Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_121

⚡ Mecademy AIENG정역학 · ch4  Problem Statement Determine the forces in members and of the loaded symmetrical truss. (Diagram shows a symmetrical arched truss with 5 vertical loads at joints . Support is at the left, is at the right. A circular arc of radius is indicated, passing through the peak joint . Radial lines are drawn from a center . The radial line through the support makes an angle of with the horizontal. The radial line passing through nodes and makes an angle of with the vertical. The truss is symmetrical about the vertical line through joint .) Problem 4/121 (a) Geometry Analysis and Global Equilibrium 1. Formula: From the symmetry of the truss and loading, the vertical reactions at the supports are equal to half the total load: 2. Substitution: There are 5 identical vertical loads acting at joints . 3. Calculation: The peak joint is at the vertical center line (). The radial line through joint and makes an angle of with the vertical, so . The radial line through support makes an angle of with the horizontal, which corresponds to an angle of with the vertical ( ). The arc subtends a total angle of . The joint is exactly at the midpoint of this arc (). DMDN LC,D,E,F,G AI24 m EO A30 ∘ D M30 ∘ E R = A R = I 2 P∑ LC,D,E,F,G R = A R = I = 2 5L 2.5L Eφ=0 ∘ DM30 ∘ φ = D φ = M 30 ∘ A30 ∘ 90− ∘ 30= ∘ 60 ∘ φ = A 60 ∘ AE60 ∘ (D,M) φ=30 ∘ Based on the labels, node (outer chord) and (inner chord) are positioned between and . Assuming equal angular divisions, and are at . Radiu