Forces on a truss (to calculate stress)

I know for a fact that it's 15.1 ksi, so, if the book says otherwise, I'd say that's a mistake.In summary, the method of joints was used to find the normal stress in each member of a pin-connected truss loaded and supported as shown in the figure. The cross sectional area of the aluminum pipes was calculated, and the normal forces of each member were determined using the sum of moments and forces equations. The normal stress was then calculated by dividing the normal force by the cross sectional area. The final answer was found to be 15.1 ksi, which may differ slightly from the answer in the book due to rounding.
  • #1
ana111790
42
0

Homework Statement


A simple pin-connected truss is loaded and supported as shown in the
figure. All members of the truss are aluminum pipes that have an
outside diameter of 4 in and a wall thickness of .226. Determine the
normal stress in each truss member.

2v83ltl.png

Homework Equations



Normal stress = Normal force/ Cross sectional area.

Sum of moments = 0
Sum of forces in x direction = 0
Sum of forces in y direction = 0


The Attempt at a Solution


In order to use this formula [Normal stress = Normal force/ Cross sectional area] I calculated the cross sectional area as diameter* thickness= .904 in^2
I also need the normal forces of each member of the truss. So I drew the FBD of the structure showing the reaction forces:
121r9rs.png


Solving for reaction forces:
1) Sum of moments around A = (72in * Fby) - (36 in*Fcy)=0
Therefore: Fby= 2.5 kips
2) Sum of forces in the x direction = Fax+Fcx=0
Therefore: Fax=2 kips
3) Sum of forces in they direction = Fay+Fby-Fcy=0
Therefore Fay=2.5 kips

Now I'm not sure how to figure out the normal force on each member given the reaction forces (I calculated the reaction forces because of an example my prof. did in class...)


Can anyone help me? Thank you lots.
 
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  • #3
Thank you for you reply. I never took a statics class so I'm having trouble with this stress analysis course now.

I read over the method of joints, but don't I need the angles though to figure out the internal forces? This is not a right triangle so I'm not sure how to solve for them...
 
  • #4
Wow, I would never imagine that your school wouldn't have statics as a prerequisite for this type of course. I suggest you talk to your instructor about getting some help with statics, as you'll need it throughout the course.

In any case, you have dimensions, so you can construct your own right triangles. And you could either solve for the angles, or use trig identities to solve for the forces. I'd suggest starting with joint B, as you already have the vertical external force, and there's only one beam at joint B that has a vertical component to it.

One other thing I noticed - your F_ax should actually point the other way. It doesn't make sense that, since sum(F_x = 0), and F_cx points to the right. Which, I figure, you either know, or didn't realize because you haven't taken a statics course. Also, your sum of moments about A is way off, as you didn't include the 2kip at point C, and it should have been 5kip*168in (6ft + 8ft) for F_cy.
 
  • #5
I fixed the moments, I don't know how I ended up with that earlier but here's what I have:

Sum of moments = (72*Fby)-(168*5)-(84*2)=0
Fby = 14 kips

Then with sum of forces:
Fax = -2 kips (compression)
Fay = -9 kips (compression)

So I went to joint B like you said:
FBD:
1zqwmt2.png

and Theta = arctan(7/8) = 41.2 degrees.

So Fby + F_CB*sin(theta) = 0
according to Fby above, F_CB*sin(theta) = 14 kips
so F_CB=14 kips/sin41.2 = 21.3kips

So this will be the normal force for member CB of the truss.
I calculated the cross sectional area of the pipe:
(Pi*Diameter^2)/4 - (Pi*(Diameter-thickness)^2)/4
so Area=1.38 in sq.

So finally:
Normal stress=Normal force /Area
21.3 kips/1.38in^2=16.0 klbs

but the answer at the end of the book is different. I don't understand what I'm doing wrong... :(
 
  • #6
Well, you did it correctly, but 21.3kip/1.38(in^2) = 15.4 ksi (kilopounds per square inch), not 16.0 ksi. When I did it, I didn't round - I just got all of the variables into one equation - and I came up with 15.1 ksi. 15.1 vs. 15.4 should be fine, as it's just a matter of rounding. Is one of those values what the book has? Because, like I said - you actually did it correctly.
 

Related to Forces on a truss (to calculate stress)

1. What is a truss and how does it work?

A truss is a structural framework made up of interconnected beams, bars, and joints. It is designed to support and distribute weight and forces, making it an efficient and sturdy structure. The individual components of a truss work together to transfer forces to the ground, allowing for a stable and strong construction.

2. What are the different types of forces that act on a truss?

The main forces that act on a truss are compression, tension, and shear. Compression is a force that pushes or squeezes the truss together, while tension is a force that pulls or stretches the truss. Shear is a force that acts parallel to the surface of the truss, causing it to slide or deform.

3. How do you calculate stress on a truss?

To calculate stress on a truss, you need to know the magnitude and direction of the forces acting on each component, as well as the properties of the material used. The stress on a truss can be calculated using the formula stress = force/area. It is important to ensure that the stress on each component of the truss does not exceed the maximum allowable stress for the material.

4. What factors can affect the stress on a truss?

The stress on a truss can be affected by various factors, such as the weight and distribution of the load it is supporting, the type and strength of the material used, the design and configuration of the truss, and external forces such as wind or seismic activity. It is important to consider all these factors when calculating stress on a truss to ensure its stability and safety.

5. Why is it important to calculate stress on a truss?

Calculating stress on a truss is crucial in ensuring its structural integrity and safety. If the stress on a truss exceeds the maximum allowable stress for the material, it can lead to deformation or failure of the structure. By accurately calculating stress, engineers and designers can make necessary adjustments to the truss design and select appropriate materials to ensure its strength and stability.

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