Statics: Two tension wires are supported by a concrete block

CE Nov. 2010 

Two tension wires are supported by a concrete block attached to an anchor ring as shown in the figure.

1. Which of the following most nearly gives the resultant force in the anchor ring?

       a.  7.28 KN                                   c.  9.07 KN

       b.  10.42 KN                                 d.  5.16 KN

2. Which of the following most nearly gives the angle that the resultant force makes with the horizontal?

       a.  43.67°                                      c.  39.55°
       b.  53.17°                                      d.  48.72



For #1

→+ΣFx     (horizontal)
Rx = -7cos15° + 3.5cos30° = -3.7304 
Rx =  -3.73 KN


↑+ΣFy     (vertical)
Ry = 7sin15° + 3.5sin30° = 3.5617 
Ry =  3.562 KN


Use the Pythagorean Theorem
R² = Rx² + Ry²
R² = (-3.73)² + (3.562)²
R = 5.16 KN


For #2

tan θ = |Ry/Rx|
tan θ = |3.562/-3.73|
θ = 43.67°