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April 2017 Workshop IABSE Conference – Future of Design Sheffield

IABSE WORKSHOP 21 April 2017

Merchant’s Bridge, Castlefield, Manchester

Outline of Natural Frequency Assessment presented at workshop in the IABSE conference 21 April 2017

Side View of Bridge
Aim of Workshop

To demonstrate how the approximation of dynamic behaviour of a long-span structure
using approximate techniques can provide an understanding of its characteristic behaviour.

Benefits of Conceptual Design

To enable the design engineer to appraise alternative designs, free from oversophistication, in terms of complex calculations and computer modelling. This in turn allows the engineer to engage their imagination and to have at their fingertips simple concepts which are readily conveyed to clients, architects and colleagues; to be able to
communicate intelligibly as professionals.

Example Structure – Whitby Bird – Merchants’ Bridge in Castlefield, Manchester

(Whitby Bird is now part of Ramboll)

It comprises a steel arch bridge, curved on plan, with 38m span across the Bridgewater Canal with ramps leading off at the end. The South support is an inclined pier aligned
with the arch. The deck is a shallow (325mm) built up depth with tubular edges
(assumed to be 323.9×12.5CHS). Top and bottom steel plates with intermediate cross beams form a closed stressed skin torsion box. Cantilever arms run out to the tubular inclined arch which restrain it from buckling out of plane, while in turn the arms and inclined arch assist in laterally restraining the bridge. The pier supports at each side sit under the perimeter tubular beams with sliding bearings. For further interest see a description of the bridge on

‘A Lively Bridge’ – Dynamic Behaviour

Of particular interest, this bridge is lively. Pedestrians on the bridge experience significant
bounciness on crossing. An individual may easily set up resonance walking or jumping on
the bridge. The weight of the main span is estimated to be circa 35 tonnes, based on the elements assumed (323.9×12.5CHS perimeter beams and arch, 10mm deck plates, and surface weight 80kg/m2, 203x133x25UB cantilever arms). Note that all of the sizes of elements and plates are assumed from observation. No drawings have been obtained or used for the exercise.


A GSA (Oasys) computer model was put together by Hugh Morrison
(hma) with the plates and constituent assumed elements. It was also
run to obtain deflections, natural frequencies and anticipated dynamic
response by Peter Debney (Oasys). In situ measurements of the
natural frequency and accelerations by Hugh Morrison (using vibrate-it-
app obtainable from Expedition Engineers’ website). vibrate-it-app-for-android/

Workshop Exercise (Time allotted 15 minutes)

Using the sketch information in the pack (overleaf) participants are to attempt to estimate
the maximum dead and live load deflections at midspan on the bridge, and hence to obtain an approximation of the fundamental natural frequency of the bridge. The formula below may be used:

Fundamental Natural Frequency (Fn) ~ 18/ö

Where ∂ = deflection in mm, due to dead load + 10% live load
Hint: Deflection occurs from two main components – bending as a composite structure
(arch and deck combined) and torsion from the curved profile).

Note: Dead Load is 4.6kPa (4.6kN/m²) and Live Load 3kPa
Data sheets provided….


Analysis Hints


Bridge Plan
Bridge Section
Nest Step: Calculate deflections due to Dead+10% Live

Separating out the bending for the straight (idealised) bridge and torsion (assuming point load in centre at 50% of the bridge total loading) these may be found.


The answers may be found here…if desired

Answers From the methods provided

Workshop Approximate Answers

Youtube Video Answers

A series of worked sheets may be found on youtube…

Also transcripts and summary are included below…..


Some Results on the Vibrate-it-App

Pages from the Powerpoint Presentation

Extract From Presentation – Vibrate-it-App

Some screen shots are shown below from the app….As a note the highest response to local walking (non random forcing frequency) in the middle of the span was around 30%g which was a little higher than predicted in the video rough calculation. With a lower damping ratio (say 2%) for the calculation the response is 3.3%g peak which is closer.

Below – midspan on the outer edge of the curve…

1.8Hz fundamental natural frequency, response factor 16 (high), max acceleration circa 30%g

Below – Quaterspan on the inner edge of the curve…

First two modes of natural frequency are close (see acceleration against frequency below) with a fundamental natural frequency of 2.9Hz given.




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