Replace the two couples acting on the pipe column in Fig. 4–33a by a resultant couple moment.

Question

Accepted Answer

The couple moment [latex]\mathbf{M}_{1}[/latex], developed by the forces at A and B , can easily be determined from a scalar formulation.

[latex]\mathbf{M}_{1} = Fd = 150 N(0.4 m) = 60 N ·m[/latex]

By the right-hand rule, [latex]\mathbf{M}_{1}[/latex] acts in the [latex]+ \mathbf{i}[/latex] direction, Fig. 4–33 b . Hence,

[latex]\mathbf{M}_{1} = \left\{60\mathbf{i}\right\} N ·m[/latex]

Vector analysis will be used to determine [latex]\mathbf{M}_{2}[/latex], caused by forces at C and D . If moments are calculated about point D , Fig. 4–33 a , [latex]\mathbf{M}_{2} = \mathbf{r}_{DC} × \mathbf{F}_{C}[/latex], then

[latex]\mathbf{M}_{2} = \mathbf{r}_{DC} × \mathbf{F}_{C} = (0.3\mathbf{i}) × \left[125(\frac{4}{5})\mathbf{j} - 125(\frac{3}{5})\mathbf{k}\right][/latex]
[latex]= (0.3\mathbf{i}) × \left[100\mathbf{j} - 75\mathbf{k}\right] = 30(\mathbf{i} × \mathbf{j}) - 22.5(\mathbf{i} × \mathbf{k})[/latex]
[latex]= \left\{22.5\mathbf{j} + 30\mathbf{k}\right\} N ·m[/latex]

Since [latex]\mathbf{M}_{1}[/latex] and [latex]\mathbf{M}_{2}[/latex] are free vectors, they may be moved to some arbitrary point and added vectorially, Fig. 4–33 c . The resultant couple moment becomes

[latex]\mathbf{M}_{R} = \mathbf{M}_{1} + \mathbf{M}_{2} = \left\{60\mathbf{i} + 22.5\mathbf{j} + 30\mathbf{k}\right\} N ·m[/latex]

Question 4.13: Replace the two couples acting on the pipe column in Fig. 4–...

Related Answered Questions

Determine the moment MAB produced by the force F in Fig. 4–23a, which tends to rotate the rod about the AB axis. ...

Verified Answer:

Determine the magnitude of the moment of force F about segment OA of the pipe assembly in Fig. 4–24a. ...

Verified Answer:

Determine the couple moment acting on the pipe shown in Fig. 4–32a. Segment AB is directed 30° below the x–y plane. ...

Verified Answer:

The granular material exerts the distributed loading on the beam as shown in Fig. 4–51a. Determine the magnitude and location of the equivalent resultant of this load. ...

Verified Answer:

A distributed loading of p = (800x) Pa acts over the top surface of the beam shown in Fig. 4–50a. Determine the magnitude and location of the equivalent resultant force. ...

Verified Answer:

Determine the magnitude and location of the equivalent resultant force acting on the shaft in Fig. 4–49a. ...

Verified Answer:

Replace the force system in Fig. 4–47a by an equivalent resultant force and specify its point of application on the pedestal. ...

Verified Answer:

Replace the force and couple moment system acting on the beam in Fig. 4–44a by an equivalent resultant force, and find where its line of action intersects the beam, measured from point O. ...

Verified Answer:

The jib crane shown in Fig. 4–45 a is subjected to three coplanar forces. Replace this loading by an equivalent resultant force and specify where the resultant’s line of action intersects the column AB and boom BC. ...

Verified Answer:

The slab in Fig. 4–46a is subjected to four parallel forces. Determine the magnitude and direction of a resultant force equivalent to the given force system, and locate its point of application on the slab. ...

Verified Answer: