Vector Analysis in Structural Engineering

00:00 7 marks

A structural engineering scenario involves analyzing forces in support rods and cables.

(a) In a 2D framework, a joint is connected to two rods. Rod 1 exerts a force of 1500 N at an angle of 30° above the horizontal. To ensure the net force on the joint is horizontal, determine the tension in Rod 2, which acts vertically upwards and cancels the vertical component of Rod 1.

(b) In a 3D building support model, a cable attached to a high-rise column makes an angle of 50° with the vertical. If the vertical component of the tension in the cable is 800 N, calculate the magnitude of the tension in the cable. Assume the cable lies in a vertical plane.

Part a

7 minutes 3 marks

Question

In the 2D framework, Rod 1 exerts a force of 1500 N at 30° above the horizontal. Calculate the vertical component of this force. Then, determine the tension in Rod 2, acting vertically upwards, that is needed to cancel this vertical component to ensure a horizontal resultant force at the joint. Give your answer to three significant figures.

Hint Hint

Hint

Calculate the vertical component using \(\sin(30^\circ)\) and equate Rod 2’s tension to this component for equilibrium.

Answer Answer
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Complete Answer

750 N

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Part b

8 minutes 4 marks

Question

In the 3D building model, a support cable is at 50° from the vertical in a vertical plane. If the vertical component of the tension is 800 N, calculate the magnitude of the total tension in the cable. Round your answer to three significant figures.

Hint Hint

Hint

Use the relationship \(T_v = T \cos(50^\circ)\) to find the total tension \(T\).

Answer Answer
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Answer Answer

Complete Answer

1.24 \times 10^3 N

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