Consider the simply supported wooden beam shown in figure 1...

Consider the simply supported wooden beam shown in (Figure 1). The modulus of elasticity of the wood is $E = 13$ GPa. Determine the slope at A, measured clockwise. Express your answer in radians to three significant figures. $\theta_A =$ rad Determine the displacement of point C. Express your answer to three significant figures and include the appropriate units. Enter positive value if the displacement is upward and negative value if the displacement is downward. $v_C =$ Value Units

Transcript

00:01 Looking at the method of superposition in the determination of the deflection and the slope of a beam subjected to loading.

00:10 Now we have a beam of rectangular cross -section before us loaded at w1 and w2.

00:17 Now to determine the slope at e, we need to determine the slope due to the load w1 separately and the slope due to the load w2 separately, as you can see.

00:32 From the diagram and add them together the same thing to determine the deflection will add the deflection due to w1 deflection at c due to w1 if you just deflection at c due to w1 if you're not c due to the two and add them together now for the deflection for the slope due to for the slope due to the low w1 is going to give us equal to minus w w, a, b, okay, into l plus b.

01:23 Okay, all over six, l sorry, l, ei.

01:45 Okay, here i is a moment of inertia based on the cross -sectional of the beam and e is the modulus of elasticity is given there.

01:56 Then to determine the slope for that low low w1 is so let's call it sorry the deflection so let's call it so the basically configuration is w minus w b b x into l squared and us b squared minus x squared so is 6lei.

03:04 So when you plug in your values, of course, to get i, i is, for a rectangular cross section is where w is the width of the beam cube over 12.

03:28 Of course, we know that the t is a thickness.

03:31 So when you plug in values into that, you don't know how that one.

03:35 So, so that our theta a1 is going to give us minus 0 .089.

04:05 Now to get the deflection, the deflection, okay, just plug in all your values into so to see one.

04:17 So it's going to give us, deflection is going to give us actually minus 15 now, when you do work in meter and do your conversion to mm, you are going to have it as 15 mm, which is actually 0 .015 meters.

04:42 Okay? then you can also look for the slope due to w2...

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