Question
Asked Sep 15, 2019
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The 30 ft long simply supported beam slopes at a 9:12 pitch and is supported by Pin C and Roller D. The beam is subjected to the distributed and point loads as shown in the image. Determine the internal normal force (N), internal shear (V), and internal moment (M) at points A and B.

4
40kip
(ROLLER
2.5 kip /H
(PrN)
10
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4 40kip (ROLLER 2.5 kip /H (PrN) 10

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Expert Answer

Step 1

The forces acting in the upward direction is positive and downward direction as negative.

The forces acting towards right direction is positive and left direction is negative.

The anticlockwise moment is positive and clockwise moment is negative.

Show the free body diagram of the simply supported beam as shown in Figure below:

2.5 k/ft
40k
C
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2.5 k/ft 40k C

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Step 2

Find the slope angle as follows:

3
sin e
5
cose
5
e=tan
4
0=36.87°
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3 sin e 5 cose 5 e=tan 4 0=36.87°

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Step 3

Apply the Equilibrium of forces,

Equate the sum of the horizontal for...

Σ-0
C-R sin 0
3
C
5
C-0.6R 0
ΣΕ-0
CyR cos2.5 x30-40 0
C0.8R 115
ΣΜ.-0
R COS x (30 cose)+ RD sinex (30 sin0)
30 cose
40x
0
30 cos
2.5x 30 x
2
2
Rp 46k(Acting at 36.87°to the verti cal)
Solve the above mentioned Equilibrium Equations.
C 27.8k
C 78.2k
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Σ-0 C-R sin 0 3 C 5 C-0.6R 0 ΣΕ-0 CyR cos2.5 x30-40 0 C0.8R 115 ΣΜ.-0 R COS x (30 cose)+ RD sinex (30 sin0) 30 cose 40x 0 30 cos 2.5x 30 x 2 2 Rp 46k(Acting at 36.87°to the verti cal) Solve the above mentioned Equilibrium Equations. C 27.8k C 78.2k

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