Explanation Given information: Consider the horizontal and vertical reaction at A are denoted by A x and A y . Consider the vertical reaction at F is denoted by F y . Assumption: Apply the sign convention for calculating the equations of equilibrium as below. For the horizontal forces equilibrium condition, take the force acting towards right side as positive ( → + ) and the force acting towards left side as negative ( ← − ) . For the vertical forces equilibrium condition, take the upward force as positive ( ↑ + ) and downward force as negative ( ↓ − ) . For moment equilibrium condition, take the clockwise moment as negative and counter clockwise moment as positive. Calculation: Draw the free body diagram of frame as in Figure (1). Refer to Figure (1). For Equilibrium condition, Consider the sum of the forces in the horizontal direction is zero. Then, ∑ F x = 0 A x + 18 kN = 0 A x = − 18 kN A x = 18 kN ( ← ) Consider the sum of the moment about the point E is zero. Then, ∑ M E = 0 − 18 kN × 4 m − A y × 3.6 m = 0 A y × 3.6 m = − 18 kN × 4 m A y = − 18 kN × 4 m 3.6 m A y = − 20 kN A y = 20 kN ( ↓ ) Thus, the horizontal and vertical reaction at A are A x = 18 kN ( ← ) _ and A y = 20 kN ( ↓ ) _ . Consider the sum of the forces in the vertical direction is zero. ∑ F y = 0 ( A y ) + F y = 0 ( − 20 kN ) + F y = 0 F y = 20 kN ( ↑ ) Draw the free body diagram of the member ABC as in Figure (2)

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Chapter 6.3, Problem 6.79P

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The components of the forces acting on member ABC.

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Question 2 Figure 3 shows the numerical solution of the advection equation for a scalar u along x at three consecutive timesteps. 1.0 0.8- 0.6- 0.4- 0.2- 0.0- -0.2- -0.4- -0.6 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 Figure 3: Advection equation, solution for three different timesteps. a) Provide an explanation what conditions and numerical setup could explain the curves. Identify which of the three curves is the first, second and third timestep. b) Consider explicit schemes with central and upwind discretisations. Explain how each of these candidate discretisations could produce the behaviour shown in Figure 3. c) Determine the CFL number that was used in the simulation for each of the candidate schemes for all possible updates. Assume that the timestep and mesh-width used are constant. Read the data to two digits of accuracy from Figure 4 shown at the end of the question, which is an enlarged version of Figure 3. Demonstrate your method and input data for one calculation, but then use a…

Chapter 6 Solutions

VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS

Ch. 6.1 - 6.1 through 6.8 Using the method of joints,...Ch. 6.1 - 6.1 through 6.8 Using the method of joints,...Ch. 6.1 - Prob. 6.3P Ch. 6.1 - 6.1 through 6.8 Using the method of joints,...Ch. 6.1 - Prob. 6.5P Ch. 6.1 - Using the method of joints, determine the force in...Ch. 6.1 - 6.1 through 6.8 Using the method of joints,...Ch. 6.1 - Prob. 6.8P Ch. 6.1 - 6.9 and 6.10 Determine the force in each member of...Ch. 6.1 - Prob. 6.10P

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