Academician LI Guohao achieved much during a long career as a civil engineer, expert in bridge mechanics and engineering educator, having dedicated his life to teaching and scientific research. Best known for solving problems related to the spatial and nonlinear analysis of large-span bridge structures and their stability and vibrational characteristics, he played a pivotal role in the development of bridge structural theory.
Overseas Study - Laying a Solid Theoretical Foundation
Master Li began his undergraduate studies in the Department of Civil Engineering of Shanghai's Tongji University in 1929, aged 16. He spent two years learning German, which facilitated his further studies when, in the autumn of 1938, he was offered an Alexander von Humboldt Foundation scholarship to pursue a PhD in that country. Because of his outstanding record at university, he was allowed to undertake doctoral research directly, without first acquiring a masters degree.
He began his doctoral research in the spring of 1939, based on an 800-metre long highway-cum-railway suspension bridge to be built in Hamburg. Applying the elastic flexure differential equations of the second order in the theory of deformation of suspension bridge stiffening girders, he concluded that the load-bearing of a suspension bridge was similar to that of a beam bearing both vertical loads and axial tension. Thus, he expanded his findings to an idea that was new in both concept and method - the "Practical Analysis Method of Suspended Bridge by Second Order Theory", his resulting doctoral thesis, was completed within less than a year. The publication of his dissertation in the journal Steel Structure won him worldwide recognition in the field of bridge engineering and became known as “Suspension Bridge Master Li” - when he was only 26.
During the Second World War, he worked at Kurt Klöppel’s Teaching and Research Group, achieving innovative analysis suspension bridges, truss bridges and stability of structures; and undertook research into problems associated with the welding of steel structures. Ten important papers were published during this time.
Continuing his study of the suspension bridge to be built in Hamburg, he discovered a three-span continuous stiffening girder bridge structural system without intermediate supports had the advantage of no peak bending moments at bearing. This approach was eventually adopted for the construction of a cable-stayed bridge in the United States in the 1970s. He also analysed the dynamic response of suspension bridges to railway load in depth. The analytical method used as well as the results filled a gap at that time.
In the summer of 1943, he took up the challenge of accurately analysing the internal forces acting on the main truss of a 90-metre-span steel truss bridge with many webbings and factual consideration of the rigid connection of chords at node points. In a paper entitled “New Method for Structural Analysis of Truss and Other Similar Structures”, he proposed a new method for analysing truss structures that is to transform the truss, a discrete system made up by chords into continuous mechanical model and then finding a solution by resolving differential equations.
Returning Home to Serve His Country
At the end of the Second World War, Master Li took an arduous journey home with his wife, Ye Jing’en and their first child Guihua, who was born in Marseilles, France, en route; his name literally meaning “returning to China”. It took the Li family several months to make it to Saigon (now Ho Chi Minh City) on a ship from France to Vietnam, in March 1946. Although the accommodation provided by the consulate in Saigon was quite poor, he took comfort in being so close to returning home.
Master Li finally arrived in Shanghai full of enthusiasm for opportunities to contribute to bridge construction, but his hopes were dashed and he ended up returning to Tongji. In 1952, Master Li spearheaded reform of the university's academic structure and established bridge engineering as a specialty profession. He also published two textbooks: Design of Steel Structures and Design of Steel Bridges, both of which were the first of their kind in the Chinese language. In 1955, while training graduate students in bridge engineering, he published his first graduate textbook, Stability and Vibration of Bridge Structures.
In 1955, the 42-year-old Li became a member of the first batch of the Academic Division of the Chinese Academy of Sciences (now Academician of the Chinese Academy of Sciences). Soon after his appointment as Vice President of Tongji University in 1956, Master Li established the Engineering Mechanics Specialty and taught Structural Dynamics and Mechanics of Plates and Shells to the first batch of Engineering Mechanics students. During the mid-1950s he was respectively a member and chairman of the Technical Advisory Committees for the construction of the Wuhan Yangtze River Bridge and Nanjing Yangtze River Bridge. He also played an important role in the construction of many other major bridges, such as the Shanghai Nanpu Bridge, Jiangyin Yangtze River Bridge, Humen Pearl River Bridge, Shantou Bay Bridge, Yangtze Estuary Sea Crossings, Hangzhou Bay Crossing, Qiongzhou Strait Crossing and Lingdingyang Bridge.
When the Cultural Revolution began in 1966, Master Li was accused of unknown crimes and kept in solitary confinement for two years. While in solitary confinement, he heard on the radio that the Nanjing Yangtze River Bridge had opened to traffic, which reminded him of the vibration phenomenon on the Wuhan Yangtze River Bridge during the opening ceremony in 1957, which was still unexplained. His passion for bridge engineering undimmed despite his predicament, he applied his superior foundation in theory, sharp creative mind and excellent memory to solving the problem. Making reference to past successful experiments, he turned the discrete truss system with members into a continuous model and used elastic flexure and differential equations to solve the problem.
Using the blank margins and the spaces between the lines in a few pieces of newspapers, he secretly worked on the theoretical analysis and calculations for almost a year. While undertaking physical labour under supervision following his period of solitary confinement, he managed to make truss bridge models and carry out torsion tests at home, to finetune his theoretical analysis. Writing under prison conditions in 1973, he finally completed the treatise, Theory of Truss Torsion: Torsion, Stability and Vibration of Truss Bridges, which illustrated the vibrational problem on Wuhan Yangtze River Bridge and created an analytical theory for truss bridge structures.
During the 1970s, Master Li focused his research on the transverse load distribution of highway bridges and wrote the treatise, The Computation of Transverse Load Distribution on Highway Bridges. He also succeeded in researching the transverse load distribution of arch bridges, curved bridges and skew girder bridges. He developed a uniform method for calculating transverse load distribution based on a principle and mechanical model that can be adapted to various roads and bridges worldwide.
The following decade, he compiled Anti-seismic Dynamics of Engineering Structures and Explosion-Resistant Dynamics of Engineering Structures as editor-in-chief and rebuilt the Structural Theory Research Institute, formed the Bridge Research Office and conducted research on spatial analysis, stability, seismic, wind and traffic-induced vibrations on bridges, nurturing a large number of doctoral students in the process. A research centre on seismic engineering, wind engineering and bridge engineering was subsequently established.
Master Li participated actively in academic activities at home and abroad from the 1950s onwards. During the 1980s, he served as chairman of the Shanghai Association for Science and Technology, president of the Bridge and Structural Engineering Institute of China Civil Engineering Society (CCES), president of China Civil Engineering Society (CCES), chairman of the Federation of Chinese Association for Science Engineering Society, and a member of and adviser to the American Society of Civil Engineers' (ASCE) Technical Committee on Cable-Supported Bridges. It was during this period that he saved a Baosteel Group project from being abandoned by solving the horizontal displacement of the pile foundation. He also edited Civil Engineering Division of “Ci Hai” - a very thick Chinese dictionary – and the civil engineering section of the Chinese Encyclopedia.
As a veteran member of IABSE, a standing committee member, and Chairman of its Chinese group, Master Li was elected in 1981 by IABSE as one of the world's best-known experts of structural engineering and awarded the International Award of Merit in Structural Engineering in 1987 in commendation of his long-standing devotion to the development of bridge theories and training of people.
Innovation - Creating A New Bridge Theory
Master Li pioneered the use of the spatial and nonlinear analysis method as well as the study of stability and vibrations in long-span bridge structures.
“Suspension Bridge Li's” Displacement Theory, a practical method
During his research into the practical method of suspension bridge displacement, Master Li's discovered the following:
1. The non-linear effect of a suspension bridge due to its displacement (deformation ) is equivalent to the effect of the horizontal tensile force in the suspension cable acting directly on the stiffening girder (Displacement on a suspension bridge has the same effect in nonlinear parts as the horizontal tension imposed by a main cable on a stiffening girder.)
2. Although the presence of nonlinear parts causes the superposition principle to lose its effects, the influence line nonetheless forms the basis for calculating the least favourable load position. Taking into account the fact that the live load on a long-span suspension bridge is smaller than its dead load, Master Li proposed the concept of a "singular" influence line, which linearises a nonlinear problem within a limited range.
3. In order to avoid repeated calculations and iteration, Li used cubic interpolation to solve the problem.
These insights provided the framework for his practical approach, which was a significant breakthrough in the 1940s. Despite the ease of complex non-linear analyses today using computers, Master Li's contribution is still widely acknowledged. His papers continue to be cited in teaching materials around the world, especially in Germany, where the reputation of "Suspension Bridge Li" has remained.
Structural Stability Theory
By the 1940s, engineers had already mastered the first type of stable branched buckling load; namely, Euler’s critical load of an axially compressed bar, while the second type of stable crushing load of eccentrically compressed bar was still under research. At the time, whether there were any branching points to compressed bending members such as compressed bending frames and arches was still unknown.
Master Li recognised the importance of distinguishing two different stability types when participating in the work of standard DIN4114. In his 1943 essay, “Ample Criterion for Branch Point of Elastic Equilibrium”, in the form of energy variation he illustrated the essential difference between the two and the identification criteria from the theoretical level, showing that the equilibrium described by the homogeneous equation is a special case among equilibrium descriptions made by non-homogeneous or integral equations. The branching point of equilibrium exists as long as the state of equilibrium is given without the deformation component of the lowest intrinsic function.
While this identification criterion does not provide for a concrete method for stability assessment, its significance lies in its applicability to actual structures having initial bending or torsion, such as buckling of plates, side-tipping girders, buckling of arches and rigid-frame structures and bars subject to flexural buckling and stability of side-tipping truss bridges.
Continuous System Analysis Method for Discrete Bar Structure Systems and Theory of Bending and Torsion for Truss Structures
Truss is a kind of discrete bar structure system. In the 1940s, before the birth of the computer, it was difficult to analyse statically indeterminate trusses with classical analytical theory even if there were only about ten degrees of redundancies. Master Li was analysing a complex multi-web chord rhombic truss system in 1942 when he was confronted with tremendous difficulties in resolving a statically indeterminate structure with over 50 degrees of redundancies. It reminded him of the application of membrane theory to the suspenders of suspension bridges that transformed the discrete truss structure system into a continuous structure and he resolved the problem by differential equations.
He carefully deduced the equivalent relationship of rigidity transformation and verified it by repeated model tests. The resulting paper, “New Structural Calculation Method for Truss and Other Similar Structures”, opened a new way for the analysis of truss structures and build a bridge between discrete and continuous structures.
Using the same concept, Master Li established the Theory of Bending and Torsion for Truss Structures thirty years later, which combined the theory of spatial bar structure system in truss bridges with the bending and torsion theory of closed thin-wall members. The theory systematically resolved the challenges of spatial, stability and vibrational analyses and also clarified the cause of the vibration phenomenon on Wuhan Yangtze River Bridge.
Master Li also brought the newly-created idea of finite elements to the analysis of truss bridges. He broke the continuous truss structure into segments to develop his "truss finite element", which included the displacement parameters of buckling and distortion of the cross sections of the truss. The separated discrete elements greatly facilitated the tackling of real situations involving variable cross sections and multi-span continuous structures. It was flexible for various combinations of truss, arch, suspended and other types of structures. For stability and vibration analyses, it also yielded more accurate results with much less time.
Theory on Bridge Vibrations
In the 1930s, the hot topics of discussion in engineering circles were the force vibrations and impact coefficient induced by steam locomotives on railway bridges. Research into the natural frequency of suspension bridges was quite neglected. Master Li was adept at synthesizing research in his field to arrive at widely applicable theories. For example, he applied Charles Inglis' insight on beam bridge vibration theory to his study of natural vibrations on suspension bridges. In the 1950s he extended his study of vibrations to arch bridges and in the 1960s, he ventured into a study of blast-resistant structures, which involved research into the elastic-plastic vibration mechanics, soil dynamics and explosive wave dynamics of underground reinforced concrete defensive and protective structures subject to sophisticated non-linear vibrations.
From 1978 onwards, Master Li pioneered the dynamic analysis cable-stayed bridges in response to the increasing number of such structures being built in China at the time. Using the finite element method to analyse the dynamics and wind resistance of cable-stayed bridges, he attracted international attention once again by coming up with the concept of “multimode coupled flutter”, which clarified ambiguities in the application of the suspension bridge flutter theory to cable-stayed bridges and improved the experimental methods and numerical calculations used in flutter analysis.
Although he was already in his twilight years in 1988, Master Li remained enthusiastic about researching fluttering on cable-stayed bridges, which had never been studied before. He wanted to make cable-stayed bridges even more economically attractive by enhancing the wind resistance of longer spans. Eventually he was able to show that fluttering on cable-stayed bridges without rapid divergence was due to the non-linear characteristic of stay cables' “effective modulus of elasticity”; rather than the non-existent “system damping”.
Master Li's contributions to the structural vibrations field straddle the advent of the computer age, marking him out as a master of classical theories as well as an expert of new technologies. His contributions in structural vibration studies filled a gap in the study of vehicle impact resistance, blast resistance, seismic and wind resistance, etc.
Load Transverse Distribution Theory and Spatial Analysis of Bridges
Bridges are spatial structures. Load transverse distribution is essential to simplify the spatial analyses in the horizontal plane. While experts and scholars worldwide have developed different solutions, their mechanical models are all approximations that have their respective weaknesses.
While Master Li was banished to hard labour on the Zhenbei Yellow River Bridge in the early 1970s, he proposed a new bridge system model with simple principles that could cover other calculation methods, after an analysis of the pros and cons of the existing methods and combining them with his engineering practice. The model involved dividing the bridge deck into several discrete longitudinal beam elements and distributing the stiffness of a few diaphragms across the bridge deck, omitting the intrinsic normal force and longitudinal shearing forces in the longitudinal profile but keeping the two main vertical shearing forces and bending moments, which are the main contributors to load distribution, in the deck slab. Finally, using the basic assumption of transverse load distribution calculations, planar sinusoidal load was substituted for the actual vehicle load in the practical calculations. The model tests verified the reasonableness and accuracy of this method and design charts were subsequently prepared for practical use. The new bridge system model was very close to the real bridge structure and more accurate than the grillage system. It overcame the shortcomings of frequent conversion of anisotropic slab models and reflected the importance of having few diaphragms in the calculation. The model is also feasible for hinge-connected slab and hinge-connected T-beam bridges simply by omitting the bending moments in the joint between slabs.
His 1977 book , Computation of Transverse Load Distribution for Highway Bridges, concluded 30 years of research into this important field. The following year he also published an article, “Theory of Transverse Load Distribution Analysis for Arch Bridges”, which greatly improved calculations of transverse load distribution in arch design. The prevailing method was either the average distribution method or rigidity distribution method, which were rough transverse load distribution methods. Load distribution on an arch bridge is different from a beam bridge as the structure is subject to both axial force and bending moments and has different characteristic in load distribution in comparison with beam bridges. In the theoretical analysis of an arch, all internal forces between the adjacent split arch elements must be considered. Master Li extended his beam bridge analysis method to arch bridges and established the theory in this area, which was verified by in-situ testing. In 1989, he further promoted this analysis method and completed the research on the calculation of curved bridge transverse load distribution.
In drawing attention to Master Li's contributions to spatial analysis, mention must also be made of his 1958 paper, “Bending Theory of Skew Anisotropic Plate and Its Application to Skew Bridges”, which extended the theory of orthotropic plate to skew beam grillage system theory through oblique coordinates as their two special cases. This pioneering work was acknowledged by mechanics experts worldwide and often cited as "Li’s Theory".
Extracted from Biography of Chinese Scientific and Technological Expert Civil Engineering and Architecture Volume
(BRIDGE Magazine Volume 2004, ISSUE 2)
Translater： Nessy Liu；Revisor： Angela Tam