 … … … … … … … … … …
: Consider ƩM@A
Prepared by: Prof. V.V. Nalawade
Support Reactions
Calculate the support reactions for the beam shown in fig.
As there are no horizontal forces
. 𝐸𝑞 1
2. (3
Put the value of RB in Eq
Step 5: Final Answer
Reaction at support A =
Reaction at support B =
Q2. Calculate the support reactions for the beam shown in fig
ANS
:
Step 1: Consider
Step 2: Consider
Prepared by: Prof. V.V. Nalawade
2
ƩM = 0
(3 × 2) + (4 × 3) + (5 × 5) − RB × 6
(3 × 2) + (4 × 3) + (5 × 5) = RB ×
RB × 6 = 6 + 12 + 25
RB =
43
6
= 7.17 KN
Put the value of RB in Eqn
1, we get
RA = 12-7.17 = 4.83 KN
Final Answer
Reaction at support A = RA = 4.83 KN
Reaction at support B = RB = 7.17 KN
Calculate the support reactions for the beam shown in fig
: Consider FBD of beam
: Consider ƩFx
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= 0
6
4.83 KN
RB = 7.17 KN
Calculate the support reactions for the beam shown in fig.
3. Prepared by: Prof. V.V. Nalawade
3
Ʃ𝐹 = 0
As there are no horizontal forces
Step 3: Consider ƩFy
Ʃ𝐹 = 0
𝑅𝐴 + 𝑅𝐵 = 4 + (2 × 1.5) + 1.5
𝑅𝐴 + 𝑅𝐵 = 8.5 𝐾𝑁 … … … … … … … … … … . 𝐸𝑞 1
Step 4: Consider ƩM@A
ƩM = 0
(4 × 1.5) + (3 × 2.25) + (1.5 × 4.5) = RB × 6
RB × 6 = 6 + 6.75 + 6.75
RB =
19.5
6
= 3.25 KN
Put the value of RB in Eqn
1, we get
RA = 8.5 – 3.25 = 5.25 KN
Step 5: Final Answer
Reaction at support A = RA = 5.25 KN
Reaction at support B = RB = 3.25 KN
Q3. A simply supported beam AB of Span 4.5 m is loaded as shown in
fig. Find the support reactions at A & B.
4. ANS
:
Step 1: Consider
Step 2: Consider
Step 3: Consider
𝑅𝐴 +
Step 4: Consider
Put the value of RB in Eq
Step 5: Final Answer
Reaction at support A =
Reaction at support B =
Prepared by: Prof. V.V. Nalawade
4
: Consider FBD of beam
: Consider ƩFx
Ʃ𝐹 = 0
As there are no horizontal forces
: Consider ƩFy
Ʃ𝐹 = 0
𝑅𝐴 + 𝑅𝐵 = 4.5 + 2.25
+ 𝑅𝐵 = 6.75 𝐾𝑁 … … … … … … … … … …
: Consider ƩM@A
ƩM = 0
(4.5 × 2.25) + (2.25 × 3) = RB × 4.
RB =
16.88
4.5
= 3.75 KN
Put the value of RB in Eqn
1, we get
RA = 6.75 – 3.75 = 3 KN
Final Answer
Reaction at support A = RA = 3
Reaction at support B = RB = 3.75
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there are no horizontal forces
… . 𝐸𝑞 1
.5
KN
3.75 KN
5. Q4. Calculate the support reactions for the beam shown in fig
ANS
:
Step 1: Consider
Step 2: Consider
As there are no horizontal
Step 3: Consider
𝑉𝐴 +
Step 4: Consider
(120 × 3
Prepared by: Prof. V.V. Nalawade
5
Calculate the support reactions for the beam shown in fig
: Consider FBD of beam
: Consider ƩFx
Ʃ𝐹 = 0
𝐻𝐴 = 0
As there are no horizontal forces acting on beam
: Consider ƩFy
Ʃ𝐹 = 0
𝑉𝐴 + 𝑅𝐵 = 120 + 30 + 90
+ 𝑅𝐵 = 240 𝐾𝑁 … … … … … … … … … …
: Consider ƩM@A
ƩM = 0
3) + (30 × 6) + (40) + (90 × 8.67) =
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Calculate the support reactions for the beam shown in fig.
forces acting on beam
… . 𝐸𝑞 1
) = RB × 10
6. Put the value of RB in Eq
Step 5: Final Answer
Horizontal Reaction at support A = H
Vertical Reaction at support A = V
Reaction at support B =
Q5. Find analytically the support reactions at B and the load P, for
the beam shown in fig. If the reaction of support A is Zero
ANS
:
Step 1: Consider
Step 2: Consider
Prepared by: Prof. V.V. Nalawade
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Put the value of RB in Eqn
1, we get
VA = 240-136.03 = 103.97 KN
Final Answer
Horizontal Reaction at support A = H
Vertical Reaction at support A = VA = 103.97
Reaction at support B = RB = 136.03
Find analytically the support reactions at B and the load P, for
shown in fig. If the reaction of support A is Zero
: Consider FBD of beam
: Consider ƩFx
Prepared by: Prof. V.V. Nalawade
Horizontal Reaction at support A = HA = 0
103.97 KN
136.03 KN
Find analytically the support reactions at B and the load P, for
shown in fig. If the reaction of support A is Zero
8. Q6. Find the support reactions at A and B for the beam loaded as
shown in fig.
ANS
:
Step 1: Consider
Step 2: Consider
𝐻𝐴
Step 3: Consider
𝑉𝐴 + 𝑅𝐵
Step 4: Consider
Prepared by: Prof. V.V. Nalawade
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Find the support reactions at A and B for the beam loaded as
: Consider FBD of beam
: Consider ƩFx
Ʃ𝐹 = 0
𝐻𝐴 − 𝑅𝐵 𝐶𝑂𝑆 60 = 0 … … … … … … 𝐸𝑞
: Consider ƩFy
Ʃ𝐹 = 0
𝑉𝐴 + 𝑅𝐵𝑠𝑖𝑛 60 = 120 + 90 + 80
𝑅𝐵 𝑠𝑖𝑛60 = 290 𝐾𝑁 … … … … … … … … …
: Consider ƩM@A
ƩM = 0
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Find the support reactions at A and B for the beam loaded as
𝐸𝑞 1
… … . 𝐸𝑞 2
9. (120 ×
Put in Eqn
1 & 2
Step 5: Final Answer
Horizontal Reaction at support A = H
Vertical Reaction at support A = V
Reaction at support B =
Q7. Find the support reactions at A and F for the beam loaded as
shown in fig.
ANS
:
Step 1: Consider
FBD of beam AC
FBD of beam DF
Prepared by: Prof. V.V. Nalawade
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× 5) + (90 × 6) + (80 × 13) = RB sin
& 2, we get
Final Answer
Horizontal Reaction at support A = HA =
Vertical Reaction at support A = VA =
Reaction at support B = RB = 251.72
Find the support reactions at A and F for the beam loaded as
: Consider FBD of beam
FBD of beam AC
DF
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sin60 × 10
A = 125.86 KN
A = 72 KN
251.72 KN
Find the support reactions at A and F for the beam loaded as
10. Consider FBD of beam DF first,
Step 2: Consider
Step 3: Consider
𝑉𝐹
Step 4: Consider
Put in Eqn
1, we get
Now Consider
Step 5: Consider
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Consider FBD of beam DF first,
: Consider ƩFx
Ʃ𝐹 = 0
𝐻𝐹 = 0
: Consider ƩFy
Ʃ𝐹 = 0
+ 𝑅𝐷 = 120 … … … … … … … … … … . 𝐸𝑞
: Consider ƩM@D
ƩM = 0
(120 × 3) − (VF × 4) = 0
1, we get
Consider the FBD of beam AC,
: Consider ƩFx
Ʃ𝐹 = 0
𝐻𝐴 + 2 cos 59.04 = 0
Prepared by: Prof. V.V. Nalawade
𝐸𝑞 1
11. Prepared by: Prof. V.V. Nalawade
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𝐻𝐴 = −1.03 𝐾𝑁
i.e. our assumed direction is wrong, Therefore
𝐻𝐴 = 1.03 𝐾𝑁 (←)
Step 6: Consider ƩFy
Ʃ𝐹 = 0
𝑉𝐴 − 𝑅𝐶 = 2 sin 59.04
𝑉𝐴 = 1.71 + 30 = 31.41 𝐾𝑁 (↑)
Step 7: Consider ƩM@A
−M − 2 sin 59.04 × 1 − (30 × 2) = 0
Step 8: Final Answer
Horizontal Reaction at support A = HA = 1.03 KN
Vertical Reaction at support A = VA = 31.41 KN
Moment at support A = MA = 61.71 KN.m
Horizontal Reaction at support F = HF = 0 KN
Vertical Reaction at support F = VF = 90 KN
Reaction at support D = RD = 30 KN
Q8. Two beams AB & CD are arranged as shown in fig. Find the
support reactions at D.
12. ANS
:
Step 1: Consider
FBD of beam AB
FBD of beam
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12
: Consider FBD of beam
FBD of beam AB
FBD of beam CD
Prepared by: Prof. V.V. Nalawade
13. Step 2: Consider
(
Step 3: Consider
Prepared by: Prof. V.V. Nalawade
13
: Consider FBD of AB & Consider ƩM@A
ƩM = 0
(600 × 4) + 2400 = RB sin 53.13 × 12
Consider FBD of CD & Consider ƩM@C
ƩM = 0
RD sin 36.87 × 10 − 500 × 4.2 = 0
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M@A
12
M@C
0