TECHNICAL PAPERS
May 1, 1987

Static Reanalysis: A Review

Publication: Journal of Structural Engineering
Volume 113, Issue 5

Abstract

The methods of static reanalysis of structures are reviewed and an update on the review written by Arora in 1976 is provided. With the advent of even less expensive computing and the introduction of optimization techniques to practical design problems, these methods are likely to become more important in the next few years.

Get full access to this article

View all available purchase options and get full access to this article.

References

1.
Abu Kassim, A. M., “The Theorems of Structural and Geometric Variation for Linear and Nonlinear Finite Element Analysis,” thesis presented to the University of Edinburgh, Edinburgh, U.K., in 1985, in fulfillment of the requirements for the degree of Doctor of Philosophy.
2.
Argyris, J. H., “The Matrix Analysis of Structures with Cutouts and Modifications,” Proceedings, 9th International Congress of Applied Mechanics, University of Brussels, Brussels, Belgium, Vol. 6, 1956, pp. 131–140.
3.
Argyris, J. H., Bronlund, O. E., Roy, J. R., and Scharpf, D. W., “A Direct Modification Procedure for the Displacement Method,” AIAA Journal, Vol. 9, No. 9, Sep., 1971, pp. 1861–1864.
4.
Argyris, J. H., and Kelsey, S., “Initial Strains in the Matrix Force Method of Structural Analysis,” Journal of the Royal Aeronautic Society, Vol. 64, Aug., 1960, pp. 493–495.
5.
Argyris, J. H., and Kelsey, S., “The Matrix Force Method of Structural Analysis and Some New Applications,” R&M No. 3034, Great British Aeronautical Research Council Technical Report, London, England, Vol. 93, Feb., 1956, pp. 787–828.
6.
Argyris, J. H., and Roy, J. R., “General Treatment of Structural Modifications,” Journal of the Structural Division, ASCE, Vol. 98, No. 2, Feb., 1972, pp. 465–492.
7.
Armen, H., “Applications of a Substructuring Technique to the Problem of Crack Extension and Closure,” Report No. NASA‐CR‐132458, RE‐480, Grumman Aerospace Corp., Research Dept., Bethpage, N.Y., 1974.
8.
Arora, J. S., “Survey of Structural Reanalysis Techniques,” Journal of the Structural Division, ASCE, Vol. 102, No. 4, Apr., 1976, pp. 783–802.
9.
Arora, J. S., and Rim, K., “An Algorithm for Fail Safe Structural Optimization and a Review of Reanalysis Techniques,” Tech. Rept. No. 11, Dept. of Mechanics and Hydraulics, College of Engineering, University of Iowa, Iowa City, Iowa, 1974.
10.
Atrek, E., “Theorems of Structural Variation: A Simplification,” International Journal for Numerical Methods in Engineering, Vol. 21, 1985, pp. 481–485.
11.
Atrek, E., Gallagher, R. H., Ragsdell, K. M., and Zienkiewicz, O. C., Eds., New Directions in Optimum Structural Design, John Wiley and Sons, New York, N.Y., 1984.
12.
Bakry, M. A. E., “Optimal Design of Transmission Towers,” thesis presented to the University of Surrey, Guildford, U.K., in 1978, in fulfillment of the requirements for the degree of Doctor of Philosophy.
13.
Bennett, J. M., “Triangular Factors of Modified Matrcies,” Numerishe Mathematik, Vol. 7, 1965, pp. 217–221.
14.
Best, G., “A Method of Structural Weight Minimization Suitable for High‐Speed Digital Computers,” AIAA Journal, Vol. 1, No. 2, Feb., 1963, pp. 478–479.
15.
Best, G. C., “The Stress‐Area Method Applied to Frames,” Journal of Aeronautical Sciences, Vol. 13, No. 3, Mar., 1946, pp. 151–155.
16.
Best, G. C., “The Stress‐Area Method of Designing Beams,” Journal of Aeronautical Sciences, Vol. 12, No. 3, Jul, 1945, pp. 298–304.
17.
Bhatia, K. G., “Rapid Iterative Reanalysis for Automated Design,” NASA TN D‐7357, NASA, Washington, D.C., 1973.
18.
Brock, J. E., “Variation of Coefficients of Simultaneous Linear Equations,” Quarterly of Applied Mathematics, Vol. 11, No. 2, 1953, pp. 234–240.
19.
Celik, T., “Nonlinear Moment Curvature Analysis by Means of Theorems of Structural Variation,” Istanbul Devlet Muhendislik ve Mimarlik Akademisi Dergisi, Vol. 6, 1981, pp. 81–103.
20.
Celik, T., “The Theorems of Structural Variation and Their Application in the Elastic‐Plastic Analysis of Frames,” Istanbul Devlet Muhendislik ve Mimarlik Akademisi Dergisi, Vol. 5, 1979, pp. 125–138.
21.
Cicala, P., “Effects of Cutouts in Semimonocoque Structures,” Journal of the Aerospace Sci., Vol. 15, No. 3, Mar., 1948, pp. 171–179.
22.
Das, P. C., “Reanalysing Structures with Small Modifications,” Computer Aided Design, Vol. 10, No. 6, Nov., 1978, pp. 371–374.
23.
Ding, H., and Gallagher, R. H., “Approximate Force Method Reanalysis Techniques in Structural Optimization,” International Journal for Numerical Methods in Engineering, Vol. 21, 1985, pp. 1253–1267.
24.
Ertas, R., and Fenves, S. J., “Automatic Analyser for Iterative Design,” Civil Engineering Studies, Structural Research Series No. 352, University of Illinois, Illinois, 1969.
25.
Fenves, S. J., and Ertas, R., Discussion of “Multiple Configuration Analysis of Structures” by R. J. Mclosh and R. Luik, Journal of the Structural Division, ASCE, Vol. 95, No. 7, Jul., 1969, pp. 1586–1589.
26.
Fletcher, R., and Powell, M. J. D., “On the Modification of LDLT Factorizations,” Mathematics of Computation, Vol. 28, No. 128, Oct., 1974, pp. 1067–1087.
27.
Fox, R. L., Optimization Methods for Engineering Design, Addison‐Wesley Publishing Co., Reading, Mass., 1971.
28.
Fox, R. L., and Miura, H., “An Approximate Analysis Technique for Design Calculations,” AIAA Journal, Vol. 9, No. 1, Jan., 1971, pp. 177–179.
29.
Gill, P. E., Golub, G. H., Murray, W., and Saunders, M. A., “Methods for Modifying Matrix Factorizations,” Mathematics of Computation, Vol. 28, No. 126, Apr., 1974, pp. 505–535.
30.
Gill, P. E., Murray, W., and Saunders, M. A., “Methods for Computing and Modifying the LDV Factors of a Matrix,” Mathematics of Computation, Vol. 29, No. 132, Oct., 1975, pp. 1051–1077.
31.
Goodey, W. J., “Notes on a General Method of Treatment of Structural Discontinuities,” Journal of the Royal Aeronautical Society, Vol. 59, Oct., 1955, pp. 695–697.
32.
Goodey, W. J., “Solution of Modified Linear Simultaneous Equations,” Aircraft Engineering, Vol. 31, Dec., 1959, pp. 358–359, and 364.
33.
Grzedzielski, A. L. M., “Note on Some Applications of the Matrix Force Method of Structural Analysis,” Journal of the Royal Aeronautical Society, Vol. 64, Jun., 1960, pp. 354–357.
34.
Grzedzielski, A. L. M., Argyris, J. H., and Kelsey, S., Discussion and Comments on “The Initial Strain Concept,” Journal of the Royal Aeronautical Society, Vol. 65, Feb., 1961, pp. 127–138.
35.
Hirai, I., Wang, B. P., and Pilkey, W. D., “An Efficient Zooming Method for Finite Element Analysis,” International Journal for Numerical Methods in Engineering, Vol. 20, 1984, pp. 1671–1683.
36.
Hoerner, S. V., “Homologous Deformations of Tiltable Telescopes,” Journal of the Structural Division, ASCE, Vol. 93, No. 5, Oct., 1967, pp. 461–485.
37.
Householder, A. S., Principles of Numerical Analysis, McGraw‐Hill Book Co., New York, N.Y., 1953.
38.
Householder, A. S., “A Survey of Some Closed Methods for Inverting Matrices,” SIAM Journal, Vol. 5, No. 3, Sep., 1957, pp. 155–169.
39.
Householder, A. S., The Theory of Matrices in Numerical Analysis, Blaisdell Pub. Co., New York, N.Y., 1964.
40.
Kavanagh, K. T., “An Approximate Algorithm for the Reanalysis of Structures by the Finite Element Method,” Computers and Structures, Vol. 2, 1972, pp. 713–722.
41.
Kavlie, D., and Powell, G. H., “Efficient Reanalysis of Modified Structures,” Journal of the Structural Division, ASCE, Vol. 97, No. 1, Jan., 1971, pp. 377–392.
42.
Kirsch, U., “Approximate Structural Reanalysis Based on Series Expansion,” Computer Methods in Applied Mechanics and Engineering, Vol. 26, 1981, pp. 205–223.
43.
Kirsch, U., “Approximate Structural Reanalysis for Optimization along a Line,” International Journal for Numerical Methods in Engineering, Vol. 18, 1982, pp. 635–651.
44.
Kirsch, U., “On Some Simplified Models for Optimal Design of Structural Systems,” Computer Methods in Applied Mechanics and Engineering, Vol. 48, 1985, pp. 155–169.
45.
Kirsch, U., “Optimal Design Based on Approximate Scaling,” Journal of the Structural Division, ASCE, Vol. 108, No. 4, Apr., 1982, pp. 888–909.
46.
Kirsch, U., Optimum Structural Design, McGraw‐Hill Book Co., New York, N.Y., 1981.
47.
Kirsch, U., and Hofman, B., “Approximate Behavior Models for Optimum Structural Design,” Proceedings International Symposium on Optimum Structural Design, Tuscon, Ariz., 1981, pp. 7.17–7.26.
48.
Kirsch, U., and Rubinstein, M. F., “Modification of Structural Analysis by the Solution of a Reduced Set of Equations,” UCLA Paper ENG‐0570, University of California, Los Angeles, Calif., 1970.
49.
Kirsch, U., and Rubinstein, M. F., “Reanalysis for Limited Structural Design Modifications,” Journal of the Engineering Mechanics Division, ASCE, Vol. 98, No. 1, Feb., 1972, pp. 61–70.
50.
Kirsch, U., and Rubinstein, M. F., “Structural Reanalysis by Iteration,” Computers and Structures, Vol. 2, 1972, pp. 497–510.
51.
Kirsch, U., and Toledano, G., “Approximate Reanalysis for Modifications of Structural Geometry,” Computers and Structures, Vol, 16, 1983, pp. 269–277.
52.
Kleiber, M., and Lutoborski, A., “Modified Triangular Factors in the Incremental Finite Element Analysis with Nonsyrnmetric Stiffness Changes,” Computers and Structures, Vol. 9, 1978, pp. 599–602.
53.
Kosko, E., “Effect of Local Modifications in Redundant Structures,” Journal of the Aerospace Sci., Vol. 21, No. 3, Mar., 1954, pp. 206–207.
54.
Kosko, E., “Matrix Inversion by Partitioning,” Aeronautical Quarterly, Vol. 8, May, 1957, pp. 157–184.
55.
Lam, H. L., Choi, K. K., and Haug, E. J., “A Sparse Matrix Finite Element Technique for Iterative Structural Optimization,” Computers and Structures, Vol. 16, 1983, pp. 289–295.
56.
Law, K. H., “Sparse Matrix Factor Modification in Structural Reanalysis,” International Journal for Numerical Methods in Engineering, Vol. 21, 1985, pp. 37–63.
57.
Law, K. H., and Fenves, S. J., “Sparse Matrices, Graph Theory, and Reanalysis,” Proceedings of the International Conference in Civil Engineering, ASCE, New York, N.Y., May 12–14, 1981, pp. 234–249.
58.
MacNeal, R. H., “Application of the Compensation Theorem to the Modification of Redundant Structures,” Journal of the Aeronautic Scientist, Vol. 20, No. 10, Oct., 1953, pp. 726–727.
59.
Majid, K. I., Optimum Design of Structures, Newnes Butterworth, London, England, 1974.
60.
Majid, K. I., and Celik, T., “The Elastic‐Plastic Analysis of Frames by the Theorems of Structural Variation,” International Journal for Numerical Methods in Engineering, Vol. 21, 1985, pp. 671–681.
61.
Majid, K. I., and Elliott, D. W. C., “Forces and Deflections in Changing Structures,” The Structural Engineer, Vol. 51, No. 3, Mar., 1973, pp. 93–101.
62.
Majid, K. I., and Elliott, D. W. C., “Topological Design of Pin Jointed Structures by Non‐linear Programming,” Proceedings of the Institution of Civil Engineers, Vol. 55, Part 2, Mar., 1973, pp. 129–149.
63.
Majid, K. I., and Saka, M. P., “Optimum Shape Design of Rigidly Jointed Frames,” Proceedings of the Symposium on the Application of Computer Methods in Engineering, Vol. 1, University of Southern California, Los Angeles, Calif., pp. 521–531.
64.
Majid, K. I., Saka, M. P., and Celik, T., “The Theorems of Structural Variation Generalised for Rigidly Jointed Frames,” Proceedings of the Institution of Civil Engineering, Vol. 65, Part 2, Dec., 1978, pp. 839–856.
65.
Meek, J. L., Matrix Structural Analysis, McGraw‐Hill Book Co., New York, N.Y., 1971.
66.
Melosh, R. J., “Structural Analysis, Fraility Evaluation and Redesign,” Tech. Report No. TR‐70‐15, Vol. 1, Air Force Flight Dynamics Lab., Wright‐Patterson Air Force Base, Ohio, 1970.
67.
Melosh, R. J., Johnson, J. R., and Luik, R., “Survivability Analysis of Structures,” Proceedings of the 2nd, Conference on Matrix Methods in Structural Mechanics, AFFDL‐TR‐68‐150, Wright‐Patterson Air Force Base, Ohio, Dec., 1969.
68.
Melosh, R. J., and Luik, R., “Approximate Multiple Configuration Analysis and Allocation for Least Weight Structural Design,” AFFDL‐TR‐67‐59, Wright‐Patterson Air Force Base, Ohio, 1967.
69.
Melosh, R. J., and Luik, R., “Multiple Configuration Analysis of Structures,” Journal of the Structural Division, ASCE, Vol. 94, No. 11, Nov., 1968, pp. 2581–2596.
70.
Melosh, R. J., and Luik, R., Closure on “Multiple Configuration Analysis of Structures,” Journal of the Structural Division, ASCE, Vol. 96, No. 6, Jun., 1970, pp. 1239–1241.
71.
Michielson, H. F., and Dijka, A., “Structural Modifications in Redundant Structures,” Journal of the Aerospace Sci., Vol. 20, No. 4, Apr., 1953, pp. 286–288.
72.
Mohraz, B., and Wright, R. N., “Solving Topologically Modified Structures,” Computers and Structures, Vol. 3, 1973, pp. 341–353.
73.
Noor, A. K., “Multiple Configuration Analysis via Mixed Method,” Journal of the Structural Division, ASCE, Vol. 100, No. 9, Sep., 1974, pp. 1991–1997.
74.
Noor, A. K., “Recent Advances in Reduction Methods for Nonlinear Problems,” Computers and Structures, Vol. 13, 1981, pp. 31–44.
75.
Noor, A. K., and Lowder, H. E., “Approximate Reanalysis Techniques with Substructuring,” Journal of the Structural Division, ASCE, Vol. 101, No. 8, Aug., 1975, pp. 1687–1698.
76.
Noor, A. K., and Lowder, H. E., “Approximate Techniques of Structural Reanalysis,” Computers and Structures, Vol. 4, 1974, pp. 801–812.
77.
Noor, A. K., and Lowder, H. E., “Structural Reanalysis via a Mixed Method,” Computers and Structures, Vol. 5, 1975, pp. 9–12.
78.
Noor, A. K., and Peters, J. M., “Nonlinear Analysis via Global‐Local Mixed Finite Element Approach,” International Journal for Numerical Methods in Engineering, Vol. 15, 1980, pp. 1363–1380.
79.
Noor, A. K., and Peters, J. M., “Reduced Basis Technique for Nonlinear Analysis of Structures,” AIAA Journal, Vol. 18, No. 4, Apr., 1980, pp. 455–462.
80.
Pestel, E. C., and Leckie, F. A., Matrix Methods in Elastomechanics, McGraw‐Hill Book Co., New York, N.Y., 1963.
81.
Phansalkar, S. R., “Matrix Iterative Methods for Structural Reanalysis,” Computers and Structures, Vol. 4, 1974, pp. 779–800.
82.
Pipes, L. A., Matrix Methods in Engineering, Prentice‐Hall Inc., Englewood Cliffs, N.J., 1963.
83.
Poppleton, E. D., “Note on the Design of Redundant Structures,” UTIA Tech. Note, No. 36, Institute of Aerophysics, University of Toronto, 1960.
84.
Poppleton, E. D., “The Redesign of Redundant Structures Having Undesirable Stress Distributions,” Journal of the Aerospace Sci., Vol. 28, No. 5, Apr., 1961, pp. 347–348.
85.
Raibstein, A. I., Kalev, I., and Pipano, A., “Efficient Reanalysis of Structures by a Direct Modification Procedure,” Fifth Nastran User's Colloquium, Berkeley, Calif., 1976.
86.
Romstad, K. M., Hutchinson, J. R., and Runge, K. H., “Design Parameter Variation and Structural Response,” International Journal for Numerical Methods in Engineering, Vol. 5, 1973, pp. 337–349.
87.
Row, D. G., Powell, G. H., and Mondkar, D. P., “Solution of Progressively Changing Equilibrium Equations for Nonlinear Structures,” Computers and Structures, Vol. 7, 1977, pp. 659–665.
88.
Sack, R. L., Carpenter, W. C., and Hatch, G. L., “Modification of Elements in the Displacement Method,” AIAA Journal, Vol. 5, No. 9, Sep., 1967, pp. 1708–1710.
89.
Schmit, L. A., “Literature Review and Assessment of the Present Position,” AGAR Dograph No. 149 on Structural Design and Applications of Mathematical Programming Techniques, 1971, pp. 34–45.
90.
Schmit, L. A., and Farshi, B., “Some Approximation Concepts for Structural Synthesis,” AIAA Journal, Vol. 12, No. 5, May, 1974, pp. 692–699.
91.
Sherman, J., and Morrison, W. J., “Adjustment of an Inverse Matrix Corresponding to a Change in One Element of a Given Matrix,” Annals of Mathematical Statistics, Vol. 21, 1950, pp. 124–126.
92.
Sherman, J., and Morrison, W. J., “Adjustment of an Inverse Matrix Corresponding to Changes in the Elements of a Given Column or a Given Row of the Original Matrix,” Annals of Mathematical Statistics, Vol. 20, 1949, pp. 621.
93.
Sobieszczanski, J., “Evaluation of Algorithms for Structural Modification,” Proceedings of the Conference on Finite Element Methods in Civil Engineering, Vanderbilt University, Nashville, Tenn., 1969, pp. 129–153.
94.
Sobieszczanski, J., “Matrix Algorithm for Structural Modification Based upon the Parallel Element Concept,” AIAA Journal, Vol. 7, No. 11, Nov., 1969, pp. 2132–2139.
95.
Sobieszczanski, J., “Structural Modification by Perturbation Method,” Journal of Hie Structural Division, ASCE, Vol. 94, No. 12, Dec., 1968, pp. 2799–2816.
96.
Storaasli, O. O., and Sobieszczanski, J., “Design Oriented Structural Analysis,” AIAA Paper 73‐338, AIAA, Williamsburgh, Va., 1973.
97.
Storaasli, O. O., Sobieszczanski, J., “On the Accuracy of Taylor Approximation,” AIAA Journal, Vol. 12, No. 2, Feb., 1974, pp. 231–233.
98.
Topping, B. H. V., “The Application of Dynamic Relaxation to the Design of Modular Space Structures,” thesis presented to City University, London, U.K., in 1978, in fulfillment of the requirements for the degree of Doctor of Philosophy.
99.
Topping, B. H. V., “The Application of the Theorems of Structural Variation to Finite Element Problems,” International Journal for Numerical Methods in Engineering, Vol. 19, 1983, pp. 141–144.
100.
Topping, B. H. V., and Chan, H. F., “An Exact Formulation of the Theorems of Geometric Variation for Statically Indeterminate Trusses,” Report, Department of Civil Engineering, University of Edinburgh, Edinburgh, U.K., 1983.
101.
Wang, B. P., and Pilkey, W. D., “Efficient Reanalysis of Locally Modified Structures,” Proceedings 1st, Chautaqua on Finite Element Modelling, Schaeffer Analysis, 1980, pp. 37–61.
102.
Wang, B. P., and Pilkey, W. D., “Efficient Reanalysis of Locally Modified Structures,” Department of Mechanical and Aerospace Engineering, Virginia University, Charlottesville, Va., 1980.
103.
Wang, B. P., and Pilkey, W. D., “Parameterization in Finite Element Analysis,” Proceedings International Symposium on Optimum Structural Design, Tuscon, Ariz., 1981, pp. 7.1–7.7.
104.
Wang, B. P., Pilkey, W. D., and Palazzolo, A. R., “Reanalysis, Modal Synthesis and Dynamic Design,” State‐of‐the‐Art Surveys on Finite Element Technology, A. K. Noor, and W. D. Pilkey, Eds., American Society of Mechanical Engineers, New York, N.Y., 1983, pp. 225–295.
105.
Weiner, B. L., “Variation of Coefficients of Simultaneous Linear Equations,” Transactions, ASCE, Vol. 113, 1948, pp. 1,349–1,390.
106.
Wiberg, N. E., Discussion of “Efficient Reanalysis of Modified Structures,” by D. Kavlie and G. H. Powell, Journal of the Structural Division, ASCE, Vol. 97, No. 10, Oct., 1971, pp. 2612–2619.
107.
Yang, W. H., “A Method for Updating Cholesky Factorization of a Band Matrix,” Computer Methods in Applied Mechanics and Engineering, Vol. 12, 1977, pp. 281–288.
108.
Young, R. C., “Efficient Nonlinear Analysis of Factored Matrix Modification,” Transactions of the 4th International Conference on Structural Mechanics in Reactor Technology, San Francisco, Calif., Aug., 1977, pp. M4/3.
109.
Zielke, G., “Inversion of Modified Symmetric Matrices,” Journal of the Association for Computing Machinery, Vol. 15, No. 3, Jul., 1968, pp. 402–408.
110.
Zimmermann, K. J., and Spence, R., “Interactive Use of Finite Element Programs—or—How to Get More Out of Your Finite Element Model,” Computers and Structures, Vol. 12, 1980, pp. 633–638.

Information & Authors

Information

Published In

Go to Journal of Structural Engineering
Journal of Structural Engineering
Volume 113Issue 5May 1987
Pages: 1029 - 1045

History

Published online: May 1, 1987
Published in print: May 1987

Permissions

Request permissions for this article.

Authors

Affiliations

A. M. Abu Kassim
Research Student, Dept. of Civ. Engrg., Univ. of Edinburgh, Edinburgh, EH9 3JL, U.K.
B. H. V. Topping
Lect. in Civ. Engrg., Univ. of Edinburgh, Edinburgh, U.K.

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share