# Backyard suspension bridge calculations

1. Apr 12, 2015

### 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 realise 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.

2. Apr 12, 2015

### PhanthomJay

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.

3. Apr 12, 2015

### Guy L'Estrange

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

4. Apr 12, 2015

### PhanthomJay

l^2 means l squared.
$T = wl^2/8H$. Express kg/m in Newtons/m!

5. Apr 12, 2015

### Guy L'Estrange

Thanks PhanthomJay:)

6. Apr 12, 2015

### PhanthomJay

Y
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.

7. Apr 12, 2015

### Guy L'Estrange

Thanks. They're all good points I will take into consideration. I found a good resource wich 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