StruCla against SCIA Engineer: foundation slab of a support frame

A steel support frame (8 HEB140 members) stands on a concrete plinth wall (1.05 × 0.9 m) that stands on a foundation slab of 1.5 × 1.5 m (slab F6 in the SCIA output). The wall and the slab are 0.4 m thick, C30/37, and the slab lies on gravel subsoil. SCIA calculated five load cases: self weight (BG1), pipes (BG2), friction and stress loads (BG3), wind in X (BG4) and wind in Y (BG5). This is a limited comparison: the forces in the slab are compared in the element centres of a 0.1 m mesh for each load case; for the wind in X the load was raised to 500 kN so that the differences are large enough to judge. The required reinforcement (A_s,req) and the shear check of both slabs are compared with the SCIA reinforcement design, and the wall and slab are compared with only point loads on the wall (no frame) so that each part can be judged on its own. The second slab (frame 1) is compared in the reinforcement only, not in the forces on the fine mesh; the combinations element by element and the steel are not compared. The results come from StruCla's new shell solver (plates in different planes joined along shared edges); it is not yet part of the online app. Project name, client, plant, licence data and author have been removed from the SCIA output.

Green: equal within the larger of 0.15 and 20 % of the SCIA value (kNm/m, kN/m). Red: a larger difference; it is described in section 7. Each cell shows SCIA on top and StruCla below. The shear force is compared as the resultant |v| of v_x and v_y because the local axes of the SCIA mesh elements are not those of StruCla. The last column is the distance between the centre of the SCIA element and that of the StruCla element.

1. Model and input

2. Slab per load case, in the element centres

SCIA table "2D internal forces", load case, location "in centres", basic magnitudes, system LCS mesh element, for elements of the slab. For each element the nearest element of StruCla is compared. The elements lie along the wall and at the ends of the slab, where the forces are largest. Moments in kNm/m, forces in kN/m.

BG1, self weight: 89 of 91 values equal

BG2, pipes: 82 of 84 values equal

BG3, friction and stress: 92 of 98 values equal

BG5, wind Y: 97 of 98 values equal

BG4, wind X, point load raised to 500 kN: 41 of 77 values equal

3. Required reinforcement and shear

The SCIA reinforcement design (EN 1992-1-1, B500B, bars Ø10, cover 25 mm, slab 400 mm thick, centres of the layers 30 mm (layer 1) and 40 mm (layer 2) from the surface, combinations UGT-Set B /1 to /5) gives for the slabs E4 and E6 maps of the required area A_s,req per layer (sheets 3 and 4 of the SCIA output; one scale for both slabs), and a few table values. StruCla takes the forces of the five load cases, combines them with the same factors, and designs with the same rule: Wood-Armer moments (m_Ed = m ± |m_xy|), n_Ed = n + |n_xy|, and a section design for N and M with the lever arm between the two layers (f_yd = 435 MPa). The nodal values are the average of the elements around the node. This design is a script next to the shell solver and not yet a part of the program.

The largest required area of the slabs (E4 and E6 together), in mm²/m:

SCIA's A_s,req is not the plain ultimate-limit-state area. The SCIA report of one node (slab E6, x = 5.30 m, y = −3.20 m, combination /3) shows A_s,req = max(A_s,ult; A_s,min) with A_s,min,2 = 1.25 · A_s,ult (126 = 1.25 · 101 mm²/m for layer 2−) and no serviceability addition (ΔA_s,serv is empty). So the SCIA maps are 1.25 times the ultimate-limit-state area, and StruCla's ultimate-limit-state value is to be compared with the SCIA value divided by 1.25 (third column), or equivalently StruCla's value times 1.25 with the SCIA value (last column: 22 / 24 / 55 / 106 against 18 / 15 / 45 / 113). The factor is a rule of the SCIA design (A_s,min,2 = k_Asmin,2 · A_s,ult, which the report cites as §9.2.1.1(1), eq. 9.1N); the text of the standard was not checked here. On the finest mesh StruCla is within 4 to 8 mm²/m of that value in all four layers (18 / 19 / 44 / 85 against 14 / 12 / 36 / 90). On the mesh of the SCIA output (0.5 m) StruCla is lower, and its largest values rise with the refinement (layer 2−: 41, 66, 85 mm²/m).

All required areas are far below the minimum reinforcement of Ø10-400 = 196 mm²/m, so in SCIA and in StruCla the minimum governs and the reinforcement is the same. The largest values lie in the nodes on the line of the plinth wall, where the load of the wall acts as a line load. Not explained: at the one SCIA node with a detailed report the design moment is 13.2 kNm/m (m_y = 13.10 kNm/m, n_y = 8.71 kN/m), while the SCIA element values around that node for BG1 to BG5 (mesh 0.1 m), combined with the same factors, give about 6.5 kNm/m, and StruCla's elements agree with SCIA's elements (for example element 759, m_y: BG1 1.14 / 1.17, BG2 1.44 / 1.49, BG3 −0.57 / −0.43, BG4 1.82 / 1.86). So the difference at this node lies between SCIA's element values and its nodal values at the free edge, not in the forces. The membrane rule itself reproduces the SCIA design report of a wall node exactly (n_Ed = 3193.6 and 9081.1 kN/m gives 3427 and 9745 mm²/m per face, with σ_s = 465.9 MPa at 45 ‰, as in SCIA).

The shear check without shear reinforcement:

v_Ed is the largest element resultant over the combinations /1 to /5 (SCIA at the node 23.73 at the wall end and 32.57 at the governing node; StruCla at the wall-end elements). v_Rd,c follows EN 1992-1-1 6.2.2 with d = 360 mm and the minimum reinforcement Ø10-400 (the minimum value of the code governs). v_Ed is between a sixth and a third of v_Rd,c in both programs.

4. Wall and slab with point loads only (no frame)

To judge the plinth wall and the slab without the frame, the frame and the self weight were removed and only four point loads were put on the top edge of the wall (z = 0.9 m): at x = 4.25 m +250 kN in X and +1000 kN upward, at x = 4.85 m +250 kN in X and −1000 kN downward; no moments. SCIA and StruCla both use a 0.1 m mesh. The slab on the soil with the wall: SCIA / StruCla in the element centres.

The plinth wall (membrane), SCIA / StruCla, with the shear flow n_xy compared in magnitude (the sign convention of the two programs is opposite):

kN/m and kNm/m. The bending moments agree within 0 to 6 % (m_x −80 / −80 at E736), the shear force within 1 to 14 %, the shear flow n_xy within 2 to 10 %, the wall within 0 to 8 %. The membrane forces n_x and n_y of the slab right next to the end of the wall differ by 20 to 34 %: see section 7. The slab alone on the soil with two point loads directly on the slab (at x = 4.025 and 5.075 m) agrees within about 10 to 20 % as well (for example m_y −265 / −237 and the shear force 3237 / 2541 kN/m next to the load).

5. The wall on two clamps and the foot moment

To separate the wall from the slab, SCIA's slab was deleted and the wall was fixed at its two bottom corners (x = 4.025 and 5.075 m, all degrees of freedom). The reactions of the two clamps, SCIA / StruCla:

The applied moment about the wall base is 500 × 2.4 + 1.17 × 1.9 + 1.17 × 1.25 = 1203.7 kNm. SCIA: 976.13 × 1.05 + 2 × 89.22 = 1203.4 kNm. In SCIA the clamps take about 15 % of the overturning moment as a moment about the wall normal; this is the foot moment of the frame (SCIA's own member forces give 110 + 94 = 204 kNm), which the stiff rotational (drilling) stiffness of SCIA's membrane nodes carries straight into the clamps. In StruCla the foot moment comes out as extra vertical reaction. Without foot moments both programs give exactly the statics. A plane-stress membrane has no physical stiffness for a rotation about its normal, so how a point moment is carried is a numerical choice of the program; the physical way for a column base to transfer a moment into a wall is a force couple over its width. Making StruCla's drilling stiffness 65 to 70 times stiffer reproduces SCIA's clamp reactions (976 kN, 89 kNm) but makes the comparison of the slab worse (the four load cases drop from 360 to 332 of 371 values equal), so it is not used.

The wall on the two clamps with the point loads only, on a 0.1 m mesh, SCIA / StruCla in the element centres (kN/m):

At the clamp element the forces are singular (a point support), so the n_x of 2132 against 917 kN/m depends on the exact position of the element centre. On SCIA's own coarse mesh of five elements with a triangle (0.5 m) the elements differ by 10 to 40 %; that mesh is not suitable for a comparison.

6. Contact stress in the ultimate limit state

SCIA draws the contact stress of the envelope of the ULS combinations over both slabs with a scale of 21.6 to 65.1 kPa (sheet 5). The table gives the largest contact stress of each slab in StruCla (spring force per m²) for the combinations /1 to /5, on a mesh of 0.5 m as in the SCIA output.

kPa. SCIA: largest value over both slabs 65.1 kPa. F4 in combination /3: 64.2 kPa against 65.1 (−1.4 %). F6 in /3: 69.1 kPa (+6 %), and under this combination the spring on one side of F6 is in tension (−4 kPa), which SCIA does not show. For the wind in X with the original load (4.7 kN in total) the vertical contact stress under the slab varies linearly from −13 to +13 kPa in SCIA (the limit of the scale) and from −14.3 to +14.3 kPa in StruCla.

7. What differs, and why

• Moments agree. 159 of 159 moment values equal for self weight, pipes, friction and wind in Y. For the wind in X (500 kN) 18 of 33 are equal: m_y at the ends of the wall is within 2 % (for example −240.7 against −235.2 and −266.1 against −262.7 kNm/m) and m_x within 16 %; the differences are in m_xy and in the elements at the middle of the wall (x = 4.55 m), where the value passes through zero and a position difference of 0.05 m between the two meshes already gives tens of kNm/m. With the point loads only (section 4) the moments agree within 0 to 6 %.
• Shear forces agree. 53 of 53 equal for the four load cases and all 11 for the wind in X (as resultants; the largest difference is +18 %).
• The required reinforcement (section 3) is far below the minimum of Ø10-400 in SCIA and in StruCla, so the reinforcement is the same. The largest required areas lie in the nodes on the line of the wall and are lower than SCIA's on the mesh of the SCIA output and approach SCIA's ultimate-limit-state values (SCIA A_s,req divided by its factor 1.25: 14 / 12 / 36 / 90 mm²/m) on a mesh of 0.0625 m (18 / 19 / 44 / 85 mm²/m). The shear check gives no shear reinforcement in both.
• Membrane force n_x (and n_y) of the slab at the ends of the wall is 20 to 35 % lower in StruCla, with the frame (for example 278 against 443 kN/m with the wind in X) and with the point loads only (261 against 398 and −106 against −146). The cause is not established. This is where the load of the wall ends: the end of a line connection is singular, and StruCla's own value there does not converge with the mesh (n_x at the first element: 104 / 261 / 271 kN/m for a mesh of 0.2 / 0.1 / 0.05 m). The total forces through a section of the slab are governed by equilibrium and the soil (V_x ≈ 485 kN and N_x ≈ 67 kN at x = 4.0 m, V_x ≈ −290 kN at the middle, StruCla), so they do not decide the question; how the in-plane force is spread across the width next to the end of the wall does. With the real wind (4.7 kN) the difference is about 1.3 kN/m, which is about 3 mm²/m of reinforcement against a minimum of 196 mm²/m. It is proportional to the load, so it would matter for a much larger horizontal load.
• The foot moment of the frame in the plinth wall is carried differently (section 5): SCIA's membrane nodes pass it on as a moment about the wall normal, StruCla as a vertical force couple. The reactions of the wall on two clamps differ by 15 % for that reason (1152 against 976 kN); without foot moments they are equal.
• Mesh dependence near the wall. On a mesh of 0.5 m the forces next to the wall differ much more (n_x a factor 5, the shear force under the middle of the wall 514 against 24 kN/m) and both programs change a lot when the mesh is refined, because the wall load acts as a line load there. That is why the comparison is made on a 0.1 m mesh.
• Contact stress of F6 is 6 % above the largest SCIA value (and tension appears under /3 in StruCla). F4 agrees.
• Not compared: the second slab (frame 1) on the fine mesh, the combinations element by element, the crack width and the deflections. The SCIA tables of this comparison come from SCIA Engineer 26.0, the output sheets of the original report from 21.1.

8. How the comparison was made

Every compared value of the slab is in the check sheet (also as json). StruCla's frame is calculated with fixed feet and with the shear deformation of the beams; the foot forces and moments of each load case are put on the plinth wall, together with the self weight of the concrete (BG1). The SCIA values were read from the SCIA results tables in the element centres; the SCIA wind in X was raised to 500 kN to make the differences larger than the accuracy of the table. Of the StruCla values the nearest element centre is taken (membrane and bending values are the average of the four integration points of the element, the shear force is taken at the middle). The model file is not offered for download because the shell solver is not in the online app yet.