poster d.indd

Calculation
Aesthetics
Welding
Concrete
Vierendeel’s criticism on contemporary calculation was a discrepancy
The morbid growth of trellis in many 19th century structures such as the
Electric arc welding was a new technique during the interwar period and it
Vierendeel has not only patented the Vierendeel as a solution to be erected
between the analytical structural theory and the building practice.
Eiffel Tower and the Galerie des Machines led Vierendeel to support his
provided opportunities in metal constructions. But there was a downside
using steel, but has also patented his beam for concrete beams. An unlike
Vierendeel solved this by working out approximate methods to determine
own patented work, the Vierendeel. The austerity of only horizontal and
when insufficient knowledge of welding techniques led to a series of
Vierendeel application was a concrete suspension bridge of which the
stresses in frameworks without diagonals
vertical lines was and still is a major ace of trumps for this structure.
serious bridge collapses.
lower part was a Vierendeel, and the upper part were steel cables.
The Vieren d e el
IN SHORT
The Vierendeel is a frame with rigid joints patented in 1896 by Belgian engineer Arthur Vierendeel (1852-1940). His invention came about after he noticed that experiments and calculation methods on iron and steel
frameworks didn’t agree, making his invention a response in the then discussion on secondary stresses. After designing a church tower and testing a full-scale bridge model during the 1897 Brussels World Fair, many bridges
‘système Vierendeel’ were erected the following decades in his homeland, as well as a few dozens around the globe. At times the discussion on the Vierendeel got heated in trade journals and amongst people, mainly due to a
lack of ‘visual’ safety and theoretical uncertainties concerning calculation, safety factors and welding techniques. Nowadays the Vierendeel principle is still topical and many (structural) designers apply his formal ideas. This
led to a broader meaning of the word Vierendeel varying from aesthetic to strictly structural.
A STRUCTURAL NOVELTY
In April 1897, Vierendeel published the structural theory of his ‘poutre à arcades’ as he used to call his invention, initially in his book Longerons en Treillis et Longerons à Arcades. Examples of structures with fully rigid joints
were very uncommon at the time. He could only refer to the Dadizele church tower. Vierendeel mentions his system for the first time in public at the Congrès International des Architectes in August 1897 in Brussels. There
he also revealed his upcoming test on a 31,5 m span bridge he was going to build at his own expense within the scope of the Brussels World Fair in Tervuren. It would be loaded to failure to verify the agreement between
calculations and measurement. “Et maintenant le treillis: grande sujétion dans l’emploi artistique du fer, car le treillis avec ses formes raides, droites, sans variété, sans elasticité, est un dispositif constructif qui n’est rien
moins qu’esthétique; mais, heureusement, du treillis nous sommes delivrés; voici, un pont dont les fermes en fer sont realisées sans intervention d’aucune diagonale, d’aucun treillis, et cette réalisation est obtenue en faisant
une économie de matière et sans rien sacrifier de la solidité, ainsi que le prouvent les expériences, actuellement en cours, à Tervueren, sur un pont analogue de 32 mètres de portée.”
While Vierendeel’s patents describe vaguely the calculations without explaining the trailing theories, his book goes into detail on how to calculate the particular case of a symmetric bridge with parallel flanges and the general
case of an asymmetric bridge with non-parallel flanges. Vierendeel’s main criticism on contemporary calculation was a discrepancy between analytical structural theory and actual building practice. Calculation assumed
pin-jointed connections whereas the execution with rivets tended to be more rigid. After Schwedler and Winkler, German scientific assistant Heinrich Manderla (1853-1889) had described a calculation method in 1880 to
determine the additional secondary stresses. He assumed that angular rotations were not possible in a framework. However Vierendeel still thought this method to be incorrect, primarily because the rigid joint was also far
from perfect: the truth balanced between a rigid joint and a pin-joint.
Dutch engineer J. Schroeder van der Kolk summarized in the Tijdschrift van het Koninklijk Instituut van Ingenieurs (edition 1889-1890) the results of an experiment that listed the secondary stresses of a truss bridge in
relation to the primary stresses. It was striking that those secondary stresses could not be ignored, as they amounted up to 60 % of the primary stresses. Secondly, Vierendeel indicated that in the diagonals the secondary
stresses were limited (ranging from 6 to 16 % of the primary stresses). In other experiments he had noted that deformations in the diagonals were nearly negligible.
Vierendeel also referred to Winkler who tried to lower these stresses by using St. Andreas crosses, i.e. doubling the diagonals. It had already been applied in the Netherlands on some railway bridges between Rotterdam and
Amsterdam. German civil engineer Otto Mohr’s method was used to calculate the basic structure, along with Manderla’s equations. However according to Vierendeel it didn’t reduce the secondary stresses. After tests in
France in 1893 ordered by the state, engineers tried to turn truss bridges into girder bridges by using a lattice-work. Though Vierendeel acknowledged some of the advantages, he still argued that “la vraie solution se trouvera,
non pas en compliquant le treillis, mais en la simplifiant encore, c’est-à-dire en supprimant la diagonale dans le canevas triangulaire.”
CONCLUSIONS
Challenging the dogma of the triangle was one of his objectives, Vierendeel said. Nevertheless this dogma was merely a rhetorical cover. Vierendeel was an engineer who believed in the prospects of iron and steel in architecture
and who had thoroughly examined frameworks and its structural and mechanical behaviour. Blindly following the tradition of trusses with improper calculation would not drive mankind to progress. So when Vierendeel
delved into the 19th century issue on secondary stresses, he seized his chance to solve this, by working out approximate methods to determine stresses in frameworks without diagonals. He had seen that during experimental
loading, the diagonals were hardly charged and their secondary stresses were limited. He found an analytical theory that matched the as-built reality.
After his first experiments and overcoming some resistance, Vierendeel convinced state principals to order dozens of Vierendeel bridges in Belgium and its African colony during the next decades. The ‘poutre à arcades’ as he
had called it initially, was also applied in some other structures as pylons and concrete spans. The Vierendeel is a crossbreed, a structural compromise. It is not as rational as a truss when it comes to loadbearing capacities,
but it remains superior when it comes to spatial qualities. In retrospect we can say that the concept of the Vierendeel has shifted. Vierendeel’s definition as described in his 1899 USA patent is a beam in “which the diagonals
are removed and the vertical members rigidly connected to the booms by rounded pieces in such manner that the booms and vertical members form practically one piece.” Nowadays calculation uses different methods and
since the breakthrough of digital calculation more complex algorithms are possible. His name is however still connected to the concept of rigid frames that gain stiffness through these rigid corners. The connotation with the
inventor is sometimes lost, but the multifunctional aspects to obtain aesthetic, formal, mechanical or structural plus-points will remain its ace of trumps.
researcher
supervisor
co-supervisors
affilliations
department
website
contact
Koen Verswijver
prof. dr. Ronny De Meyer
prof. dr. Rudi Denys
prof. dr. Emiel De Kooning
prof. dr. Jan Belis
Ghent University
Faculty of Engineering
Architecture and Urban Planning
Jozef Plateaustraat 22
9000 Gent
www.architecture.ugent.be/steel
[email protected]
department of Architecture and Urban Planning
department of Architecture and Urban Planning
department of Mechanical Construction and Production
department of Architecture and Urban Planning
department of Structural Engineering
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