Skip to content

formula_6_18_sub_av

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_18_sub_av

Subformula a through g from 6.18 from EN 1993-1-1:2005: Chapter 6 - Ultimate Limit State.

Classes:

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_18_sub_av.Form6Dot18SubARolledIandHSection 

Form6Dot18SubARolledIandHSection(
    a: MM2,
    b1: MM,
    b2: MM,
    hw: MM,
    r1: MM,
    r2: MM,
    tf1: MM,
    tf2: MM,
    tw: MM,
    eta: DIMENSIONLESS,
)

Bases: Formula

Class representing formula 6.18suba for the calculation of shear area for a rolled I and H section.

The equation has been slightly modified to split effects of top and bottom flange, when they are not identical.

[\(A_v\)] Calculation of the shear area for a rolled I and H section with load parallel to web [\(mm^2\)].

EN 1993-1-1:2005 art.6.2.6(3) - Formula (6.18suba)

Notes

The original formula has been slightly modified to split effects of top and bottom flange, when they are not identical. When they do be identical, b2, r2, and tf2 should be equal to b1, r1, and tf1 respectively.

Parameters:

  • a (MM2) –

    [\(A\)] Cross-sectional area [\(mm^2\)].

  • b1 (MM) –

    [\(b\)] Overall breadth of flange 1 [\(mm\)].

  • b2 (MM) –

    [\(b\)] Overall breadth of flange 2 [\(mm\)].

  • hw (MM) –

    [\(h_w\)] Depth of the web [\(mm\)].

  • r1 (MM) –

    [\(r\)] Root radius at flange 1 [\(mm\)].

  • r2 (MM) –

    [\(r\)] Root radius at flange 2 [\(mm\)].

  • tf1 (MM) –

    [\(t_f\)] Flange thickness 1 [\(mm\)].

  • tf2 (MM) –

    [\(t_f\)] Flange thickness 2 [\(mm\)].

  • tw (MM) –

    [\(t_w\)] Web thickness [\(mm\)]. If the web thickness is not constant, tw should be taken as the minimum thickness.

  • eta (DIMENSIONLESS) –

    [\(\eta\)] Dimensionless conversionfactor, see EN 1993-1-5 5.1. Note, \(eta\) may be conservatively taken equal to 1.0.

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_18_sub_av.py 
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
def __init__(
    self,
    a: MM2,
    b1: MM,
    b2: MM,
    hw: MM,
    r1: MM,
    r2: MM,
    tf1: MM,
    tf2: MM,
    tw: MM,
    eta: DIMENSIONLESS,
) -> None:
    r"""[$A_v$] Calculation of the shear area for a rolled I and H section with load parallel to web [$mm^2$].

    EN 1993-1-1:2005 art.6.2.6(3) - Formula (6.18suba)

    Notes
    -----
    The original formula has been slightly modified to split effects of top and bottom flange, when they are not identical.
    When they do be identical, b2, r2, and tf2 should be equal to b1, r1, and tf1 respectively.

    Parameters
    ----------
    a : MM2
        [$A$] Cross-sectional area [$mm^2$].
    b1 : MM
        [$b$] Overall breadth of flange 1 [$mm$].
    b2 : MM
        [$b$] Overall breadth of flange 2 [$mm$].
    hw : MM
        [$h_w$] Depth of the web [$mm$].
    r1 : MM
        [$r$] Root radius at flange 1 [$mm$].
    r2 : MM
        [$r$] Root radius at flange 2 [$mm$].
    tf1 : MM
        [$t_f$] Flange thickness 1 [$mm$].
    tf2 : MM
        [$t_f$] Flange thickness 2 [$mm$].
    tw : MM
        [$t_w$] Web thickness [$mm$]. If the web thickness is not constant, tw should be taken as the minimum thickness.
    eta : DIMENSIONLESS, optional
        [$\eta$] Dimensionless conversionfactor, see EN 1993-1-5 5.1. Note, $eta$ may be conservatively taken equal to 1.0.
    """
    super().__init__()
    self.a = a
    self.b1 = b1
    self.b2 = b2
    self.hw = hw
    self.r1 = r1
    self.r2 = r2
    self.tf1 = tf1
    self.tf2 = tf2
    self.tw = tw
    self.eta = eta

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_18_sub_av.Form6Dot18SubARolledIandHSection.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.18suba.

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_18_sub_av.py 
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.18suba."""
    if self.b1 == self.b2 and self.tf1 == self.tf2 and self.r1 == self.r2:
        _equation: str = r"max(A - 2 \cdot b \cdot t_f + (t_w + 2 \cdot r) \cdot t_f; \eta \cdot h_w \cdot t_w)"
        _numeric_equation: str = latex_replace_symbols(
            _equation,
            {
                r"A": f"{self.a:.{n}f}",
                r"b": f"{self.b1:.{n}f}",
                r"h_w": f"{self.hw:.{n}f}",
                r"r": f"{self.r1:.{n}f}",
                r"t_f": f"{self.tf1:.{n}f}",
                r"t_w": f"{self.tw:.{n}f}",
                r"\eta": f"{self.eta:.{n}f}",
            },
            False,
        )
    else:
        _equation: str = (
            r"\max(A - b_1 \cdot t_{f1} - b_2 \cdot t_{f2} + (t_w + 2 \cdot r_1) \cdot \frac{t_{f1}}{2} + "
            r"(t_w + 2 \cdot r_2) \cdot \frac{t_{f2}}{2}; \eta \cdot h_w \cdot t_w)"
        )
        _numeric_equation: str = latex_replace_symbols(
            _equation,
            {
                r"A": f"{self.a:.{n}f}",
                r"b_1": f"{self.b1:.{n}f}",
                r"b_2": f"{self.b2:.{n}f}",
                r"h_w": f"{self.hw:.{n}f}",
                r"r_1": f"{self.r1:.{n}f}",
                r"r_2": f"{self.r2:.{n}f}",
                r"t_{f1}": f"{self.tf1:.{n}f}",
                r"t_{f2}": f"{self.tf2:.{n}f}",
                r"t_w": f"{self.tw:.{n}f}",
                r"\eta": f"{self.eta:.{n}f}",
            },
            False,
        )

    return LatexFormula(
        return_symbol=r"A_v",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="mm^2",
    )

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_18_sub_av.Form6Dot18SubBRolledChannelSection 

Form6Dot18SubBRolledChannelSection(a: MM2, b: MM, tf: MM, tw: MM, r: MM)

Bases: Formula

Class representing formula 6.18subb for the calculation of shear area for a rolled channel section.

[\(A_v\)] Calculation of the shear area for a rolled channel section with load parallel to web [\(mm^2\)].

EN 1993-1-1:2005 art.6.2.6(3) - Formula (6.18subb)

Parameters:

  • a (MM2) –

    [\(A\)] Cross-sectional area [\(mm^2\)].

  • b (MM) –

    [\(b\)] Overall breadth [\(mm\)].

  • tf (MM) –

    [\(t_f\)] Flange thickness [\(mm\)].

  • tw (MM) –

    [\(t_w\)] Web thickness [\(mm\)]. If the web thickness is not constant, tw should be taken as the minimum thickness.

  • r (MM) –

    [\(r\)] Root radius [\(mm\)].

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_18_sub_av.py 
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
def __init__(
    self,
    a: MM2,
    b: MM,
    tf: MM,
    tw: MM,
    r: MM,
) -> None:
    r"""[$A_v$] Calculation of the shear area for a rolled channel section with load parallel to web [$mm^2$].

    EN 1993-1-1:2005 art.6.2.6(3) - Formula (6.18subb)

    Parameters
    ----------
    a : MM2
        [$A$] Cross-sectional area [$mm^2$].
    b : MM
        [$b$] Overall breadth [$mm$].
    tf : MM
        [$t_f$] Flange thickness [$mm$].
    tw : MM
        [$t_w$] Web thickness [$mm$]. If the web thickness is not constant, tw should be taken as the minimum thickness.
    r : MM
        [$r$] Root radius [$mm$].
    """
    super().__init__()
    self.a = a
    self.b = b
    self.tf = tf
    self.tw = tw
    self.r = r

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_18_sub_av.Form6Dot18SubBRolledChannelSection.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.18subb.

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_18_sub_av.py 
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.18subb."""
    _equation: str = r"A - 2 \cdot b \cdot t_f + (t_w + r) \cdot t_f"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"A": f"{self.a:.{n}f}",
            r"b": f"{self.b:.{n}f}",
            r"t_f": f"{self.tf:.{n}f}",
            r"t_w": f"{self.tw:.{n}f}",
            r"r": f"{self.r:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"A_v",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="mm^2",
    )

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_18_sub_av.Form6Dot18SubCTSectionRolled 

Form6Dot18SubCTSectionRolled(a: MM2, b: MM, tf: MM, tw: MM, r: MM)

Bases: Formula

Class representing formula 6.18subc for the calculation of shear area for a rolled T-section with load parallel to web.

[\(A_v\)] Calculation of the shear area for a T-section with load parallel to web [\(mm^2\)].

EN 1993-1-1:2005 art.6.2.6(3) - Formula (6.18subc)

Parameters:

  • a (MM2) –

    [\(A\)] Cross-sectional area [\(mm^2\)].

  • b (MM) –

    [\(b\)] Overall breadth [\(mm\)].

  • tf (MM) –

    [\(t_f\)] Flange thickness [\(mm\)].

  • tw (MM) –

    [\(t_w\)] Web thickness [\(mm\)]. If the web thickness is not constant, tw should be taken as the minimum thickness.

  • r (MM) –

    [\(r\)] Root radius [\(mm\)].

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_18_sub_av.py 
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
def __init__(
    self,
    a: MM2,
    b: MM,
    tf: MM,
    tw: MM,
    r: MM,
) -> None:
    r"""[$A_v$] Calculation of the shear area for a T-section with load parallel to web [$mm^2$].

    EN 1993-1-1:2005 art.6.2.6(3) - Formula (6.18subc)

    Parameters
    ----------
    a : MM2
        [$A$] Cross-sectional area [$mm^2$].
    b : MM
        [$b$] Overall breadth [$mm$].
    tf : MM
        [$t_f$] Flange thickness [$mm$].
    tw : MM
        [$t_w$] Web thickness [$mm$]. If the web thickness is not constant, tw should be taken as the minimum thickness.
    r : MM
        [$r$] Root radius [$mm$].
    """
    super().__init__()
    self.a = a
    self.b = b
    self.tf = tf
    self.tw = tw
    self.r = r

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_18_sub_av.Form6Dot18SubCTSectionRolled.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.18subc.

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_18_sub_av.py 
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.18subc."""
    _equation: str = r"A - b \cdot t_f + (t_w + 2 \cdot r) \cdot \frac{t_f}{2}"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"A": f"{self.a:.{n}f}",
            r"b": f"{self.b:.{n}f}",
            r"t_f": f"{self.tf:.{n}f}",
            r"t_w": f"{self.tw:.{n}f}",
            r" r": f" {self.r:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"A_v",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="mm^2",
    )

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_18_sub_av.Form6Dot18SubCTSectionWelded 

Form6Dot18SubCTSectionWelded(tf: MM, tw: MM, h: MM)

Bases: Formula

Class representing formula 6.18subc for the calculation of shear area for a welded T-section with load parallel to web.

[\(A_v\)] Calculation of the shear area for a T-section with load parallel to web [\(mm^2\)].

EN 1993-1-1:2005 art.6.2.6(3) - Formula (6.18subc)

Parameters:

  • tf (MM) –

    [\(t_f\)] Flange thickness [\(mm\)].

  • tw (MM) –

    [\(t_w\)] Web thickness [\(mm\)]. If the web thickness is not constant, tw should be taken as the minimum thickness.

  • h (MM) –

    [\(h\)] Overall depth [\(mm\)].

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_18_sub_av.py 
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
def __init__(
    self,
    tf: MM,
    tw: MM,
    h: MM,
) -> None:
    r"""[$A_v$] Calculation of the shear area for a T-section with load parallel to web [$mm^2$].

    EN 1993-1-1:2005 art.6.2.6(3) - Formula (6.18subc)

    Parameters
    ----------
    tf : MM
        [$t_f$] Flange thickness [$mm$].
    tw : MM
        [$t_w$] Web thickness [$mm$]. If the web thickness is not constant, tw should be taken as the minimum thickness.
    h : MM
        [$h$] Overall depth [$mm$].
    """
    super().__init__()
    self.tf = tf
    self.tw = tw
    self.h = h

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_18_sub_av.Form6Dot18SubCTSectionWelded.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.18subc.

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_18_sub_av.py 
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.18subc."""
    _equation: str = r"t_w \cdot (h \cdot t_f / 2)"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"t_f": f"{self.tf:.{n}f}",
            r"t_w": f"{self.tw:.{n}f}",
            r"h": f"{self.h:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"A_v",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="mm^2",
    )

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_18_sub_av.Form6Dot18SubDWeldedIHandBoxSection 

Form6Dot18SubDWeldedIHandBoxSection(
    hw_list: list[MM], tw_list: list[MM], eta: DIMENSIONLESS
)

Bases: Formula

Class representing formula 6.18subd for the calculation of shear area for welded I, H, and box sections with load parallel to web.

[\(A_v\)] Calculation of the shear area for welded I, H, and box sections with load parallel to web [\(mm^2\)].

EN 1993-1-1:2005 art.6.2.6(3) - Formula (6.18subd)

Parameters:

  • hw_list (list[MM]) –

    [\(h_w\)] List of depths of the web [\(mm\)].

  • tw_list (list[MM]) –

    [\(t_w\)] List of web thicknesses [\(mm\)]. If the web thickness is not constant, tw should be taken as the minimum thickness.

  • eta (DIMENSIONLESS) –

    [\(\eta\)] See EN 1993-1-5. Note, \(eta\) may be conservatively taken equal to 1.0.

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_18_sub_av.py 
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
def __init__(
    self,
    hw_list: list[MM],
    tw_list: list[MM],
    eta: DIMENSIONLESS,
) -> None:
    r"""[$A_v$] Calculation of the shear area for welded I, H, and box sections with load parallel to web [$mm^2$].

    EN 1993-1-1:2005 art.6.2.6(3) - Formula (6.18subd)

    Parameters
    ----------
    hw_list : list[MM]
        [$h_w$] List of depths of the web [$mm$].
    tw_list : list[MM]
        [$t_w$] List of web thicknesses [$mm$]. If the web thickness is not constant, tw should be taken as the minimum thickness.
    eta : DIMENSIONLESS
        [$\eta$] See EN 1993-1-5. Note, $eta$ may be conservatively taken equal to 1.0.
    """
    super().__init__()
    self.hw_list: list[MM] = hw_list
    self.tw_list: list[MM] = tw_list
    self.eta = eta

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_18_sub_av.Form6Dot18SubDWeldedIHandBoxSection.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.18subd.

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_18_sub_av.py 
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.18subd."""
    _equation: str = r"\eta \cdot \sum (h_{w} \cdot t_{w})"
    _numeric_equation: str = rf"{self.eta:.{n}f} \cdot (" + rf"{self.hw_list[0]:.{n}f} \cdot {self.tw_list[0]:.{n}f}"
    for i in range(1, len(self.hw_list)):
        _numeric_equation += rf" + {self.hw_list[i]:.{n}f} \cdot {self.tw_list[i]:.{n}f}"
    _numeric_equation += ")"
    return LatexFormula(
        return_symbol=r"A_v",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="mm^2",
    )

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_18_sub_av.Form6Dot18SubEWeldedIHandBoxSection 

Form6Dot18SubEWeldedIHandBoxSection(
    a: MM2, hw_list: list[MM], tw_list: list[MM]
)

Bases: Formula

Class representing formula 6.18sube for the calculation of shear area for welded I, H, channel, and box sections with load parallel to flanges.

[\(A_v\)] Calculation of the shear area for welded I, H, channel, and box sections with load parallel to flanges [\(mm^2\)].

EN 1993-1-1:2005 art.6.2.6(3) - Formula (6.18sube)

Parameters:

  • a (MM2) –

    [\(A\)] Cross-sectional area [\(mm^2\)].

  • hw_list (list[MM]) –

    [\(h_w\)] List of depths of the web [\(mm\)].

  • tw_list (list[MM]) –

    [\(t_w\)] List of web thicknesses [\(mm\)]. If the web thickness is not constant, tw should be taken as the minimum thickness.

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_18_sub_av.py 
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
def __init__(
    self,
    a: MM2,
    hw_list: list[MM],
    tw_list: list[MM],
) -> None:
    r"""[$A_v$] Calculation of the shear area for welded I, H, channel, and box sections with load parallel to flanges [$mm^2$].

    EN 1993-1-1:2005 art.6.2.6(3) - Formula (6.18sube)

    Parameters
    ----------
    a : MM2
        [$A$] Cross-sectional area [$mm^2$].
    hw_list : list[MM]
        [$h_w$] List of depths of the web [$mm$].
    tw_list : list[MM]
        [$t_w$] List of web thicknesses [$mm$]. If the web thickness is not constant, tw should be taken as the minimum thickness.
    """
    super().__init__()
    self.a = a
    self.hw_list: list[MM] = hw_list
    self.tw_list: list[MM] = tw_list

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_18_sub_av.Form6Dot18SubEWeldedIHandBoxSection.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.18sube.

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_18_sub_av.py 
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.18sube."""
    _equation: str = r"A - \sum (h_{w} \cdot t_{w})"
    _numeric_equation: str = rf"{self.a:.{n}f} - (" + rf"{self.hw_list[0]:.{n}f} \cdot {self.tw_list[0]:.{n}f}"
    for i in range(1, len(self.hw_list)):
        _numeric_equation += rf" + {self.hw_list[i]:.{n}f} \cdot {self.tw_list[i]:.{n}f}"
    _numeric_equation += ")"
    return LatexFormula(
        return_symbol=r"A_v",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="mm^2",
    )

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_18_sub_av.Form6Dot18SubF1RolledRectangularHollowSectionDepth 

Form6Dot18SubF1RolledRectangularHollowSectionDepth(a: MM2, b: MM, h: MM)

Bases: Formula

Class representing formula 6.18subf1 for the calculation of shear area for rolled rectangular hollow sections of uniform thickness with load parallel to depth.

[\(A_v\)] Calculation of the shear area for rolled rectangular hollow sections of uniform thickness with load parallel to depth [\(mm^2\)].

EN 1993-1-1:2005 art.6.2.6(3) - Formula (6.18subf1)

Parameters:

  • a (MM2) –

    [\(A\)] Cross-sectional area [\(mm^2\)].

  • b (MM) –

    [\(b\)] Overall breadth [\(mm\)].

  • h (MM) –

    [\(h\)] Overall depth [\(mm\)].

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_18_sub_av.py 
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
def __init__(
    self,
    a: MM2,
    b: MM,
    h: MM,
) -> None:
    r"""[$A_v$] Calculation of the shear area for rolled rectangular hollow sections of uniform thickness with load parallel to depth [$mm^2$].

    EN 1993-1-1:2005 art.6.2.6(3) - Formula (6.18subf1)

    Parameters
    ----------
    a : MM2
        [$A$] Cross-sectional area [$mm^2$].
    b : MM
        [$b$] Overall breadth [$mm$].
    h : MM
        [$h$] Overall depth [$mm$].
    """
    super().__init__()
    self.a = a
    self.b = b
    self.h = h

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_18_sub_av.Form6Dot18SubF1RolledRectangularHollowSectionDepth.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.18subf1.

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_18_sub_av.py 
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.18subf1."""
    _equation: str = r"\frac{A \cdot h}{b + h}"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"A": f"{self.a:.{n}f}",
            r"b": f"{self.b:.{n}f}",
            r"h": f"{self.h:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"A_v",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="mm^2",
    )

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_18_sub_av.Form6Dot18SubF2RolledRectangularHollowSectionWidth 

Form6Dot18SubF2RolledRectangularHollowSectionWidth(a: MM2, b: MM, h: MM)

Bases: Formula

Class representing formula 6.18subf2 for the calculation of shear area for rolled rectangular hollow sections of uniform thickness with load parallel to width.

[\(A_v\)] Calculation of the shear area for rolled rectangular hollow sections of uniform thickness with load parallel to width [\(mm^2\)].

EN 1993-1-1:2005 art.6.2.6(3) - Formula (6.18subf2)

Parameters:

  • a (MM2) –

    [\(A\)] Cross-sectional area [\(mm^2\)].

  • b (MM) –

    [\(b\)] Overall breadth [\(mm\)].

  • h (MM) –

    [\(h\)] Overall depth [\(mm\)].

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_18_sub_av.py 
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
def __init__(
    self,
    a: MM2,
    b: MM,
    h: MM,
) -> None:
    r"""[$A_v$] Calculation of the shear area for rolled rectangular hollow sections of uniform thickness with load parallel to width [$mm^2$].

    EN 1993-1-1:2005 art.6.2.6(3) - Formula (6.18subf2)

    Parameters
    ----------
    a : MM2
        [$A$] Cross-sectional area [$mm^2$].
    b : MM
        [$b$] Overall breadth [$mm$].
    h : MM
        [$h$] Overall depth [$mm$].
    """
    super().__init__()
    self.a = a
    self.b = b
    self.h = h

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_18_sub_av.Form6Dot18SubF2RolledRectangularHollowSectionWidth.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.18subf2.

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_18_sub_av.py 
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.18subf2."""
    _equation: str = r"\frac{A \cdot b}{b + h}"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"A": f"{self.a:.{n}f}",
            r"b": f"{self.b:.{n}f}",
            r"h": f"{self.h:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"A_v",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="mm^2",
    )

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_18_sub_av.Form6Dot18SubGCircularHollowSection 

Form6Dot18SubGCircularHollowSection(a: MM2)

Bases: Formula

Class representing formula 6.18subg for the calculation of shear area for circular hollow sections and tubes of uniform thickness.

[\(A_v\)] Calculation of the shear area for circular hollow sections and tubes of uniform thickness [\(mm^2\)].

EN 1993-1-1:2005 art.6.2.6(3) - Formula (6.18subg)

Parameters:

  • a (MM2) –

    [\(A\)] Cross-sectional area [\(mm^2\)].

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_18_sub_av.py 
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
def __init__(
    self,
    a: MM2,
) -> None:
    r"""[$A_v$] Calculation of the shear area for circular hollow sections and tubes of uniform thickness [$mm^2$].

    EN 1993-1-1:2005 art.6.2.6(3) - Formula (6.18subg)

    Parameters
    ----------
    a : MM2
        [$A$] Cross-sectional area [$mm^2$].
    """
    super().__init__()
    self.a = a

codes.eurocode.en_1993_1_1_2005.chapter_6_ultimate_limit_state.formula_6_18_sub_av.Form6Dot18SubGCircularHollowSection.latex 

latex(n: int = 3) -> LatexFormula

Returns LatexFormula object for formula 6.18subg.

Source code in blueprints/codes/eurocode/en_1993_1_1_2005/chapter_6_ultimate_limit_state/formula_6_18_sub_av.py 
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
def latex(self, n: int = 3) -> LatexFormula:
    """Returns LatexFormula object for formula 6.18subg."""
    _equation: str = r"\frac{2 \cdot A}{\pi}"
    _numeric_equation: str = latex_replace_symbols(
        _equation,
        {
            r"A": f"{self.a:.{n}f}",
        },
        False,
    )
    return LatexFormula(
        return_symbol=r"A_v",
        result=f"{self:.{n}f}",
        equation=_equation,
        numeric_equation=_numeric_equation,
        comparison_operator_label="=",
        unit="mm^2",
    )