Analysis of Structures (Method of Sections)

[timeforplanb]

Homework Statement

Using the method of sections, determine the force in members BD, CD, and CE of the roof truss shown in the figure

(the red line is the cutting plane and the green arrows are my assumed directions of the unknown forces)

Homework Equations

summation of moments=0
summation of horizontal forces=0
summation of vertical forces=0

The Attempt at a Solution

i assumed there's a reaction at F (upward), and since i didn't know its value i tried taking the moments at pt. F, N, O to make that reaction disappear. But so far, it doesn't seem like i'll be getting any unknown force anytime soon. please help! am i wrong with my assumption that there's a reaction at F? and also, i tried assuming that there's no reaction at F but i still can't find any unknown force at all.

 

[SteamKing]

The link to your diagram is broken.

 

[timeforplanb]

The link to your diagram is broken.

looks okay to me.

 

[PhanthomJay]

The reactions at A and F should be solved first, by looking at the entire truss and summing forces in x direction = 0 and summing moments about one of the reactions to get the other reaction, etc.

 

[DeeNos]

I would approach this problem by first understanding the basic principles of the method of sections. This method involves cutting a structure into two parts and analyzing the forces in each part separately. In this case, the red line represents the cutting plane, and the green arrows represent the assumed directions of the unknown forces.

Next, I would carefully examine the given figure and identify all the known and unknown forces acting on the structure. It is important to note that the structure is in equilibrium, meaning that the sum of all forces acting on it must be equal to zero in both the horizontal and vertical directions, and the sum of all moments must also be equal to zero.

Based on this information, I would then apply the equations of equilibrium (sum of forces and moments) to each part of the structure, taking into account the assumed directions of the unknown forces. This would allow me to solve for the unknown forces in members BD, CD, and CE.

It is important to note that the assumption of a reaction at point F may not be necessary, as the structure is in equilibrium without it. However, if the assumption is made, it should be taken into account in the analysis.

In conclusion, the method of sections is a useful tool for analyzing structures and can be applied to solve for unknown forces in a systematic and logical manner. By carefully considering all known and unknown forces and applying the equations of equilibrium, the forces in members BD, CD, and CE can be determined.