a) Explanation Apply the sign conventions for calculating reactions using the three equations of equilibrium as shown below. For summation of forces along x -direction is equal to zero ( ∑ F x = 0 ) , consider the forces acting towards right side as positive ( → + ) and the forces acting towards left side as negative ( ← − ) . For summation of forces along y -direction is equal to zero ( ∑ F y = 0 ) , consider the upward force as positive ( ↑ + ) and the downward force as negative ( ↓ − ) . For summation of moment about a point is equal to zero ( ∑ M at a point = 0 ) , consider the clockwise moment as positive and the counter clockwise moment as negative. Show the deflected shape rectangular ring as in Figure (1). Refer Figure (1), Express the relationship between slope at A , B , C , and D using the symmetry of the ring section as follows: θ A = − θ B = − θ D = θ C Determine the fixed end moment AD using the formula; FEM A D = W L 2 12 = 2 ( 12 ) 2 12 = 24 kips-ft Determine the member end moment AD using the formula; M A D = 2 E I L ( 2 θ A + θ D ) + FEM A D = 2 E I 12 ( 2 θ A − θ A ) + 24 = E I 6 θ A + 24 (1) Determine the member end moment AB using the formula; M A B = 2 E I L ( 2 θ A b) To determine Find the axial force in member AD and AB .

Find the member end moments for the rectangular ring and draw the shear force and bending moment diagram for members AB and AD .

Fundamentals of Structural Analysis

5th Edition

ISBN: 9780073398006

Author: Kenneth M. Leet Emeritus, Chia-Ming Uang, Joel Lanning

Publisher: McGraw-Hill Education

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Beams

In structural engineering, a beam is a component made of a variety of materials (including steel alloys, and wood) that can resist loads applied laterally to the beam axis. Members, elements, rafters, shafts, and purlins are all terms used to describe be…

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Chapter 10, Problem 12P

To determine

Find the member end moments for the rectangular ring and draw the shear force and bending moment diagram for members AB and AD.

To determine

Find the axial force in member AD and AB.

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