Mastering Engineering

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Question 1 Part A Question Two- and three-force members are two particular types of members that occur frequently in structures. Two- and three-force members play an important role in simplifying the analysis of structures in equilibrium. Two-Force Members: A two-force member is an object in equilibrium on which forces act at exactly two points. Because the object is in force equilibrium, the resultant forces acting at the two points must have equal magnitudes and opposite directions. And because the object is in moment equilibrium, the two resultant forces must be collinear (i.e., they act along the same line of action). Three-Force Members: A three-force member is an object in equilibrium on which forces act at exactly three points. For the object to be in moment equilibrium, the three resultant forces acting at the three points must be either concurrent or parallel. Identify the two- and three-force members in the following figure. Consider only the members labeled AB and assume that P is the load's magnitude. Answer 2 Force Members: D, E 3 Force Members: A, B, F Neither: C Only two forces act on a two-force member and those forces are collinear, equal in magnitude, and oppositely oriented. In a three-force member the forces are either parallel or concurrent.

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Transcript of Mastering Engineering

Page 1: Mastering Engineering

Question 1

Part A

Question

Two- and three-force members are two particular types of members that occur frequently in

structures. Two- and three-force members play an important role in simplifying the analysis of

structures in equilibrium.

Two-Force Members: A two-force member is an object in equilibrium on which forces act at

exactly two points. Because the object is in force equilibrium, the resultant forces acting at

the two points must have equal magnitudes and opposite directions. And because the object

is in moment equilibrium, the two resultant forces must be collinear (i.e., they act along the

same line of action).

Three-Force Members: A three-force member is an object in equilibrium on which forces act

at exactly three points. For the object to be in moment equilibrium, the three resultant

forces acting at the three points must be either concurrent or parallel.

Identify the two- and three-force members in the following figure. Consider only the members

labeled AB and assume that P is the load's magnitude.

Answer

2 Force Members: D, E 3 Force Members: A, B, F Neither: C

Only two forces act on a two-force member and those forces are collinear, equal in magnitude, and

oppositely oriented. In a three-force member the forces are either parallel or concurrent.

Page 2: Mastering Engineering

Part B

Question

As shown, an L-shaped bar is supported by a pin at joint A. The bar's dimensions are = 700 and

= 400 , and the bar is subjected to a force with magnitude = 5.75 at joint B. Ignoring the

bar's weight, find the actual orientation of the applied force. What is the value of the angle ?

Answer The beam is static meaning that the sum of the moments around point A must be equal to zero. The only way for this to be true if force F acts through point A (as we can neglect the mass of the bar). Thus:

The load at B and the reaction at A are shown below.

The two forces are collinear, equal in magnitude, and oppositely oriented.

Page 3: Mastering Engineering

Part C

Question

As shown, a load of magnitude is applied to a structure. Assuming that all members are weightless and that ABEF and BCD are rigid bodies, find the magnitudes of the reactions at D and G needed to maintain the structure in equilibrium.

Assume the following values: = 3.00 , = 2.00 , and = 100 .

Answer

Consider FG: from FBD of Gy = 0, take the moments around B

( ) ( )

( )

( )

( )

Page 4: Mastering Engineering

Considering equilibrium in x and y directions:

X direction:

Y direction:

Page 5: Mastering Engineering