Title PSAD Solutions.pdf ✅

01 Statics (2D) SITUATION 1. A cylindrical drum 2 m in radius and weighing 1200 N is held by a rigid bar AB as shown. One end of the bar (point A) is hinged, and the other end (point B) is supported by a flexible cable BC. Neglect friction on all contact surfaces. ▣ 1. Which of the following most nearly gives the force (N) between the drum and the bar? SOLUTION: Free Body Diagram of the Drum:
Note: Normal Force is always perpendicular to point/surface of contact. Solving for N1: ∑Fvertical = 0 N1 sin 30 = 1200 N1 = 2400 N ▣ 2. Which of the following most nearly gives the tension (N) in the cable? SOLUTION: Solving for angle: Recall: Two-Tangent Theorem 2θ + 60 = 90 θ = 15° Solving for distances: Law of Sines
2 sin 15 = x sin 75 x = 7.4641 m Free Body Diagram of Bar: tan θ = 3 4 θ = 36.8699° Solving for T: ∑MA = 0 T cos 36.8699 [10 sin 60] + T sin 36.8699 [10 cos 60] = 2400(7.4641) T = 1804.3386 N ▣ 3. Which of the following most nearly gives the reaction (N) at pin A? SOLUTION: Solving for Ax: ∑Fhorizontal = 0
Ax + 1804.3386 cos 36.8699 = 2400 cos 30 Ax = 634.9901 N Solving for Ay: ∑Fvertical = 0 Ay + 1804.3386 sin 36.8699 = 2400 sin 30 Ay = 117.3968 N Solving for reaction at A: RA = √Ax 2 + Ay 2 RA = √634.99012 + 117.39682 RA = 645.7511 N SITUATION 2. A semicircular beam is loaded as shown. Given: P1 = 1.8 kN P2 = 0.9 kN P3 = 0.45 kN θ = 30° β = 45°