# How Do You Calculate Distributed Load on a Roof Truss Due to Snow?

• arestes
In summary, the problem involves determining the force in members BC, BG, CG, and GH of a Howe truss with a distributed load of 20 lb/ft measured along the slope of the roof. The method of joints and method of sections are used to solve the problem, with the former requiring the sum of vertical and horizontal forces to equal zero. There is a discrepancy between the solutions manual and the student's solution regarding how the distributed load is reduced, with the student using the horizontal length while the manual uses the diagonal length. The student questions this discrepancy, but the given information states that the weight is measured along the roof, not horizontally.
arestes

## Homework Statement

Snow on a roof supported by the Howe truss of the figure can be approximated as a distributed load of 20 lb/ft (measured along the roof). Treat the distributed load as you would the weight of the members; that is, replace the total load on each of the upper members as a vertical force, half applied to the joint at each end of the member. Determine the force in members BC, BG, CG, and GH.

## Homework Equations

joint equilibrium, method of joints and method of sections.

Method of joints: Sum of vertical forces = 0 and Sum of horizontal forces =0.

## The Attempt at a Solution

The only part I'm not sure about is the distributed load reduction. The book shows the figure I'm attaching. I also happen to have (supposedly) the solutions with which I contrasted my solution. The solutions manual reduces the distributed load differently than what I did: I thought that because the load was uniform in "magnitude" the load would be just 20 lb/ft multiplied by the HORIZONTAL length, not the diagonal length as they do in the solution (where they use Pythagoras' theorem).

Am I right or wrong? shouldn't the resultant load on members AB, BC, CD and DE be equal to 8ft * 20 lb/ft = 160 lb. And then I can proceed and put half of this onto the joints?

#### Attachments

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arestes said:
I thought that because the load was uniform in "magnitude" the load would be just 20 lb/ft multiplied by the HORIZONTAL length, not the diagonal length as they do
It clearly states
arestes said:
measured along the roof

haruspex said:
It clearly states
Hi, yeah but looking at the direction of the load, it is vertical, therefore, I can imagine that the "area" of the distributed force would be computed by using a horizontal span. I can also imagine that I can transmit each differential element dF downward, leveling the height and getting a horizontal rectangle.
Why can't I do this?

arestes said:
I can imagine that the "area" of the distributed force would be computed by using a horizontal span.
Imagine what you like, but it tells you, very clearly, that the given weight is 20lb per foot, measuring along the slope of the roof. As you go up the slope, the weight of snow on each foot you cover is 20lb.
If you prefer, you can use that to calculate the total weight and then calculate the weight per horizontal foot, but it will be more than 20lb.

## 1. What is a roof truss?

A roof truss is a structural framework designed to support the weight of a roof. It typically consists of triangular-shaped units connected by joints and arranged in a series to form a stable and strong structure.

## 2. What is a distributed load?

A distributed load refers to a load or force that is spread out over a given area or length. It can be thought of as a continuous load that is applied evenly across a surface or structure.

## 3. How does a roof truss handle a distributed load?

A roof truss is designed to distribute the weight of the roof evenly to the supporting walls or columns. The triangular shape of the truss allows for the load to be evenly distributed to the ends of the truss, rather than concentrating all the weight on a single point.

## 4. What factors affect the strength of a roof truss under a distributed load?

The strength of a roof truss under a distributed load is affected by several factors, including the type and quality of materials used, the design of the truss, and the spacing between trusses. The angle and direction of the load, as well as the overall weight of the roof, also play a role in determining the strength of the truss.

## 5. How do you calculate the maximum load a roof truss can withstand?

The maximum load a roof truss can withstand can be calculated using mathematical equations and structural analysis software. Factors such as material strength, truss design, and load distribution are taken into consideration to determine the maximum safe load for a roof truss.

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