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**FE/Graduate Seminar Review Examples**

Department of Civil and Environment Engineering CGN 4980/CGN 6939 FE/Graduate Seminar Review Examples Fall 2005

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

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FDC FDE

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FAB

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FFE FFB

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FFE FFB

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FBA FBE FBC

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FEC FEF FED

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FCD FCB

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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:

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**Impending Motion at All Points**

FB W NB L sin q FA NA FA

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FB Equilibrium Eqs. W NB L sin q FA NA FA

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**slipping must occur at A & B**

FB W NB L sin q FA NA FA

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The three bars have a weight of WA = 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:

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WABC T FAD NAD

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**If blocks A & B move first**

WC FCB T NCB NCB=WC+Tsinq FBC WAB FAD NAD

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**If blocks A & B move first**

WC FCB T NCB NCB=WC+Tsinq FBC WAB FAD NAD

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**Therefore block A moves first**

If blocks A move first NAD NAB FAB T WCB WA FAB FAD NAB NAD T Therefore block A moves first

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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:

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**Locate the centroid of the quarter circle shown in the figure.**

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Find the Centroid

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3 2 1

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3 2 1

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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:

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1 2 3

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1 2 3

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1 2 3

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**Determine the moment of inertia Iy for the slender rod**

Determine the moment of inertia 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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EQUATIONS OF EQUILIBRIUM & TWO- AND THREE-FORCE MEMBERS

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