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LimitState:SLAB Validation Tests
Below are a selection of example problems considered in the literature which have been analysed using LimitState:SLAB for validation purposes.
Generally coarse numerical discretizations have been used, which enables solutions to be obtained in a second or two on a desktop PC; the accuracy obtained is generally sufficient for engineering purposes, though improved (lower) load factors can generally be obtained if desired by using a finer numerical discretization.
In some cases it can be observed that LimitState:SLAB finds a failure mechanism and associated load factor which is lower than the compared benchmark (i.e. an improved solution is found). This is particularly noticeable when complex yield patterns are critical, which would be very difficult to find by hand.
Isotropic
Square with fixed supports, modelled with eighth symmetry
Benchmark | 42.85 |
Result | 43.04 |
Discrepancy on Collapse Load | 0.43% |
General Description
Square reinforced concrete slabKey Dimensions
1m x 1mAdequacy Factor on Load
Unit area loadBoundary Conditions
One fixed edge and two lines of symmetryConcrete Properties
m = 1kNm/mPartial Factors
UnityBenchmark Solution
42.851Reference
M.P. Nielsen, Limit analysis and concrete plasticity, CRC Press (1998), p 506. Available from http://books.google.co.uk/books?id=HNJNwkDlI3kC&lpg=PP1&pg=PP1Square with fixed supports
Benchmark | 42.85 |
Result | 43.26 |
Discrepancy on Collapse Load | 0.94% |
General Description
Square reinforced concrete slabKey Dimensions
1m x 1mAdequacy Factor on Load
Unit area loadBoundary Conditions
Four fixed edgesConcrete Properties
m = 1kNm/mPartial Factors
UnityBenchmark Solution
42.851Reference
M.P. Nielsen, Limit analysis and concrete plasticity, CRC Press (1998), p 506. Available from http://books.google.co.uk/books?id=HNJNwkDlI3kC&lpg=PP1&pg=PP1Irregular hexagon with simple supports, modelled with quarter symmetry
Benchmark | 5.5 |
Result | 5.5 |
Discrepancy on Collapse Load | 0.02% |
General Description
Hexagonal reinforced concrete slabKey Dimensions
a = 1.414m, b = 1mAdequacy Factor on Load
Unit area loadBoundary Conditions
One simply supported edge and two lines of symmetryConcrete Properties
m = 1kNm/mPartial Factors
UnityBenchmark Solution
5.5Reference
M.P. Nielsen, Limit analysis and concrete plasticity, CRC Press (1998), p 504. Available from http://books.google.co.uk/books?id=HNJNwkDlI3kC&lpg=PP1&pg=PP1Irregular hexagon with simple supports
Benchmark | 5.5 |
Result | 5.5 |
Discrepancy on Collapse Load | 0.02% |
General Description
Hexagonal reinforced concrete slabKey Dimensions
a = 1.414m, b = 1mAdequacy Factor on Load
Unit area loadBoundary Conditions
Six simply supported edgesConcrete Properties
m = 1kNm/mPartial Factors
UnityBenchmark Solution
5.5Reference
M.P. Nielsen, Limit analysis and concrete plasticity, CRC Press (1998), p 504. Available from http://books.google.co.uk/books?id=HNJNwkDlI3kC&lpg=PP1&pg=PP1Square with simple supports, modelled with eighth symmetry
Benchmark | 24 |
Result | 24 |
Discrepancy on Collapse Load | 0% |
General Description
Square reinforced concrete slabKey Dimensions
1m x 1mAdequacy Factor on Load
Unit area loadBoundary Conditions
Four simply supported edgesConcrete Properties
m = 1kNm/mPartial Factors
UnityBenchmark Solution
24Reference
M.P. Nielsen, Limit analysis and concrete plasticity, CRC Press (1998), p 504. Available from http://books.google.co.uk/books?id=HNJNwkDlI3kC&lpg=PP1&pg=PP1Square with simple supports
Benchmark | 24 |
Result | 24 |
Discrepancy on Collapse Load | 0% |
General Description
Square reinforced concrete slabKey Dimensions
1m x 1mAdequacy Factor on Load
Unit area loadBoundary Conditions
Four simply supported edgesConcrete Properties
m = 1kNm/mPartial Factors
UnityBenchmark Solution
24Reference
M.P. Nielsen, Limit analysis and concrete plasticity, CRC Press (1998), p 506. Available from http://books.google.co.uk/books?id=HNJNwkDlI3kC&lpg=PP1&pg=PP1Square with three simply supported edges
Benchmark | 14.14 |
Result | 14.16 |
Discrepancy on Collapse Load | 0.14% |
General Description
Square reinforced concrete slabKey Dimensions
1m x 1mAdequacy Factor on Load
Unit area loadBoundary Conditions
Three simply supported edges and one free edgeConcrete Properties
m = 1kNm/mPartial Factors
UnityBenchmark Solution
14.14Reference
J. Wüst and W. Wagner, Systematic prediction of yield-line configurations for arbitrary polygonal plates, Engineering Structures 30 (2008), pp. 2081-2093. Available from http://dx.doi.org/10.1016/j.engstruct.2008.01.005Triangle with two simply supported edges, mp = 100kNm/m
Benchmark | 12 |
Result | 12.01 |
Discrepancy on Collapse Load | 0.09% |
General Description
Triangular reinforced concrete slabKey Dimensions
10m x 10mAdequacy Factor on Load
Unit area loadBoundary Conditions
Two simply supported edges and one free edgeConcrete Properties
m = 100kNm/mPartial Factors
UnityBenchmark Solution
12Reference
A. Thavalingam, A. Jennings, D. Sloan and J.J. McKeown, Computer-assisted generation of yield-line patterns for uniformly loaded isotropic slabs using an optimisation strategy, Engineering Structures 21 (1999), pp. 488-496. Available from http://dx.doi.org/10.1016/S0141-0296(97)00228-9Rectangle with indent, with three fixed edges, two simply supported edges and one free edge, mp = 100kNm/m
Benchmark | 29.2 |
Result | 29.17 |
Discrepancy on Collapse Load | -0.1% |
General Description
Rectangular reinforced concrete slab with indentKey Dimensions
6m x 10m, indent 2.5m x 1.5mAdequacy Factor on Load
Unit area loadBoundary Conditions
Fixed edges around indent and on adjoining edge, simply supported on two opposite short edges and free on one long edgeConcrete Properties
m = 100kNm/mPartial Factors
UnityBenchmark Solution
29.2Reference
A. Thavalingam, A. Jennings, D. Sloan and J.J. McKeown, Computer-assisted generation of yield-line patterns for uniformly loaded isotropic slabs using an optimisation strategy, Engineering Structures 21 (1999), pp. 488-496. Available from http://dx.doi.org/10.1016/S0141-0296(97)00228-9Rectangle with two alcoves, with seven fixed edges, mp = 100kNm/m
Benchmark | 35.8 |
Result | 35.79 |
Discrepancy on Collapse Load | -0.03% |
General Description
Rectangular reinforced concrete slab with two alcovesKey Dimensions
6m x 10m, alcoves 2m x 2mAdequacy Factor on Load
Unit area loadBoundary Conditions
Fixed on all edges except long edge facing alcovesConcrete Properties
m = 100kNm/mPartial Factors
UnityBenchmark Solution
35.8Reference
A. Thavalingam, A. Jennings, D. Sloan and J.J. McKeown, Computer-assisted generation of yield-line patterns for uniformly loaded isotropic slabs using an optimisation strategy, Engineering Structures 21 (1999), pp. 488-496. Available from http://dx.doi.org/10.1016/S0141-0296(97)00228-9Trapezium with three simply supported edges, modelled with symmetry
Benchmark | 0.28 |
Result | 0.28 |
Discrepancy on Collapse Load | 1.54% |
General Description
Trapezoidal reinforced concrete slabKey Dimensions
Long edge 10m, width 10m, short edge 5mAdequacy Factor on Load
Unit area loadBoundary Conditions
Simply supported on three edges and free on fourth edge modelled with one line of symmetryConcrete Properties
m = 1kNm/mPartial Factors
UnityBenchmark Solution
0.28Reference
A. Thavalingam, A. Jennings, D. Sloan and J.J. McKeown, Computer-assisted generation of yield-line patterns for uniformly loaded isotropic slabs using an optimisation strategy, Engineering Structures 21 (1999), pp. 488-496. Available from http://dx.doi.org/10.1016/S0141-0296(97)00228-9L-shaped with two simply supported edges and four free edges, mp = 11.72kNm/m
Benchmark | 10 |
Result | 10.03 |
Discrepancy on Collapse Load | 0.31% |
General Description
L-shaped reinforced concrete slabKey Dimensions
2.5m x 1.2mAdequacy Factor on Load
Unit area loadBoundary Conditions
Simply supported on opposite endsConcrete Properties
m = 11.72kNm/mPartial Factors
UnityBenchmark Solution
10Reference
A.C.A. Ramsay and D. Johnson, Analysis of practical slab configurations using automated yield-line analysis and geometric optimization of fracture patterns, Engineering Structures 20 (1998), pp. 647-654. Available from http://dx.doi.org/10.1016/S0141-0296(97)00111-9Rectangle supported as a propped cantilever, mp = 5kNm/m
Benchmark | 14.57 |
Result | 14.57 |
Discrepancy on Collapse Load | 0.01% |
General Description
Rectangular reinforced concrete slabKey Dimensions
2m x 1mAdequacy Factor on Load
Unit area loadBoundary Conditions
Fixed and simply supported on opposite short edgesConcrete Properties
m = 5kNm/mPartial Factors
UnityBenchmark Solution
14.57Reference
A.C.A. Ramsay and D. Johnson, Geometric optimization of yield-line patterns using a direct search method, Structural and Multidisciplinary Optimization 14 (1997), pp. 108-115. Available from http://www.springerlink.com/content/g022p37175707016/Square with three simply supported edges
Benchmark | 0.14 |
Result | 0.14 |
Discrepancy on Collapse Load | 1.13% |
General Description
Square reinforced concrete slabKey Dimensions
10m x 10mAdequacy Factor on Load
Unit area loadBoundary Conditions
Simply supported on three edges and free on fourth edgeConcrete Properties
m = 1kNm/mPartial Factors
UnityBenchmark Solution
0.14Reference
A.C.A. Ramsay and D. Johnson, Geometric optimization of yield-line patterns using a direct search method, Structural and Multidisciplinary Optimization 14 (1997), pp. 108-115. Available from http://www.springerlink.com/content/g022p37175707016/Square with fixed supports, modelled with eighth symmetry
Benchmark | 2.68 |
Result | 2.69 |
Discrepancy on Collapse Load | 0.37% |
General Description
Square reinforced concrete slabKey Dimensions
4m x 4mAdequacy Factor on Load
Unit area loadBoundary Conditions
One fixed edge and two lines of symmetryConcrete Properties
m = 1kNm/mPartial Factors
UnityBenchmark Solution
2.68Reference
S. Krenk, L. Damkilde and O. Høyer, Limit Analysis and Optimal Design of Plates with Equilibrium Elements, Journal of Engineering Mechanics 120 (1994), pp. 1237-1254. Available from http://dx.doi.org/10.1061/(ASCE)0733-9399(1994)120:6(1237)Hexagon with simple supports, modelled with sixth symmetry
Benchmark | 6 |
Result | 6 |
Discrepancy on Collapse Load | 0% |
General Description
Hexagonal reinforced concrete slabKey Dimensions
h = 1mAdequacy Factor on Load
Unit area loadBoundary Conditions
One simply supported edge and two lines of symmetryConcrete Properties
m = 1kNm/mPartial Factors
UnityBenchmark Solution
6Reference
M.P. Nielsen, Limit analysis and concrete plasticity, CRC Press (1998). Available from http://books.google.co.uk/books?id=HNJNwkDlI3kC&lpg=PP1&pg=PP1Trapezium with three simply supported edges
Benchmark | 0.285 |
Result | 0.285 |
Discrepancy on Collapse Load | 0% |
General Description
Trapezoidal reinforced concrete slabKey Dimensions
Long edge 10m, width 10m, short edge 5mAdequacy Factor on Load
Unit area loadBoundary Conditions
Three simply supported edges and one free edgeConcrete Properties
m = 1kNm/mPartial Factors
UnityBenchmark Solution
0.285Reference
A.K.H. Kwan, Dip and strike angles method for yield line analysis of reinforced concrete slabs, Magazine of Concrete Research 56 (2004), pp. 487-498. Available from http://www.atypon-link.com/TELF/doi/pdf/10.1680/macr.56.8.487.49450Square with two simply supported edges and one column
Benchmark | 10.67 |
Result | 10.261 |
Discrepancy on Collapse Load | -3.98% |
General Description
Square reinforced concrete slabKey Dimensions
1m x 1mAdequacy Factor on Load
Unit area loadBoundary Conditions
Two adjacent simply supported edges with column at corner of free edges (column as simple support from x/y = 0.9999 to x/y = 1.0)Concrete Properties
m = 1kNm/mPartial Factors
UnityBenchmark Solution
10.67Reference
A.K.H. Kwan, Dip and strike angles method for yield line analysis of reinforced concrete slabs, Magazine of Concrete Research 56 (2004), pp. 487-498. Available from http://www.atypon-link.com/TELF/doi/pdf/10.1680/macr.56.8.487.49450Square with one simply supported edge and one column
Benchmark | 5.17 |
Result | 4.055 |
Discrepancy on Collapse Load | -21.57% |
Note | It is evident that the failure mechanism identified using LimitState:SLAB (adjacent to the column) is different to that proposed by Kwan (single yield-line diagonally across the center of the slab). This is the reasoning for the discrepancy in collapse load obtained. |
General Description
Square reinforced concrete slabKey Dimensions
1m x 1mAdequacy Factor on Load
Unit area loadBoundary Conditions
One simply supported edge and one column at corner of two free edges (column as simple support over distance of 0.0001m in x and y directions)Concrete Properties
m = 1kNm/mPartial Factors
UnityBenchmark Solution
5.17Reference
A.K.H. Kwan, Dip and strike angles method for yield line analysis of reinforced concrete slabs, Magazine of Concrete Research 56 (2004), pp. 487-498. Available from http://www.atypon-link.com/TELF/doi/pdf/10.1680/macr.56.8.487.49450Irregular polygon with two fixed edges and two columns
Benchmark | 0.1967 |
Result | 0.1865 |
Discrepancy on Collapse Load | -5.2% |
General Description
Polygonal reinforced concrete slabKey Dimensions
12m x 10mAdequacy Factor on Load
Unit area loadBoundary Conditions
Two adjacent fixed edges with two columns at corners of free edges (columns as simple support over distance of < 0.0001m in x and y directions)Concrete Properties
m = 1kNm/mPartial Factors
UnityBenchmark Solution
0.1967Reference
A.K.H. Kwan, Dip and strike angles method for yield line analysis of reinforced concrete slabs, Magazine of Concrete Research 56 (2004), pp. 487-498. Available from http://www.atypon-link.com/TELF/doi/pdf/10.1680/macr.56.8.487.4945045 degree triangle with two simply supported edges
Benchmark | 35.3 |
Result | 35.53 |
Discrepancy on Collapse Load | 0.65% |
General Description
Triangular reinforced concrete slabKey Dimensions
Side lengths 1m, angle 45 degreesAdequacy Factor on Load
Unit area loadBoundary Conditions
Two simply supported edges and one free edgeConcrete Properties
m = 1kNm/mPartial Factors
UnityBenchmark Solution
35.3Reference
D. Johnson, Yield-line analysis by sequential linear programming, International Journal of Solids and Structures 32 (1995), pp. 1395-1404. Available from http://dx.doi.org/10.1016/0020-7683(94)00200-G90 degree triangle with two simply supported edges
Benchmark | 12 |
Result | 12 |
Discrepancy on Collapse Load | 0% |
General Description
Triangular reinforced concrete slabKey Dimensions
Side lengths 1m, angle 90 degreesAdequacy Factor on Load
Unit area loadBoundary Conditions
Two simply supported edges and one free edgeConcrete Properties
m = 1kNm/mPartial Factors
UnityBenchmark Solution
12Reference
D. Johnson, Yield-line analysis by sequential linear programming, International Journal of Solids and Structures 32 (1995), pp. 1395-1404. Available from http://dx.doi.org/10.1016/0020-7683(94)00200-GOrthotropic
Octagon with simple supports, orthotropically reinforced with m = 5.83kNm/m, m' = 1kNm/m, modelled with eighth symmetry
Benchmark | 34.97 |
Result | 34.97 |
Discrepancy on Collapse Load | 0% |
General Description
Octagonal reinforced concrete slabKey Dimensions
h = 1mAdequacy Factor on Load
Unit area loadBoundary Conditions
One simply supported edge and two lines of symmetryConcrete Properties
m = 5.83kNm/m, m' = 1kNm/mPartial Factors
UnityBenchmark Solution
34.971Reference
M.P. Nielsen, Limit analysis and concrete plasticity, CRC Press (1998), p 506. Available from http://books.google.co.uk/books?id=HNJNwkDlI3kC&lpg=PP1&pg=PP1Irregular hexagon (a) with simple supports, orthotropically reinforced with m = 1kNm/m, m' = 0kNm/m
Benchmark | 17.75 |
Result | 16.09 |
Discrepancy on Collapse Load | -9.34% |
General Description
Hexagonal reinforced concrete slabKey Dimensions
1.5m x 1mAdequacy Factor on Load
Unit area loadBoundary Conditions
Six simply supported edgesConcrete Properties
m = 1kNm/m, m' = 0kNm/mPartial Factors
UnityBenchmark Solution
17.75Reference
J. Wüst and W. Wagner, Systematic prediction of yield-line configurations for arbitrary polygonal plates, Engineering Structures 30 (2008), pp. 2081-2093. Available from http://dx.doi.org/10.1016/j.engstruct.2008.01.005Irregular hexagon (b) with simple supports, orthotropically reinforced with m = 1kNm/m, m' = 0kNm/m
Benchmark | 54.4 |
Result | 48.42 |
Discrepancy on Collapse Load | -10.99% |
General Description
Hexagonal reinforced concrete slabKey Dimensions
1m x 1mAdequacy Factor on Load
Unit area loadBoundary Conditions
Six simply supported edgesConcrete Properties
m = 1kNm/m, m' = 0kNm/mPartial Factors
UnityBenchmark Solution
54.4Reference
J. Wüst and W. Wagner, Systematic prediction of yield-line configurations for arbitrary polygonal plates, Engineering Structures 30 (2008), pp. 2081-2093. Available fromhttp://dx.doi.org/10.1016/j.engstruct.2008.01.005
Pentagon with simple supoorts, orthotropically reinforced with m = 1.89kNm/m, m' = 1kNm/m, modelled with fifth symmetry
Benchmark | 11.37 |
Result | 11.37 |
Discrepancy on Collapse Load | 0.03% |
General Description
Pentagonal reinforced concrete slabKey Dimensions
h = 1mAdequacy Factor on Load
Unit area loadBoundary Conditions
One simply supported edge and two lines of symmetryConcrete Properties
m = 1.89kNm/m, m' = 1kNm/mPartial Factors
UnityBenchmark Solution
11.367Reference
M.P. Nielsen, Limit analysis and concrete plasticity, CRC Press (1998). Available from http://books.google.co.uk/books?id=HNJNwkDlI3kC&lpg=PP1&pg=PP1Septagon with simple supports, orthotropically reinforced with m = 4.31kNm/m, m' = 1kNm/m, modelled with seventh symmetry
Benchmark | 25.87 |
Result | 25.87 |
Discrepancy on Collapse Load | 0.01% |
General Description
Septagonal reinforced concrete slabKey Dimensions
h = 1mAdequacy Factor on Load
Unit area loadBoundary Conditions
One simply supported edge and two lines of symmetryConcrete Properties
m = 4.31kNm/m, m' = 1kNm/mPartial Factors
UnityBenchmark Solution
25.872Reference
M.P. Nielsen, Limit analysis and concrete plasticity, CRC Press (1998). Available from http://books.google.co.uk/books?id=HNJNwkDlI3kC&lpg=PP1&pg=PP1Rectangle with three simply supported edges, orthotropically reinforced with mx = 0.4kNm/m, my = 1kNm/m
Benchmark | 19.06 |
Result | 19.06 |
Discrepancy on Collapse Load | 0% |
General Description
Rectangular reinforced concrete slabKey Dimensions
1m x 0.4mAdequacy Factor on Load
Unit area loadBoundary Conditions
Three simply supported edges and one free edgeConcrete Properties
mx = m'x = 0.4kNm/m, my = m'y = 1kNm/mPartial Factors
UnityBenchmark Solution
19.06Reference
A.K.H. Kwan, Dip and strike angles method for yield line analysis of reinforced concrete slabs, Magazine of Concrete Research 56 (2004), pp. 487-498. Available from http://www.atypon-link.com/TELF/doi/pdf/10.1680/macr.56.8.487.49450Rectangle with three simply supported edge and one fixed edge, orthotropically reinforced with mx = 1kNm/m, my = 0.3kNm/m
Benchmark | 0.15 |
Result | 0.15 |
Discrepancy on Collapse Load | 0.48% |
General Description
Rectangular reinforced concrete slabKey Dimensions
20m x 10mAdequacy Factor on Load
Unit area loadBoundary Conditions
Three simply supported edges and one fixed edgeConcrete Properties
mx = m'x = 1kNm/m, my = m'y = 0.3kNm/mPartial Factors
UnityBenchmark Solution
0.151Reference
A.K.H. Kwan, Dip and strike angles method for yield line analysis of reinforced concrete slabs, Magazine of Concrete Research 56 (2004), pp. 487-498. Available from http://www.atypon-link.com/TELF/doi/pdf/10.1680/macr.56.8.487.49450Triangle with two simply supported edges, orthotropically reinforced with m = 100kNm/m, m' = 50kNm/m
Benchmark | 11.72 |
Result | 11.66 |
Discrepancy on Collapse Load | -0.53% |
General Description
Triangular reinforced concrete slabKey Dimensions
10m x 10mAdequacy Factor on Load
Unit area loadBoundary Conditions
Two simply supported edges and one free edgeConcrete Properties
m = 100kNm/m, m' = 50kNm/mPartial Factors
UnityBenchmark Solution
11.72Reference
A. Thavalingam, A. Jennings, D. Sloan and J.J. McKeown, Computer-assisted generation of yield-line patterns for uniformly loaded isotropic slabs using an optimisation strategy, Engineering Structures 21 (1999), pp. 488-496. Available from http://dx.doi.org/10.1016/S0141-0296(97)00228-9Triangle with two simply supported edges, orthotropically reinforced with m = 100kNm/m, m' = 0kNm/m
Benchmark | 9.5 |
Result | 9.43 |
Discrepancy on Collapse Load | -0.76% |
General Description
Triangular reinforced concrete slabKey Dimensions
10m x 10mAdequacy Factor on Load
Unit area loadBoundary Conditions
Two simply supported edges and one free edgeConcrete Properties
m = 100kNm/m, m' = 0kNm/mPartial Factors
UnityBenchmark Solution
9.5Reference
A. Thavalingam, A. Jennings, D. Sloan and J.J. McKeown, Computer-assisted generation of yield-line patterns for uniformly loaded isotropic slabs using an optimisation strategy, Engineering Structures 21 (1999), pp. 488-496. Available from http://dx.doi.org/10.1016/S0141-0296(97)00228-9Rectangle with fixed supports, orthotropically reinforced with mx = 2kNm/m, my = 1kNm/m, modelled with quarter symmetry
Benchmark | 104 |
Result | 94.44 |
Discrepancy on Collapse Load | -9.19% |
General Description
Rectangular reinforced concrete slabKey Dimensions
1m x 0.75mAdequacy Factor on Load
Unit area loadBoundary Conditions
Two fixed edges and two lines of symmetryConcrete Properties
mx = m'x = 2kNm/m, my = m'y = 1kNm/mPartial Factors
UnityBenchmark Solution
104Reference
D. Johnson, Automated yield-line analysis of orthotropic slabs, International Journal of Solids and Structures 33 (1996), pp. 1-10. Available from http://dx.doi.org/10.1016/0020-7683(95)00025-6Rectangle with three simply supported edges, orthotropically reinforced with mx = 1kNm/m, my = 2kNm/m
Benchmark | 8.87 |
Result | 8.84 |
Discrepancy on Collapse Load | -0.37% |
General Description
Rectangular reinforced concrete slabKey Dimensions
2m x 1mAdequacy Factor on Load
Unit area loadBoundary Conditions
Three simply supported edges and one free edgeConcrete Properties
mx = m'x = 2kNm/m, my = m'y = 1kNm/mPartial Factors
UnityBenchmark Solution
8.87Reference
D. Johnson, Yield-line analysis by sequential linear programming, International Journal of Solids and Structures 32 (1995), pp. 1395-1404. Available from http://dx.doi.org/10.1016/0020-7683(94)00200-GRectangle with one fixed edge and two columns, orthotropically reinforced with m = 1kNm/m, m' = 1.5kNm/m
Benchmark | 3.33 |
Result | 3.33 |
Discrepancy on Collapse Load | 0.04% |
General Description
Rectangular reinforced concrete slabKey Dimensions
1m x 2mAdequacy Factor on Load
Unit area loadBoundary Conditions
One short fixed edge with one column on opposite edge and one line of symmetryConcrete Properties
m = 1kNm/m, m' = 1.5kNm/mPartial Factors
UnityBenchmark Solution
3.333Reference
D. Johnson, Yield-line analysis by sequential linear programming, International Journal of Solids and Structures 32 (1995), pp. 1395-1404. Available from http://dx.doi.org/10.1016/0020-7683(94)00200-G45 degree triangle with two simply supported edges, orthotropically reinforced with m = 1kNm/m, m' = 0kNm/m
Benchmark | 30.1 |
Result | 28.55 |
Discrepancy on Collapse Load | -5.14% |
General Description
Triangular reinforced concrete slabKey Dimensions
Side lengths 1m, angle 45 degreesAdequacy Factor on Load
Unit area loadBoundary Conditions
Two simply supported edges and one free edgeConcrete Properties
m = 1kNm/m, m' = 0kNm/mPartial Factors
UnityBenchmark Solution
30.1Reference
D. Johnson, Yield-line analysis by sequential linear programming, International Journal of Solids and Structures 32 (1995), pp. 1395-1404. Available from http://dx.doi.org/10.1016/0020-7683(94)00200-G45 degree triangle with two simply supported edges, orthotropically reinforced with m = 1kNm/m, m' = 0.5kNm/m
Benchmark | 34.03 |
Result | 33.15 |
Discrepancy on Collapse Load | -2.6% |
General Description
Triangular reinforced concrete slabKey Dimensions
Side lengths 1m, angle 45 degreesAdequacy Factor on Load
Unit area loadBoundary Conditions
Two simply supported edges and one free edgeConcrete Properties
m = 1kNm/m, m' = 0.5kNm/mPartial Factors
UnityBenchmark Solution
34.03Reference
D. Johnson, Yield-line analysis by sequential linear programming, International Journal of Solids and Structures 32 (1995), pp. 1395-1404. Available from http://dx.doi.org/10.1016/0020-7683(94)00200-G90 degree triangle with two simply supported edges, orthotropically reinforced with m = 1kNm/m, m' = 0kNm/m
Benchmark | 10.17 |
Result | 9.5 |
Discrepancy on Collapse Load | -6.57% |
General Description
Triangular reinforced concrete slabKey Dimensions
Side lengths 1m, angle 90 degreesAdequacy Factor on Load
Unit area loadBoundary Conditions
Two simply supported edges and one free edgeConcrete Properties
m = 1kNm/m, m' = 0kNm/mPartial Factors
UnityBenchmark Solution
10.17Reference
D. Johnson, Yield-line analysis by sequential linear programming, International Journal of Solids and Structures 32 (1995), pp. 1395-1404. Available from http://dx.doi.org/10.1016/0020-7683(94)00200-G90 degree triangle with two simply supported edges, orthotropically reinforced with m = 1kNm/m, m' = 0kNm/m
Benchmark | 11.7 |
Result | 11.66 |
Discrepancy on Collapse Load | -0.36% |
General Description
Triangular reinforced concrete slabKey Dimensions
Side lengths 1m, angle 90 degreesAdequacy Factor on Load
Unit area loadBoundary Conditions
Two simply supported edges and one free edgeConcrete Properties
m = 1kNm/m, m' = 0.5kNm/mPartial Factors
UnityBenchmark Solution
11.7Reference
D. Johnson, Yield-line analysis by sequential linear programming, International Journal of Solids and Structures 32 (1995), pp. 1395-1404. Available from http://dx.doi.org/10.1016/0020-7683(94)00200-GSquare with simple supports, orthotropically reinforced with m = 1kNm/m, m' = 0.5kNm/m, modelled with eighth symmetry
Benchmark | 24 |
Result | 23.56 |
Discrepancy on Collapse Load | -1.82% |
General Description
Square reinforced concrete slabKey Dimensions
1m x 1mAdequacy Factor on Load
Unit area loadBoundary Conditions
One simply supported edge and two lines of symmetryConcrete Properties
m = 1kNm/m, m' = 0.5kNm/mPartial Factors
UnityBenchmark Solution
23.262Reference
S. Krenk, L. Damkilde and O. Høyer, Limit Analysis and Optimal Design of Plates with Equilibrium Elements, Journal of Engineering Mechanics 120 (1994), pp. 1237-1254. Available from http://dx.doi.org/10.1061/(ASCE)0733-9399(1994)120:6(1237)Square with simple supports, orthotropically reinforced with m = 1kNm/m, m' = 0.333kNm/m, modelled with eighth symmetry
Benchmark | 23.26 |
Result | 23.17 |
Discrepancy on Collapse Load | -0.38% |
General Description
Square reinforced concrete slabKey Dimensions
1m x 1mAdequacy Factor on Load
Unit area loadBoundary Conditions
One simply supported edge and two lines of symmetryConcrete Properties
m = 1kNm/m, m' = 0.333kNm/mPartial Factors
UnityBenchmark Solution
22.801Reference
S. Krenk, L. Damkilde and O. Høyer, Limit Analysis and Optimal Design of Plates with Equilibrium Elements, Journal of Engineering Mechanics 120 (1994), pp. 1237-1254. Available from http://dx.doi.org/10.1061/(ASCE)0733-9399(1994)120:6(1237)Square with simple supports, orthotropically reinforced with m = 1kNm/m, m' = 0.25kNm/m, modelled with eighth symmetry
Benchmark | 22.8 |
Result | 22.89 |
Discrepancy on Collapse Load | 0.38% |
General Description
Square reinforced concrete slabKey Dimensions
1m x 1mAdequacy Factor on Load
Unit area loadBoundary Conditions
One simply supported edge and two lines of symmetryConcrete Properties
m = 1kNm/m, m' = 0.25kNm/mPartial Factors
UnityBenchmark Solution
22.419Reference
S. Krenk, L. Damkilde and O. Høyer, Limit Analysis and Optimal Design of Plates with Equilibrium Elements, Journal of Engineering Mechanics 120 (1994), pp. 1237-1254. Available from http://dx.doi.org/10.1061/(ASCE)0733-9399(1994)120:6(1237)Square with simple supports, orthotropically reinforced with m = 1kNm/m, m' = 0.125kNm/m, modelled with eighth symmetry
Benchmark | 22.42 |
Result | 22.33 |
Discrepancy on Collapse Load | -0.41% |
General Description
Square reinforced concrete slabKey Dimensions
1m x 1mAdequacy Factor on Load
Unit area loadBoundary Conditions
One simply supported edge and two lines of symmetryConcrete Properties
m = 1kNm/m, m' = 0.125kNm/mPartial Factors
UnityBenchmark Solution
21.878Reference
S. Krenk, L. Damkilde and O. Høyer, Limit Analysis and Optimal Design of Plates with Equilibrium Elements, Journal of Engineering Mechanics 120 (1994), pp. 1237-1254. Available from http://dx.doi.org/10.1061/(ASCE)0733-9399(1994)120:6(1237)Square with simple supports, orthotropically reinforced with m = 1kNm/m, m' = 0kNm/m, modelled with eighth symmetry
Benchmark | 22 |
Result | 21.53 |
Discrepancy on Collapse Load | -2.14% |
General Description
Square reinforced concrete slabKey Dimensions
1m x 1mAdequacy Factor on Load
Unit area loadBoundary Conditions
One simply supported edge and two lines of symmetryConcrete Properties
m = 1kNm/m, m' = 0kNm/mPartial Factors
UnityBenchmark Solution
22Reference
S. Krenk, L. Damkilde and O. Høyer, Limit Analysis and Optimal Design of Plates with Equilibrium Elements, Journal of Engineering Mechanics 120 (1994), pp. 1237-1254. Available from http://dx.doi.org/10.1061/(ASCE)0733-9399(1994)120:6(1237)Trapezium with three simply supported edges, orthotropically reinforced with mx = 1kNm/m, my = 2kNm/m, m' = 0kNm/m
Benchmark | 8.45 |
Result | 7.28 |
Discrepancy on Collapse Load | -13.9% |