Attached you will find four figures, each showing a beam with different loads and supports.$$

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For each beam, draw a full free body diagram.$$ For that, you just draw the beam and you show forces at each point where forces are applied $$ the support$($s$)$ and the load points.$$

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Show the coordinate system and a separate figure to show $(+)$ directions for forces and moments $($drawing that by itself keeps it out of your way$).$

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For the applied loads as shown, show the force and, if the force is applied at an angle, show the x and y components.$$

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For each support show any possible reaction forces $($x and y components$)$ and $$ IF possible, a reaction moment.$$

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For a pinned connection anchored in place $($no rollers$),$ this can support a reaction force in the x and y directions.$$ It CANNOT support a reaction moment.$$ See left end of fig $1.$

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For a pinned connection on rollers $($a roller support$),$ this can only support a reaction force at right angles to the rollers.$$ If the rollers run on a horizontal surface, this can only support a reaction force in the vertical direction.$$ That is limited to a reaction force against the rollers.$$ In the figures I$$ve drawn, that would be a reaction force upwards, meaning that the beam end is being pushed down on the rollers by the other forces.$$ If the other forces would lift the end of the beam, it will be lifted off the rollers.$$ See right end of figure $1.$

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ENGT $3020$ Statics and Strength of Materials $3$rd Homework Assignment

For a fixed end $($cantilever beam$),$ this can support reaction forces in both the x and y directions AND a reaction moment.$$ See right end of figure $2.$

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About moments $...$ IF the line of action of the applied force goes through the pivot point $($point O in my figures$),$ it cannot create a moment.$$ IF the line of action does NOT go through the pivot point, it will cause a moment.$$

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For example, Fig $1,$ force at B $...$ that will cause a moment equal to the distance from O to B times the force.$$

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In figure $2,$ for force E$,$ only the y component of the force will cause a moment.$$ The x component acts on a line of action that passes through point O$.$

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Think about force F in #$3.$ The y component will cause a moment.$$ The x component is applied along a line that does NOT pass through the pivot point O$.$ Will it create a moment about O$?($HINT: YES$)$

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Here$$s what I want you to do$.$

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For each problem, $1)$ draw the free body diagram.$2)$ Use the conditions for static equilibrium to find the reaction forces and $$ if possible $$ reaction moment.$$ You$$ll sum the forces in the x direction, then the forces in the y direction, and, finally, look at moments.$$ I$$d start by looking at moments about Point O$.$ Looking at moments about Point O takes the reaction forces at O out of the picture.$$ In #$1,$ the sum of the moments will give you the reaction force in the y direction at the roller support at C$.$

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In problem $4,$ I want to introduce something from the strength of materials side.$$ Rod

AC has a diameter of $0\mathrm{.}5$ inches.$$ The normal stress due to the load in the rod is given by

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$=$ F$/$A$$

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$...$ where F is the force in the rod and A is the cross section area.$$ Once you find the force in the rod, you can calculate the normal stress.$$

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This is in units of Force$/$Area $...$ pounds per square inch in English units; something related to Pascals in metric units $$ either megaPascals $(1$ MPa $=1,000,000$ N$/$m$2$; this is also $1$ N$/$mm$2).$