# Backyard suspension bridge calculations

• Guy L'Estrange
In summary, Guy is planning to build a suspension bridge in his backyard and he wants help with sag and force calculations. He needs help estimating the sag at the anchors and calculating the force at the anchors.
Guy L'Estrange
Hi there,
I'm planning to build a suspension bridge in my backyard and i'd like some help with sag and force calculations.

The bridge will span 18m across a stream (anchor to anchor) in my backyard. I'll have 2 x strands of wire rope (1 at either side of the walkway) to span the gap. I've calculated that the weight of the wire rope, timber planks, and fastners will be approximately 650kg total for this span. I'd like up to 4 adults to be able to cross the bridge at any time so that would equate to an extra 320kg (4 x 80kg). I'd like to minimise the sag as it's only a shallow creek however I realize that the smaller the sag, the more force I'm generating at the anchors. I'm estimating the sag would be between 5-10% at the anchors although this would be difficult for me to measure acurately in the field. The easiest way for me to measure the sag would be to stringline the actual span then measure the vertical distance (with a tape measure) to the bottom of the curve.

Is there a version of a catenary equation (or other) whereby measuring the sag in the middle of the bridge (with my tape measure), I could therefore calculate the sag in degrees at the anchors and thereby calculate the estimated force at the anchors?

Any help would be greatly appreciated, also if anyone could point me towards any reference material for "suspension bridges calculations for dummies".

Thanks,

Guy.

You'll need an engineer to design this for proper wire size , anchorage , supports , and design details.etc.
Assuming a parabolic curve and equal height supports, the horizontal tension in the wire is wl^2/8H , where w is the weight on the cable per meter, l is the span, and H is the vertical sag . the horiz tension at supports combined with the vert load at supports (half the weight on the cable) will give you the angle using trig. Tension will increase when weight is added in the span.

Thanks PhantomJay. I really appreciate your reply. Sorry for the dumb question but what does the up arrow stand for between l & 2?

w = 18.056kg (cable weight plus evenly spaces treads and associated fasteners)
l = 18m
H = 1m

Guy L'Estrange said:
Thanks PhantomJay. I really appreciate your reply. Sorry for the dumb question but what does the up arrow stand for between l & 2?

w = 18.056kg (cable weight plus evenly spaces treads and associated fasteners)
l = 18m
H = 1m
l^2 means l squared.
$T = wl^2/8H$. Express kg/m in Newtons/m!

Thanks PhanthomJay:)

Y
Guy L'Estrange said:
Thanks PhanthomJay:)
You're welcome. But be very cautious designing a suspension bridge to carry people, even though your span is small. Sidesway, wind, proper anchorage and so many other factors are of concern. I note that you used full load less humanity in your weight of cable calc. Sags and tensions will increase when load is added, the degree of which depends in part on the elasticity of the rope . If you sag in the rope as a first step with say 1 m sag and using cable weight only, both it's tension and sag will increase when you add the timbers and girder.

Thanks. They're all good points I will take into consideration. I found a good resource which covers most of these aspects with equations I can work through. It's an army engineers bridge building manual from the 60's: http://www.tramway.net/US Army.pdf

## 1. How do you calculate the maximum weight a backyard suspension bridge can hold?

The maximum weight a backyard suspension bridge can hold is determined by several factors, including the type of materials used, the length of the bridge, and the design of the supports. To calculate the maximum weight, engineers use a formula that takes into account the tensile strength of the materials, the angle of the suspension cables, and the weight distribution of the load. It is important to consult a professional engineer for accurate calculations.

## 2. What is the ideal length for a backyard suspension bridge?

The ideal length for a backyard suspension bridge depends on the specific needs and desires of the homeowner. Generally, a backyard suspension bridge can range from 10 feet to 100 feet in length. The length of the bridge should be proportional to the size of the backyard and the intended use. Longer bridges may require additional supports and a stronger foundation.

## 3. How do you determine the spacing of the supports for a backyard suspension bridge?

The spacing of the supports for a backyard suspension bridge is determined by the length of the bridge and the weight it needs to support. As a general rule, the supports should be placed at equal distances along the bridge and closer together towards the center. The closer the supports are, the stronger the bridge will be. Again, it is important to consult a professional engineer for accurate calculations.

## 4. What are the best materials to use for a backyard suspension bridge?

The best materials to use for a backyard suspension bridge are high-strength steel cables and wooden or steel beams for the deck. These materials are durable, strong, and can withstand the outdoor elements. It is important to use materials that are specifically designed for suspension bridges to ensure the safety and stability of the structure.

## 5. Are there any safety precautions to consider when building a backyard suspension bridge?

Yes, there are several safety precautions to consider when building a backyard suspension bridge. It is important to have the bridge designed and constructed by a professional engineer to ensure it can safely support the intended weight. Additionally, regular inspections and maintenance should be conducted to ensure the bridge remains structurally sound. It is also important to limit the number of people on the bridge at one time and to never exceed the weight limit. Lastly, proper signage and warnings should be in place to alert people of potential hazards when crossing the bridge.

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