@@ -492,7 +492,7 @@ def shear_centres():
492492 * (1 + self .section_props .nu_eff )
493493 * (
494494 self .section_props .ixx_c * self .section_props .iyy_c
495- - self .section_props .ixy_c ** 2
495+ - self .section_props .ixy_c ** 2
496496 )
497497 )
498498 x_se = (1 / Delta_s ) * (
@@ -511,14 +511,14 @@ def shear_centres():
511511 - self .section_props .iyy_c * i_yomega
512512 ) / (
513513 self .section_props .ixx_c * self .section_props .iyy_c
514- - self .section_props .ixy_c ** 2
514+ - self .section_props .ixy_c ** 2
515515 )
516516 y_st = (
517517 self .section_props .ixx_c * i_xomega
518518 - self .section_props .ixy_c * i_yomega
519519 ) / (
520520 self .section_props .ixx_c * self .section_props .iyy_c
521- - self .section_props .ixy_c ** 2
521+ - self .section_props .ixy_c ** 2
522522 )
523523
524524 return (Delta_s , x_se , y_se , x11_se , y22_se , x_st , y_st )
@@ -543,7 +543,7 @@ def shear_centres():
543543 # calculate warping constant
544544 self .section_props .gamma = (
545545 i_omega
546- - q_omega ** 2 / self .section_props .ea
546+ - q_omega ** 2 / self .section_props .ea
547547 - y_se * i_xomega
548548 + x_se * i_yomega
549549 )
@@ -579,14 +579,14 @@ def assemble_shear_deformation():
579579 (kappa_x , kappa_y , kappa_xy ) = assemble_shear_deformation ()
580580
581581 # calculate shear areas wrt global axis
582- self .section_props .A_sx = Delta_s ** 2 / kappa_x
583- self .section_props .A_sy = Delta_s ** 2 / kappa_y
584- self .section_props .A_sxy = Delta_s ** 2 / kappa_xy
582+ self .section_props .A_sx = Delta_s ** 2 / kappa_x
583+ self .section_props .A_sy = Delta_s ** 2 / kappa_y
584+ self .section_props .A_sxy = Delta_s ** 2 / kappa_xy
585585
586586 # calculate shear areas wrt principal bending axis:
587- alpha_xx = kappa_x * self .section_props .area / Delta_s ** 2
588- alpha_yy = kappa_y * self .section_props .area / Delta_s ** 2
589- alpha_xy = kappa_xy * self .section_props .area / Delta_s ** 2
587+ alpha_xx = kappa_x * self .section_props .area / Delta_s ** 2
588+ alpha_yy = kappa_y * self .section_props .area / Delta_s ** 2
589+ alpha_xy = kappa_xy * self .section_props .area / Delta_s ** 2
590590
591591 # rotate the tensor by the principal axis angle
592592 phi_rad = self .section_props .phi * np .pi / 180
@@ -716,11 +716,11 @@ def calculate_frame():
716716 # calculate second moments of area about the centroidal xy axis
717717 self .section_props .ixx_c = (
718718 self .section_props .ixx_g
719- - self .section_props .qx ** 2 / self .section_props .ea
719+ - self .section_props .qx ** 2 / self .section_props .ea
720720 )
721721 self .section_props .iyy_c = (
722722 self .section_props .iyy_g
723- - self .section_props .qy ** 2 / self .section_props .ea
723+ - self .section_props .qy ** 2 / self .section_props .ea
724724 )
725725 self .section_props .ixy_c = (
726726 self .section_props .ixy_g
@@ -730,7 +730,7 @@ def calculate_frame():
730730 # calculate the principal axis angle
731731 Delta = (
732732 ((self .section_props .ixx_c - self .section_props .iyy_c ) / 2 ) ** 2
733- + self .section_props .ixy_c ** 2
733+ + self .section_props .ixy_c ** 2
734734 ) ** 0.5
735735
736736 i11_c = (self .section_props .ixx_c + self .section_props .iyy_c ) / 2 + Delta
@@ -4248,7 +4248,7 @@ def plot_mohrs_circles(self, x, y, title=None, **kwargs):
42484248 tractions = []
42494249 for col in range (3 ):
42504250 ss = n_inv [:, col ].T @ np .diag (s ) @ n_inv [:, col ]
4251- ts = np .sqrt (np .linalg .norm (np .diag (s ) @ n_inv [:, col ]) ** 2 - ss ** 2 )
4251+ ts = np .sqrt (np .linalg .norm (np .diag (s ) @ n_inv [:, col ]) ** 2 - ss ** 2 )
42524252 tractions .append ((ss , ts ))
42534253
42544254 def plot_circle (ax , c , R , col , label = None , fill = None ):
@@ -4470,23 +4470,23 @@ def calculate_combined_stresses(self):
44704470 self .sig_zz_m = (
44714471 self .sig_zz_mxx + self .sig_zz_myy + self .sig_zz_m11 + self .sig_zz_m22
44724472 )
4473- self .sig_zxy_mzz = (self .sig_zx_mzz ** 2 + self .sig_zy_mzz ** 2 ) ** 0.5
4474- self .sig_zxy_vx = (self .sig_zx_vx ** 2 + self .sig_zy_vx ** 2 ) ** 0.5
4475- self .sig_zxy_vy = (self .sig_zx_vy ** 2 + self .sig_zy_vy ** 2 ) ** 0.5
4473+ self .sig_zxy_mzz = (self .sig_zx_mzz ** 2 + self .sig_zy_mzz ** 2 ) ** 0.5
4474+ self .sig_zxy_vx = (self .sig_zx_vx ** 2 + self .sig_zy_vx ** 2 ) ** 0.5
4475+ self .sig_zxy_vy = (self .sig_zx_vy ** 2 + self .sig_zy_vy ** 2 ) ** 0.5
44764476 self .sig_zx_v = self .sig_zx_vx + self .sig_zx_vy
44774477 self .sig_zy_v = self .sig_zy_vx + self .sig_zy_vy
4478- self .sig_zxy_v = (self .sig_zx_v ** 2 + self .sig_zy_v ** 2 ) ** 0.5
4478+ self .sig_zxy_v = (self .sig_zx_v ** 2 + self .sig_zy_v ** 2 ) ** 0.5
44794479 self .sig_zz = self .sig_zz_n + self .sig_zz_m
44804480 self .sig_zx = self .sig_zx_mzz + self .sig_zx_v
44814481 self .sig_zy = self .sig_zy_mzz + self .sig_zy_v
4482- self .sig_zxy = (self .sig_zx ** 2 + self .sig_zy ** 2 ) ** 0.5
4482+ self .sig_zxy = (self .sig_zx ** 2 + self .sig_zy ** 2 ) ** 0.5
44834483 self .sig_1 = self .sig_zz / 2 + np .sqrt (
4484- (self .sig_zz / 2 ) ** 2 + self .sig_zxy ** 2
4484+ (self .sig_zz / 2 ) ** 2 + self .sig_zxy ** 2
44854485 )
44864486 self .sig_3 = self .sig_zz / 2 - np .sqrt (
4487- (self .sig_zz / 2 ) ** 2 + self .sig_zxy ** 2
4487+ (self .sig_zz / 2 ) ** 2 + self .sig_zxy ** 2
44884488 )
4489- self .sig_vm = (self .sig_zz ** 2 + 3 * self .sig_zxy ** 2 ) ** 0.5
4489+ self .sig_vm = (self .sig_zz ** 2 + 3 * self .sig_zxy ** 2 ) ** 0.5
44904490
44914491
44924492@dataclass
@@ -4692,8 +4692,8 @@ def calculate_centroidal_properties(self, mesh):
46924692 """
46934693
46944694 # calculate second moments of area about the centroidal xy axis
4695- self .ixx_c = self .ixx_g - self .qx ** 2 / self .ea
4696- self .iyy_c = self .iyy_g - self .qy ** 2 / self .ea
4695+ self .ixx_c = self .ixx_g - self .qx ** 2 / self .ea
4696+ self .iyy_c = self .iyy_g - self .qy ** 2 / self .ea
46974697 self .ixy_c = self .ixy_g - self .qx * self .qy / self .ea
46984698
46994699 # calculate section moduli about the centroidal xy axis
@@ -4712,7 +4712,7 @@ def calculate_centroidal_properties(self, mesh):
47124712 self .ry_c = (self .iyy_c / self .ea ) ** 0.5
47134713
47144714 # calculate principal 2nd moments of area about the centroidal xy axis
4715- Delta = (((self .ixx_c - self .iyy_c ) / 2 ) ** 2 + self .ixy_c ** 2 ) ** 0.5
4715+ Delta = (((self .ixx_c - self .iyy_c ) / 2 ) ** 2 + self .ixy_c ** 2 ) ** 0.5
47164716 self .i11_c = (self .ixx_c + self .iyy_c ) / 2 + Delta
47174717 self .i22_c = (self .ixx_c + self .iyy_c ) / 2 - Delta
47184718
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