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Department of Civil and Environment Engineering

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Department of Civil and Environment Engineering

CGN 4980/CGN 6939

FE/Graduate Seminar Review Examples

Fall 2005

Determine the force in each member of the truss and state if the members are in tension or compression.

Solution:

F the members are in tension or compression.DC

FDE

F the members are in tension or compression.AB

F the members are in tension or compression.FE

FFB

F the members are in tension or compression.FE

FFB

F the members are in tension or compression.CD

FCB

The rod has a weight W and rests against the floor and wal for which the coefficients of static friction are mA and mB, respectively. Determine the smallest value of q for which the rod will not move.

Given:

Find:

Solution:

Impending Motion at All Points for which the coefficients of static friction are

FB

W

NB

L sin q

FA

NA

FA

slipping must occur at A & B for which the coefficients of static friction are

FB

W

NB

L sin q

FA

NA

FA

The three bars have a weight of W for which the coefficients of static friction are A = 20 lb, WB = 40 lb and WC = 60 lb, respectively. If the coefficients of static friction at the surfaces are as shown, determine the smallest horizontal force P needed to move block A.

Given:

Find:

Solution:

If blocks A & B move first for which the coefficients of static friction are

WC

FCB

T

NCB

NCB=WC+Tsinq

FBC

WAB

FAD

NAD

If blocks A & B move first for which the coefficients of static friction are

WC

FCB

T

NCB

NCB=WC+Tsinq

FBC

WAB

FAD

NAD

If blocks A move first for which the coefficients of static friction are

NAD

NAB

FAB

T

WCB

WA

FAD

FAB

NAB

NAD

T

Therefore block A moves first

Determine the distance x to the center of mass of the homogeneous rod bent into the shape shown. If the rod has a mass per unit length of 0.5 kg/m, determine the reactions at the fixed support O.

Given: rod, r

Find: x

Solution:

Find the Centroid figure.

Each of the three members of the frame has a mass per unit length of 6 kg/m Locate the position (x, y) of the center of gravity. Neglect the size of the pins at the joints and the thickness of the members. Also, locate the reactions at the pin A and roller E.

Solution:

1 length of 6 kg/m Locate the position (x, y) of the center of gravity. Neglect the size of the pins at the joints and the thickness of the members. Also, locate the reactions at the pin A and roller E.

2

3

1 length of 6 kg/m Locate the position (x, y) of the center of gravity. Neglect the size of the pins at the joints and the thickness of the members. Also, locate the reactions at the pin A and roller E.

2

3

1 length of 6 kg/m Locate the position (x, y) of the center of gravity. Neglect the size of the pins at the joints and the thickness of the members. Also, locate the reactions at the pin A and roller E.

2

3

Determine the moment of inertia length of 6 kg/m Locate the position (x, y) of the center of gravity. Neglect the size of the pins at the joints and the thickness of the members. Also, locate the reactions at the pin A and roller E.Iy for the slender rod. The rod’s density r and cross-sectional area A are constant. Express the results in terms of the rod’s total mass m.

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