Problem 815 Find the moment at R2 and R3 of the continuous beam shown in Fig. P- 815. Solution 815 300 lb 300 lb 135 lb/ft MATHali MATHalin 4 ft R: 4 ft 4 ft' 10 ft 8 ft Rz R Figure P-815 ▾ Click here to expand or collapse this section Y 135 8 18 y = 60 lb/ft Ri 300 lb 300 lb 135 lb/ft MATHalino.com MATHаinc.com 4ft 4ft 4 ft 10 ft 8 ft R₂ Ra Moment under R3 M3 = (8y)|(8)]=-32y = -32 (60) M3 =-640 lb ft answer Solving for moment under R2 6A₁ā₁ 6A252 M1L1+2M2(L1 + L2) + M3L2 + + = 0 L1 L2 Where M₁ = 0 L₁ =3(4) 12 ft L2 = 10 ft 6A₁ā₁ Pa Στ (Ι? - ?) L₁ 6A₁ā₁ L1 12 300(4) (122-42)+ 300(8) (122 - 82) 12 6A₁ā₁ =28 800 lb ft² Li 6A252 8w,L³ 7yL³ + L2 60 60 6A252 8(135) (103) 7(60) (103) + L2 60 60 6A252 = 25 000 lb ft². L2 Thus, 6A₁ā₁ 6A252 M1L1+2M2(L1 + L2) + M3L2 + + = 0 L₁ L2 0+2M2 (12+ 10) - M2-1077.27 lb.ft 640(10) + 28 800 + 25 000 = 0 answer

Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
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can you explain why there is a moment at support 3? also what are the instances when M1, M2, and M3 become zero? please provide a thorough and understandable explanation. Sample figures are also appreciated. 

Problem 815
Find the moment at R2 and R3 of the continuous beam shown in Fig. P-
815.
Solution 815
300 lb
300 lb
135 lb/ft
MATHali
MATHalin
4 ft
R:
4 ft 4 ft'
10 ft
8 ft
Rz
R
Figure P-815
▾ Click here to expand or collapse this section
Y
135
8
18
y = 60 lb/ft
Ri
300 lb 300 lb
135 lb/ft
MATHalino.com
MATHаinc.com
4ft 4ft 4 ft
10 ft
8 ft
R₂
Ra
Moment under R3
M3 = (8y)|(8)]=-32y = -32 (60)
M3 =-640 lb ft
answer
Solving for moment under R2
6A₁ā₁
6A252
M1L1+2M2(L1 + L2) + M3L2 +
+
= 0
L1
L2
Where
M₁ = 0
L₁ =3(4) 12 ft
L2
= 10 ft
6A₁ā₁
Pa
Στ (Ι? - ?)
L₁
6A₁ā₁
L1
12
300(4) (122-42)+
300(8)
(122 - 82)
12
6A₁ā₁
=28 800 lb ft²
Li
6A252
8w,L³
7yL³
+
L2
60
60
6A252
8(135) (103) 7(60) (103)
+
L2
60
60
6A252
= 25 000 lb ft².
L2
Thus,
6A₁ā₁
6A252
M1L1+2M2(L1 + L2) + M3L2 +
+
= 0
L₁
L2
0+2M2 (12+ 10)
-
M2-1077.27 lb.ft
640(10) + 28 800 + 25 000 = 0
answer
Transcribed Image Text:Problem 815 Find the moment at R2 and R3 of the continuous beam shown in Fig. P- 815. Solution 815 300 lb 300 lb 135 lb/ft MATHali MATHalin 4 ft R: 4 ft 4 ft' 10 ft 8 ft Rz R Figure P-815 ▾ Click here to expand or collapse this section Y 135 8 18 y = 60 lb/ft Ri 300 lb 300 lb 135 lb/ft MATHalino.com MATHаinc.com 4ft 4ft 4 ft 10 ft 8 ft R₂ Ra Moment under R3 M3 = (8y)|(8)]=-32y = -32 (60) M3 =-640 lb ft answer Solving for moment under R2 6A₁ā₁ 6A252 M1L1+2M2(L1 + L2) + M3L2 + + = 0 L1 L2 Where M₁ = 0 L₁ =3(4) 12 ft L2 = 10 ft 6A₁ā₁ Pa Στ (Ι? - ?) L₁ 6A₁ā₁ L1 12 300(4) (122-42)+ 300(8) (122 - 82) 12 6A₁ā₁ =28 800 lb ft² Li 6A252 8w,L³ 7yL³ + L2 60 60 6A252 8(135) (103) 7(60) (103) + L2 60 60 6A252 = 25 000 lb ft². L2 Thus, 6A₁ā₁ 6A252 M1L1+2M2(L1 + L2) + M3L2 + + = 0 L₁ L2 0+2M2 (12+ 10) - M2-1077.27 lb.ft 640(10) + 28 800 + 25 000 = 0 answer
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