Eurocode 2 04 rc pn 001

Eurocode 2 04 rc pn 001 Eurocode 2 04 rc pn 001 Eurocode 2 04 rc pn 001 Eurocode 2 04 rc pn 001 Eurocode 2 04 rc pn 001 Eurocode 2 04 rc pn 001 Eurocode 2 04 rc pn 001 Eurocode 2 04 rc pn 001 Eurocode 2 04 rc pn 001 Eurocode 2 04 rc pn 001 Eurocode 2 04 rc pn 001 Eurocode 2 04 rc pn 001 Eurocode 2 04 rc pn 001 Eurocode 2 04 rc pn 001 Eurocode 2 04 rc pn 001 Eurocode 2 04 rc pn 001 Eurocode 2 04 rc pn 001 Eurocode 2 04 rc pn 001 Eurocode 2 04 rc pn 001 Eurocode 2 04 rc pn 001 Eurocode 2 04 rc pn 001 Eurocode 2 04 rc pn 001 Eurocode 2 04 rc pn 001 Eurocode 2 04 rc pn 001 Eurocode 2 04 rc pn 001 Eurocode 2 04 rc pn 001 Eurocode 2 04 rc pn 001 Eurocode 2 04 rc pn 001 Eurocode 2 04 rc pn 001 Eurocode 2 04 rc pn 001 Eurocode 2 04 rc pn 001 Eurocode 2 04 rc pn 001 Eurocode 2 04 rc pn 001

Software Verification PROGRAM NAME: REVISION NO.: SAFE EXAMPLE EUROCODE 2-04 RC-PN-001 Slab Punching Shear Design PROBLEM DESCRIPTION The purpose of this example is to verify slab punching shear design in SAFE The numerical example is a flat slab that has three 8-m spans in each direction, as shown in Figure 0.3 m A B 8m C 8m D 0.3 m 8m 0.6 m 0.25 m thick flat slab 8m Columns are 0.3 m x 0.9 m with long side parallel to the Y-axis, typical 8m Concrete Properties Unit weight = 24 kN/m3 f'c = 30 N/mm2 8m Y X Loading DL = Self weight + 1.0 kN/m LL = 4.0 kN/m2 0.6 m Figure 1: Flat Slab for Numerical Example The slab overhangs beyond the face of the column by 0.15 m along each side of the structure The columns are typically 0.3 m x 0.9 m with the long side parallel to the Y-axis Thick plate properties are used for the slab The concrete has a unit weight of 24 kN/m3 and a f'c of 30 N/mm2 The dead load consists of the self weight of the structure plus an additional kN/m2 The live load is kN/m2 EXAMPLE EUROCODE 2-04 RC-PN-001 - Software Verification PROGRAM NAME: REVISION NO.: SAFE TECHNICAL FEATURES OF SAFE TESTED ¾ Calculation of punching shear capacity, shear stress and D/C ratio RESULTS COMPARISON Table shows the comparison of the punching shear capacity, shear stress ratio and D/C ratio obtained from SAFE with the punching shear capacity, shear stress ratio and D/C ratio obtained by the analytical method They match exactly for this problem Table Comparison of Design Results for Punching Shear at Grid B-2 Method Shear Stress Shear Capacity (N/mm2) (N/mm2) D/C ratio SAFE 0.932 0.542 1.720 Calculated 0.932 0.560 1.664 COMPUTER FILE: EUROCODE 2-04 RC-PN-001.FDB CONCLUSION The SAFE results show a very close comparison with the independent results EXAMPLE EUROCODE 2-04 RC-PN-001 - Software Verification PROGRAM NAME: REVISION NO.: SAFE HAND CALCULATION Hand Calculation For Interior Column Using SAFE Method d = [(250 − 26) + (250 − 38)] / = 218 mm Refer to Figure b0 = 1172+ 1772 + 1772 + 1172 = 5888 mm 1172 Note: All dimensions in millimeters Critical section for punching shear shown dashed Y 436 150 150 436 B A Column Side Side Side 436 450 X 1772 450 Center of column is point (x1, y1) Set this equal to (0,0) 436 Side D C Figure 2: Interior Column, Grid B-2 in SAFE Model γ VX =1− γ VY =1− ⎛ ⎞ 900 1+ ⎜ ⎟ ⎝ ⎠ 300 ⎛ ⎞ 300 1+ ⎜ ⎟ ⎝ ⎠ 900 = 0.536 = 0.278 The coordinates of the center of the column (x1, y1) are taken as (0, 0) EXAMPLE EUROCODE 2-04 RC-PN-001 - Software Verification SAFE PROGRAM NAME: REVISION NO.: The following table is used for calculating the centroid of the critical section for punching shear Side 1, Side 2, Side 3, and Side refer to the sides of the critical section for punching shear as identified in Figure Item x2 y2 L d Ld Ldx2 Ldy2 Side −586 1772 218 386296 −226369456 x3 = ∑ Ldx y3 = ∑ Ldy Ld Ld Side 886 1172 218 255496 226369456 = = mm 1283584 = = mm 1283584 Side 586 1772 218 386296 226369456 Side −886 1172 218 255496 −226369456 Sum N.A N.A b0 = 5888 N.A 1283584 0 The following table is used to calculate IXX, IYY and IXY The values for IXX, IYY and IXY are given in the "Sum" column Item L d x2 - x3 y2 - y3 Parallel to Equations IXX IYY IXY Side 1772 218 −4586 Y-Axis 5b, 6b, 1.03E+11 1.33E+11 Side 1172 218 886 X-axis 5a, 6a, 2.01E+11 3.03E+10 Side 1772 218 586 Y-Axis 5b, 6b, 1.035E+11 1.33E+11 Side 1172 218 −886 X-axis 5a, 6a, 2.01E+11 3.03E+10 From the SAFE output at Grid B-2: VU = 1110.040 kN MUX = −25993.080 kN-mm MUY =1.6028.908 kN-mm At the point labeled A in Figure 2, x4 = −586 and y4 = 886, thus: EXAMPLE EUROCODE 2-04 RC-PN-001 - Sum N.A N.A N.A N.A N.A N.A 6.06E+11 3.26E+11 Software Verification PROGRAM NAME: REVISION NO.: vU = SAFE 1110.040 • 103 25993.080 • 103 [3.26 • 1011 (886 − 0) − (0)(−586 − 0)] − + 5888 • 218 (6.06 • 1011 )(3.26 o 1011 ) − (0)2 16028.908 • 103 [6.06 • 1011 (−586 − 0) − (0)(886 − 0)] (6.06 o 1011 )(3.26 • 1011 ) − (0) vU = 0.8648 − 0.0380 − 0.0277 = 0.7980 N/mm2 at point A At the point labeled B in Figure 2, x4 = 586 and y4 = 886, thus: vU = 1110.040 • 103 25993.080 • 103 [3.26 • 1011 (886 − 0) − (0)(−586 − 0)] − + 5888 • 218 (6.06 • 1011 )(3.26 o 1011 ) − (0)2 16028.908 • 103 [6.06 • 1011 (−586 − 0) − (0)(886 − 0)] (6.06 o 1011 )(3.26 • 1011 ) − (0) vU = 0.8648 − 0.0380 + 0.0277 = 0.8556 N/mm2 at point B At the point labeled C in Figure 2, x4 = 586 and y4 = −886, thus: vU = 1110.040 • 103 25993.080 • 103 [3.26 • 1011 (886 − 0) − (0)(−586 − 0)] − + 5888 • 218 (6.06 • 1011 )(3.26 o 1011 ) − (0)2 16028.908 • 103 [6.06 • 1011 (−586 − 0) − (0)(886 − 0)] (6.06 o 1011 )(3.26 • 1011 ) − (0) vU = 0.8648 + 0.0380 + 0.0277 = 0.9316 N/mm2 at point C At the point labeled D in Figure 2, x4 = −586 and y4 = −886, thus: vU = 1110.040 • 103 25993.080 • 103 [3.26 • 1011 (886 − 0) − (0)(−586 − 0)] − + 5888 • 218 (6.06 • 1011 )(3.26 o 1011 ) − (0)2 16028.908 • 103 [6.06 • 1011 (−586 − 0) − (0)(886 − 0)] (6.06 o 1011 )(3.26 • 1011 ) − (0) vU = 0.8648 − 0.0380 + 0.0277 = 0.8556 N/mm2 at point D Point C has the largest absolute value of vu, thus vmax = 0.932 N/mm2 EXAMPLE EUROCODE 2-04 RC-PN-001 - Software Verification PROGRAM NAME: REVISION NO.: SAFE The shear capacity is calculated based on the minimum of the following three limits: k = 1+ v Ed = 200 ≤ 2.0 = 1.9578 d VEd ud ⎡ M Ed u1 ⎤ ⎢1 + k ⎥ = 0.560 N/mm VEdW1 ⎦ ⎣ (EC2 6.4.4(1)) (EC2 6.4.4(2)) CP 3.7.7.3 yields the value of v = 0.560 N/mm2, and thus this is the shear capacity Shear Ratio = vU 0.932 = = 1.720 v 0.560 EXAMPLE EUROCODE 2-04 RC-PN-001 -