Engineering Mechanics

Situation
The three-hinged arch shown below is loaded with symmetrically placed concentrated loads as shown in the figure below.
 

2015-may-design-three-hinged-arch-given.png

 

The loads are as follows:
$$P_1 = 90 ~ \text{kN} \qquad P_2 = 240 ~ \text{kN}$$
 

The dimensions are:
$$H = 8 ~ \text{m} \qquad S = 4 ~ \text{kN}$$
 

Calculate the following:
 

1.   The horizontal reaction at A.

A.   0 C.   330 kN
B.   285 kN D.   436 kN

2.   The total reaction at B.

A.   0 C.   330 kN
B.   285 kN D.   436 kN

3.   The vertical reaction at C.

A.   0 C.   330 kN
B.   285 kN D.   436 kN

 

Problem
A 150 g ball at the end of a string is revolving uniformly in a horizontal circle of radius 0.600 m. The ball makes 2 revolutions in a second. What is the centripetal acceleration?

A.   74.95 m/sec2 C.   49.57 m/sec2
B.   94.75 m/sec2 D.   59.47 m/sec2

 

Problem
What is the angle between zero-based vectors ${\bf V_1} = (-\sqrt{3}, ~ 1)$ and ${\bf V_2} = (2\sqrt{3}, ~ 2)$ in an x-y coordinate system?

A.   0° C.   150°
B.   180° D.   120°

 

Problem
Compute the value of b if A and B are orthogonal.
$${\bf A} = 2{\bf i} + b{\bf j} + {\bf k}$$

$${\bf B} = 4{\bf i} - 2{\bf j} - 2{\bf k}$$

A.   6 C.   4
B.   5 D.   3

 

Problem
A catapult is placed 100 ft from the castle wall, which is 35 feet high. The soldier wants the burning bale of hay to clear the top of the wall and land 50 feet inside the castle wall. If the initial velocity of the bale is 70 feet per second, then at what angle should the bale of hay be launched so that it travel 150 feet and pass over the castle wall. Use g = 32 ft/sec2.
 

2016-may-math-catapult.jpg

 

A.   49.8° C.   39.2°
B.   50.8° D.   40.2°

 

Situation
Diagonals BG, CF, CH, and DG of the truss shown can resist tension only.
 

2016-may-design-truss-with-tension-diagonals.gif

 

If W = 3 kN and P = 0, find the following:
1.   the force in member CF.

A.   4.76 kN C.   4.67 kN
B.   4.32 kN D.   4.23 kN

2.   the force in member BF.

A.   3.2 kN C.   3.4 kN
B.   3.3 kN D.   3.5 kN

3.   the force in member DH.

A.   2.8 kN A.   2.5 kN
B.   2.8 kN D.   2.7 kN

 

Situation
Flexible cables BE and CD are used to brace the truss shown below.
 

2016-may-design-3panel-truss-counter-diagonals.gif

 

1.   Determine the load W to cause a compression force of 8.9 kN to member BD.

A.   7.80 kN C.   26.70 kN
B.   35.64 kN D.   13.35 kN

2.   Which cable is in tension and what is the tensile reaction?

A.   BE = 12.58 kN C.   BE = 6.29 kN
B.   CD = 6.29 kN D.   CD = 12.58 kN

3.   If W = 20 kN, what will be the tensile reaction of member CE?

A.   6.67 kN C.   0
B.   13.33 kN D.   10 kN

 

 
 
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