KMJ16203 Statics Assignment 1 – Engineering Mechanics: 2D Static Equilibrium Analysis of a Hoist Structure

KMJ16203 Assignment 1

Submission Instructions

Please follow these guidelines carefully when preparing and submitting your assignment:

• Due Date & Time: 5:00 PM on Friday, 5 June 2026.
• The class representative may collect all the assignments and submit them together to lecturer’s office.
• Format: The assignment must be strictly hand-written.
• Student Details: Write your Name and Matric No. clearly at the top of the first page.
• Working & Calculations: You must show your step-by-step solutions and calculations clearly. Do not forget to include the correct units and related directional signs (+/–) in your answers.
• Late Penalty: Please submit on time. Late submissions will result in a deduction of marks.

(a) The inclined hoist beam in Figure 1 is designed to support two vertical loads, P₁ and P₂. The cable ED has a maximum tension capacity of 2000 N before it breaks. Assume the structural system is currently in static equilibrium.

Figure 1: Inclined hoist beam supporting two vertical loads.

i) Define the term “Free Body Diagram” (FBD).

(3 Marks)

ii) Based on the connections shown in Figure 1, describe the nature of the unknown support reactions that exist at pin A and cable ED.

(2 Marks)

(b) The hoist system (Figure 1) is being tested to determine its maximum safe operational limits. Given the constraint that the cable ED reaches its absolute maximum load capacity of 2000 N and the operational relationship between the lifted loads is P₁ = 3P₂:

i) Draw the Free Body Diagram (FBD) of the inclined beam AD.

(3 Marks)

ii) Analyse the moment equilibrium of the structural system to determine the maximum critical loads P₁ and P₂ it can safely support.

(6 Marks)

iii) Apply the principles of force equilibrium to calculate the magnitude of the resultant reaction force at pin A.

(4 Marks)

(c) An operator suggests sliding the load P₁ down the beam from point B to point D, meaning both P₁ and P₂ would hang simultaneously from the far end of the beam. Evaluate the structural impact of this change. Using the principle of moments, justify whether this modification will cause the cable ED in Figure 1 to fail if the load magnitudes remain exactly the same as calculated in (b)(ii).

(3 Marks)

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