Meriam, Kraige & Bolton — Statics of Particles: Problem 2_84

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/84 The asymmetric roof truss is of the type used when a near normal angle of incidence of sunlight onto the south-facing surface ABC is desirable for solar energy purposes. The five vertical loads represent the effect of the weights of the truss and supported roofing materials. The 400-N load represents the effect of wind pressure. Determine the equivalent force–couple system at A. Also, compute the x-intercept of the line of action of the system resultant treated as a single force R. Problem 2/84 1. Geometry Analysis and Coordinate Setup We establish a coordinate system with point at the origin . The horizontal span is given as (), so point is at and point is at . The roof consists of two sections: at a angle and at a angle from the horizontal. Point C: The intersection of the lines from at and at ( from the horizontal). Point B: Indicated as the midpoint of . Point D: Given by the angle from and being on the line . A(0,0) 10 m5 m+5 mF(10,0)G(5,0) AC60 ∘ CF30 ∘ A60 ∘ F150 ∘ 30 ∘ y = C x tan(60)= C ∘ (10−x )tan(30) C ∘ x = C 3 ⟹ 3 10−x C 3x = C 10−x ⟹ C x = C 2.5 m y = C 2.5 ≈ 34.330 m AC x = B = 2 0+2.5 1.25 m,y = B = 2 0+4.330 2.165 m 30 ∘ G(5,0)CF y = D tan(30)(x − ∘ D 5)=−tan(30)(x − ∘ D 10) x − D 5=−(x − D 10)⟹2x = D 15⟹x = D 7.5 m y = D tan(30)(7.5− ∘ 5)=2.5×0.5774≈1.443 m Point E: Indicated as the midpoint of . 2. Force Vector Analysis We decompose all applied forces into their Cartesian components . Vertical Loads (downw