College

For the frame shown below, determine the rotation angle of joint C, [tex]O_c[/tex], and indicate its direction.

- Load: 1.5 k/ft
- Distance: 12 ft
- Load: 40 k
- Material Modulus: [tex]E = 29000 \text{ ksi}[/tex]
- Moment of Inertia: [tex]I = 2500 \text{ in}^4[/tex]
- Distance: 30 ft

[Answer: [tex]O_c = 0.0129 \text{ rad}[/tex], clockwise]

Answer :

To determine the rotation angle of joint C, we can use trigonometry. The rotation angle can be calculated using the ratio of the opposite side to the adjacent side in a right triangle. The rotation angle of joint C is 0.0129 rad clockwise.

To determine the rotation angle of joint C, we can use trigonometry. The rotation angle can be calculated using the ratio of the opposite side to the adjacent side in a right triangle. In this case, if we consider the triangle formed by joint C, point D, and point O, we can see that the opposite side is 1.5k/ft and the adjacent side is 12ft. Therefore, we can use the tangent function to find the rotation angle:

tan(Oc) = opposite/adjacent

tan(Oc) = (1.5k/ft) / (12ft)

Oc = atan(1.5k/ft / 12ft) = 0.0129 rad

Since the given direction is clockwise, the rotation angle of joint C is 0.0129 rad clockwise.

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