Table Of Content

http://www.block.arch.ethz.ch/eq/ Structural Design I Philippe Block ∙ Joseph Schwartz Structural design I+II Structural design I 2. Equilibrium and graphic static 1. Introduction 3.+4. Cables 5.+7. Arches 6.+8. Arch-cable- 9. Trusses 10.+11. Beams structures and frames 13. Cable-net and 14.+15. Vaults, 16. Spatial arch- 17. Spacial trusses 16. Shear walls 20. Columns membrane structures domes and shells cable-structures and plates Structural design II 12. Materials and 19. Bending dimensioning Course overview 3 Stiffening of arch structures >> Thrust lines Spatial profiling old Stand 03.08.2016 Q Q Q Q Q Q Q Q Q Q Q Q Q A B A B A B Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q A B Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q A B A B 1 1 1 1 F A B A B F F B A A B B F B A A A B F F A B F F F F A B B A A B F B A F F F A B A B F A B F 2 2 2 2 A B Q Q Q Q QQ Q Q A B A B A AA BB A A 2 1 2 1 2 22 11 2 1 Q Q Q Q QQ Q Q Q Q Q Q QQ Q Q Q Q Q Q QQ Q Q B A B A B BB AA B B 2 1 2 1 2 22 11 2 1 Q Q Q Q QQ Q Q Q Q Q Q Q Q Q Q Q Q QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ Q Q Q Q Q Q Q Q Q Q A B A B AA BB A B 1 1 1 1 11 11 1 1 A B A B AA BB A B 2 2 2 2 22 22 2 2 3 3 3 3 Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q A A A A 1 1 1 1 Q Q Q Q Q Q B B H1 h1 A 1 BV1 B A Bv1 Bv1 Q A Bv1 H1 Bv1 Q A Bv1 H1 Bv1 Q V1 1 1 1 Q Q Q B B H H H1 h1 1 1 Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q A A A A 2 2 2 2 Q Q Q Q Q Q Q Q Q B B B B BV2 B v2 v2 v2 H2 h2 Q Q Q 4 4 4 H 4 H A B B B 2 B 2 2 V2 v2 v2 v2 A A A BH2 2 B 2 H 2 H h2 2 2 F F F F 1 2 1 2 A B A B 1 1 1 1 F F F F A A F A B A B 2 2 2 2 F F F F 1 2 1 2 F B B B A B A A B A B 1 2 1 2 F F F F 2 1 2 1 F F F F 1 2 1 2 A B A B 1 2 1 2 5 5 5 5 q g A B A B q q q q f f B A2 B2 A2 2 f f A B 1 1 f f A B A B A B 1 1 g f f q A A A1 A2 1 2 R R R R B1 B2 B1 B2 6 6 6 6 F F 1 2 F F 1 2 A B A B 2 2 2 2 A B G G G G 1 1 A A A B G G 1 1 F F F F 1 2 1 2 G G B B A B A B A A A1 F F A2 1 F F 2 1 1 1 1 F B1 F2 F2 B2 B F2 2 B 1 2 7 7 7 7 q q q q A B 2 2 Q Q Q Q A2 B2 Q Q G G A G G A A B 1 1 A B G G 1 1 Q Q B B A B G A B G A1 A2 A1 A2 R R R R B1 B2 B1 B2 8 8 8 8 R Q Q R F1 F2 F3 F1 F1 F2 F3 F4 F1 G G G G F2 F2 -∆l -∆l P +∆l +∆l o' R R F F 3 3 F F 4 4 A B A B 9 9 9 9 G G G G G G A A A G G G G G G G G G B B B R G G G R A Ah Q B Q B Q B h A G A G A G G G G r'' F1 F2 F3 F4 Av A 1 F1 F1 F2 F3 F4 Av A 1 F1 AQ AQ AQ Q Q Q 2 F2 2 F2 B B B P o'' Q Q Q 2 3 3 2 3 3 R 4 4 R F3 4 4 F3 Q Q Q B 1 5 Bv 5 1 5 Bv B 5 A BQ A BQ A BQ Q Q Q F F 4 4 G G G G A G G Q A Q Q Q Q B Bh B Bh A A A A A G A G G G G B Q B Q 10 10 10 10 B B B B A B G G A B G A B G G Q Q Q Q Q Q G G A G G A G G A B A B Q Q B R'' B R'' B B Q Q A B G A B G A A Q Q R' R' A Q Q A B B Q Q Q Q A A Q B Q B Q Q Q Q q q G G G G 1 1 q q 2 2 A A R' R'' G G R' R'' 11 11 11 11 G G B B A B A B Q Q Q G G G G G G R' R'' 1 1 1 R' R'' I I I II q q 1 1 2 2 2 3 4 q q 2 2 B B R' R' A B A B A B Q Q A R'' A R'' Q Q Q 2 G G G G G G 1 1 1 1 I I II A B A B 3 G 2 2 4 12 12 12 12 15a Q Q Q G G G G G G 1 1 1 I I I II 2 2 2 3 4 G G G G A A G G A B A B A B G Q Q B G B Q Q Q 2 2 A B A B G G 2 G G G G 3 1 1 1 1 1 I I II 1 3 4 G 2 2 4 13 13 13 13 15b Q Q Q G G G G G G 1 1 1 I I I II Q G Q Q Q Q 2 2 2 3 4 A G G A G G G G A B A B A B Q Q Q Q B Q Q Q B 2 2 A B G A B G G G 2 G G G G 3 1 1 1 1 1 I I II 2 2 1 3 4 G 4 14 14 14 14 15c Q Q Q G G G G G G 1 1 1 I I I II 2 2 2 3 4 G G G G A A G G A B A B A B G Q Q B G B Q Q Q 2 2 A B A B G G 2 G G G G 3 1 1 1 1 1 I I II 2 2 1 3 4 G 4 15 15 15 15 15d Q Q A A Q Q B B B A B A 16 16 16 16 g Q Q Q G G Q G G G G G A A G G A G G G G G G G G G B B G B A B A B G A B 17 17 17 17 q q Q Q Q F Q 3 Q G G G G A min Q F A 2 A G A G max f Q max fmin Bmax F1 Q G G Bmin Q B B B A B A B Q A B A B min min A L B max min max L max 18 18 18 18 q Q G Q Q Q Q A A 2 1 F A G G A 3 Q G G Q G G F2 F 3 Q Q Q F 1 Q Q B B B A B G A B G Q B B 2 1 A B A B 1 1 A B 2 2 19 19 19 19 q q q F Q 3 Q Q Q F 2 A A F 2 F Q 3 Q Q F 1 Q B B Q B A B A B Q A B A B max max min min A B 20 20 20 20 q Q Q Q F Q 3 Q G G G G Q F A 2 A G F F G 1 2 F 3 Q F 1 Q q G Q G B B B A B A B Q A B 21 21 21 21 A B C D F g A G G G G G G C q B F G 3 Q G D Q A A F G 2 G F F 1 2 G A F G 3 Q G F G 1 Q F F G G Q B B B G G Q A B A B A B 22 22 22 22 A B C D R q 1 Q Q Q q q q 2 q Q Q Q R' R'' F F 3 3 R' Q Q F2 F2 R F1 F2 F1 F2 A F A F 3 3 Q F1 Q F1 Q Q R'' Q f Q Q B max f B min Q Q Q A B A B A B 23 23 23 23 g q q G G Q Q Q F 1 G G G q F F 3 Q 2 A G g G F Q G 2 F 3 G Q A Q A Q t F1 Q b Q B Q b G B Q Q Q A B B G A B A B Q G 24 24 24 24 R G G G G G G g g q G G G G G G 1 A Q Q Q q R q q 2 1 g Q Q Q F R1 R2 R F1 1 G G F3 F2 F3 F2 G G G A G A G G G F2 F F2 F3 B R2 A G 3 G G G G G F Q F 1 1 Q G G G G B Q Q G A B B G B G A B A B Q Q G G Drawing Conventions - Latest Update 17.09.2015 symbol meaning units 3.4 mm text Arial Narrow / subscript 2.3 mm 25 25 25 A B 25 γ generic security factor Arrows & Arrowheads - Lengths Position of arrowheads γ= 1,35 security factor self-weight A B C D E F G H P Q R N N P γ= 1,5 security factor external load A B C D E F G H P Q R N N P 1 1 1 1 1 1 1 1 1 1 1 1 1 1 External force, 1 mm distance to structure / forces γ security factor material Resultant Force: 2 cm long and arrowhead 4.5 mm Support forces, use margin symbol support M A B C D E F G H P Q R N N P 2 2 2 2 2 2 2 2 2 2 2 2 2 2 σ generic stress N/mm2 MPa kN/cm2 A B C D E F G H P Q R N N P 3 3 3 3 3 3 3 3 3 3 3 3 3 3 generic strain ε mm/mm G G G G G G 20.00 15.00 F generic force kN A4 B4 C4 D4 E4 F4 G4 H4 P4 Q4 R4 N4 N4 P4 g g 1.00 N internal tension force kN A5 B5 C5 D5 E5 F5 G5 H5 P5 Q5 R5 N5 N5 P5 G G G G G G g Q Q Q External point force and support force: 1.5 cm long and arrowhead 3.5 mm N internal compression force kN A6 B6 C6 D6 E6 F6 G6 H6 P6 Q6 R6 N6 N6 P6 q q q 15.00 P prestress force kN A B C D E F G H P Q R N N P Q Q Q 7 7 7 7 7 7 7 7 7 7 7 7 7 7 15.00 15.00 Q life load kN A B C D E F G H P Q R N N P 15.00 8 8 8 8 8 8 8 8 8 8 8 8 8 8 F G dead load kN 3 Q A B C D E F G H P Q R N N P q linear life load kN/m 9 9 9 9 9 9 9 9 9 9 9 9 9 9 A B L F Q 2 F Uniformly distributed load: 0.5 cm and arrowhead 2mm A B C D R' 1 area life load kN/m2 v v v v F2 A g linear dead load kN/m Ah Bh Ch Dh R'' F 3 5.00 Q area dead load kN/m2 G Q F G Q 1 Q support force is 1.5 cm long, but in case it its represented in R resultant force kN n1 q1 Lmax Ai fa1+ fa1- fa1,d+ fa1,d- R1 R1 R1 R1 G hreolarizteodn ttaol tahned m vaegrtnicitauld ceomponents it is relatively A B C nsuopdpeos ritn r edaiacgtiroanm fso r(cwehere necessary) kN n2 q2 Lmin Ni fg1+ fg1- fg1,d+ fg1,d- G A Q G A G A B Q I II IIIIV Q Q R 15.00 15.00 1A2 3 4 5 asurebasystems (force elements where necessary) m2 mm2 nn43 ANedrf ffsc11++ ffsc11-- ffcs11,,dd++ ffsc11,,dd-- 1 R1 R1 R1 A B G B G A B G B G B A B Q l length m n5 f f R Q r1+ r1- 1 bh dweidptthh m n6 fmx+ fmx- fmx,d+ fmx,d- R1 R1 R1 G G m 26 26 26 26 n7 t thickness m ft ll+ ft ll- ft l l ,d+ ft l l ,d- R Notation - Form Diagram Case 1: vertical forces --> name always on the right side of the force, in the center E Elastic/Young’s modulus N/mm2 n8 f f f f 1 R R1 pick text from the library! t + t - t ,d+ t ,d- 1 element / subsystem numbers, from library. always in the center of the line f generic strength of material N/mm2 n9 R1 F ρ density kg/m3 I moment of inertia m4 /mm4 2.3 mm text Arial Narrow 1 2 hinge support I II IIIIV V VI VII VIIIIX X CS I q * L1 q * L2 I 3 1 2 3 4 5 6 7 8 9 CS II F CSIII 1 2 q sliding support G G G G G G A B Text for dimensions 2 mm Arial Narrow g g q chosen point by the designer resulting point (intersection etc.) G G G G G G f N kN mm cm m Case 2: diagonal forces --> name always in the interior of the structure. hinge A node numbers (Roman) (I,II, etc) from the library. Corner point in the center of the arrow. f1 8 8N 8kN 8mm 8cm 8m if possible, place the node number to the right of the node pick text from the library! symmetry 8.8 8.8N 8.8kN 8.8mm 8.8cm 8.8m G Q G also if possible below the node F f2 8.88 8.88N 8.88kN 8.88mm 8.88cm 8.88m L L B F Q otherwise use your eye. A 88 88N 88kN 88mm 88cm 88m A G A 1 2 2 I f3 88.8 88.8N 88.8kN 88.8mm 88.8cm 88.8m G L section mark 88.88 88.88N 88.88kN 88.88mm 88.88cm 88.88m G arch 1 2 A' f4 888 888N 888kN 888mm 888cm 888m G Q f G F I 5 G 1 direction of rotation in cremona A B f6 f6 88kN G G B o o' o'' o''' trial pole (force diagram) B I f A B r' r'' r''' rise point (form diagram) 7 f6 88kN 88kN 88kN G G f A 8 A B cable i intersection point of closing string A B q * L A B f 1 and line of action of resultant 9 1 2 I geometric planes m n F closing string F CS CS I B 27 27 27 27 parallel lines q * L 2 Notation - Force Diagram Cremona- Construction without notation Cremona- Construction with notation only external forces..full arrow head external eq..corner point of name goes to the center of the line q * L q * L F F 1 2 F A q Q Q Q q q q F B Q Q Q A B A B F3 F 3 Q Cremona- Construction without notation Cremona- Construction with notation A B inner forces always precise without arrowhead, internal eq..offset from inner to external 1.5 mm F2 F2 F L1 L2 Q external with an offset of 1.0 mm and with half arrow heads when internal eq is also shown Node number goes to barycenter of the triangle F1 1 F F2 2 L A A F F 2/3 1/3 3 3 Q F F 1.00 1.50 F1 Q F1 Q A Q I A Q 1 Q 1 2 I F B B Q 2 Q Q B B A B Q A B A A B A B A B q * L 1 I F 28 28 28 28 B q * L 2 Dimensioning Thrust lines 4 Step 1: Pick the dimension from the library Step 2: manually adapt it to the line of the drawing by Step 3: separate the line of the dimension from rotating and streching one of its sides. drawing line a distance of 3.6 mm. dimension from the library 88kN Q Q Q q q 88 kN 88 kN q g Q Q Q line of the drawing F 2 F 2 Step 4: Pick the text box from the library which Step 5: Ungroup and erase the old text. Step 6: Copy the perpendicular line and place it fits to the text you wish to write and modify the text Build a perpendicular line through the mid point through the corner of the text margin which is of the dimension line and place the center of the text on it. more near to the dimension line. Then, move the text box to the dimension line keeping the center of the box on the first perperdicular. Then group F I F I 1 1 the text and the dimension line. 88m 13m 13m I I A B 13m A B Case 1 Case 2 Case 3 29 29 0 6 29 b 3. 29 1 Dimensioning f f min max example: 54.9kN q Q Q Q q q Q Q Q g q 80.2kN A max 54.9kN A min f max A A f Bmin min Q Q B Q max Q Q B B A A B Q B Please add the units (m) (mm) like in the following way. A B max A L B max H 25 m or 25.12 m min min min min 250 mm or 25 cm 5 L H 25.1 cm or 251 mm 30 30 30 b 5.1 30 max max 1 Point types - hinges / selected points / resulting points f f min max A hinge is a hinge --cicrle with no hatch A choosen geometric point is a thin black circle with grey hatch A resulting point is black point ---> take them from the library point selected on the closing string G G G G G G intersection point --> result g g g B G G G G G G A A min max A F B 1 G G G III G G G G A G A G G II F R A 2 I G G G III G G I F G 1 II F A G G 3 F 3 B G F B G G 2 B G G G A B B B A B A B min max A B R max A B max min min 31 31 31 31 Free-Body diagram In case you draw a free body diagram, make the lines of the bars manually thicker--> 0.35 mm Force 0.28 mm Bar 0.35 mm Q Q Q q q q Q Q Q F F 3 3 F2 F2 F3 Q Force- change line properties 0.28 mm Q F 2 F F1 F 1 F 2 2 Bars - keep line properties F1 A F3 F1 A F3 q q Q G F Q 1 Q B G B Q Q B G Q Q A B A B A B 32 32 32 32 A B A B Q Q Q q q q Q Q Q F 3 Q Q F 2 F 3 Q A A G F Q 1 Q q G Q Q B B B G Q Q A B A B A B 33 33 33 33 A B C D F G G G G G G g g A G G G G G G C Q Q Q q q q F F 1 1 Q Q Q F3 G F3 G F F 2 2 F2 F2 F3 Q B A G A G D Q F F F 2 3 3 F 2 F1 G F1 G F3 Q Q F Q 1 Q F F G G Q B Q Q Q B B A B G G A B A B Q Q 34 G 34 G 34 34 A B C D R G G G G G G g g q G G G G G G 1 Q Q Q q q q q 2 Q Q Q R' R'' F 3 Q R' Q F 2 R F F 1 2 F 3 Q G Q A F G Q 1 Q R'' G f A G Q max f G B min G Q Q Q B A B G G G A B G A B Q Q B 35 35 35 35 G G q q F 3 Q F Q F F2 g F F 1 2 A F 3 Q F1 Q t b Q b B Q A B A A 36 36 36 36 R q 1 A q R q 2 1 R R 1 2 R I Q A A I N F N Q F B R 2 F F Q Q N N Q Q I I A B A A 37 37 37 37 A B g q g G G F 1 G G G P P F3 Q F2 G F Q G A G A L B 2 F 3 G Q F 1 Q G A Q B G A B B Q G 38 38 38 38 g * g * L L 1 2 Q g g P P A G G G B G G A L1 L2 G N G I I N G G G N N G B G I I A A B g * L 1 Q B 39 39 39 39 g * L 2 g * g * L L 1 2 Q P P g q N=0 N = 0 F A 3 Q A F A I F I F Q L L B 2 F 1 2 1 F 2 A F F F 3 Q F 1 Q N N Q B Q I I A A B g * L A A 1 40 40 40 40 Q B g * L 2 q g q Q F Q 2 Q F I 1 I A B 41 41 41 41 0 6 b 3. 1 q g q Q Q Q A Q Q B A B Q 42 42 42 42 5 b 5.1 1 43 43 44 44 45 45 46 46 R R q 1 q 1 q 2 q 2 R' R'' R' R'' B A R' R' R R B R'' A R'' 47 A B 47 A B R R q 1 q 1 q 2 q 2 R' R'' R' R'' R' R' R R R'' R'' max min fmax f f f min 48 48 q q A A B v max B v max B f max Bh min max Bh min f Ah min Bh min Ah min B h min A B A B v max v max v max v max L L 49 min 49 min q q A A B v min B B v min Bh max Bh max min fmin f Ah max Bh max Ah min Bh min A B A B v max v max v min v min L 50 Lmax 50 max q q A A B v max B v max B B Bh min h min Ah min Bh min Ah min B h min A B A B v max v max v max v max 51 51 q q A A B v min B B v min Bh max Bh max Ah max Bh max Ah min Bh min A B A B v max v max v min v min 52 52 q q A A B v max B v max B f max Bh min max Bh min f Ah min Bh min Ah min B h min A B A B v max v max v max v max L L min 53 min 53 ? A A A2 A1 2 1 B B B B 2 1 2 1 A B A1 B2 B1 1 A2 B2 1 A 2 54 54 q q 5r 5r 5 5 1 1 0. 0. r r A B A B 55 55 q q A B A B 56 56 q q 57 57 A B C D A B C D F F A A / C C B B / D D F F F F 58 58 A B C D A B C D q q g g N N d σd ≤ 2· b d· t σd ≤ 2· b · t t t b b b b N N d b ≤ d b ≤ 2· b · f d 2· b ·f d 59 59 R R q 1 q B 1 A q 2 q R 2 1 R' R'' R R R' R 1 2 R B R A R'' 2 60 60 A B A B 61 61 A B A B F F q q 62 62 R’’’ R 3 R'' R F R 1 2 R' F q R’ q R1 R 3 R’’’ F F R A R’ A 1 R 3 R’’’ F F R’’ R B 2 B 63 63 A B A B R F R 1 2 R' F R'' q q R’ R 1 A A F F R’’ R 2 B B 64 64 A B A B F F q q 65 65 A B A B 66 66 R 3 R' R R'' R R 1 R 2 qq q R' R 1 A A R'' R 2 B B A B A B 67 67 q q A B A B A A B B 68 68 R R 1 2 F F q q A A B B A A q R 1 1 F F B B 69 69 q R 2 2 R R 1 2 F F q q A A B B A A q R 1 1 F F B B 70 70 q R 2 2 R R 1 2 F F q q A B A B A q1 A R1 F F B B 71 71 q R 2 2 q A B v max B v max f max Bh min max Bh min f Ah min Bh min Ah min B h min A B A B v max v max v max v max L L 72 min 72 min R R q 1 q 1 q 2 q 2 R' R'' R' R'' R' R R 1 R'' R R 2 max min fmax f f f min 73 73 q g g q 0 0 6 6 b 3. b 3. 1 1 74 74 f f min max f f min max g g q q 5 5 b 5.1 b 5.1 1 1 75 75 f f min max f f min max Thrust lines 5 Case 1 old Stand 03.08.2016 Q Q Q Q Q Q Q Q Q Q Q Q Q A B A B A B Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q A B Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q A B A B 1 1 1 1 F A B A B F F B A A B B F B A A A B F F A B F F F F A B B A A B F B A F F F A B A B F A B F 2 2 2 2 A B Q Q Q Q QQ Q Q A B A B A AA BB A A 2 1 2 1 2 22 11 2 1 Q Q Q Q QQ Q Q Q Q Q Q QQ Q Q Q Q Q Q QQ Q Q B A B A B BB AA B B 2 1 2 1 2 22 11 2 1 Q Q Q Q QQ Q Q Q Q Q Q Q Q Q Q Q Q QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ Q Q Q Q Q Q Q Q Q Q A B A B AA BB A B 1 1 1 1 11 11 1 1 A B A B AA BB A B 2 2 2 2 22 22 2 2 3 3 3 3 Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q A A A A 1 1 1 1 Q Q Q Q Q Q B B H1 h1 A 1 BV1 B A Bv1 Bv1 Q A Bv1 H1 Bv1 Q A Bv1 H1 Bv1 Q V1 1 1 1 Q Q Q B B H H H1 h1 1 1 Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q A A A A 2 2 2 2 Q Q Q Q Q Q Q Q Q B B B B BV2 B v2 v2 v2 H2 h2 Q Q Q 4 4 4 H 4 H A B B B 2 B 2 2 V2 v2 v2 v2 A A A BH2 2 B 2 H 2 H h2 2 2 F F F F 1 2 1 2 A B A B 1 1 1 1 F F F F A A F A B A B 2 2 2 2 F F F F 1 2 1 2 F B B B A B A A B A B 1 2 1 2 F F F F 2 1 2 1 F F F F 1 2 1 2 A B A B 1 2 1 2 5 5 5 5 q g A B A B q q q q f f B A2 B2 A2 2 f f A B 1 1 f f A B A B A B 1 1 g f f q A A A1 A2 1 2 R R R R B1 B2 B1 B2 6 6 6 6 F F 1 2 F F 1 2 A B A B 2 2 2 2 A B G G G G 1 1 A A A B G G 1 1 F F F F 1 2 1 2 G G B B A B A B A A A1 F F A2 1 F F 2 1 1 1 1 F B1 F2 F2 B2 B F2 2 B 1 2 7 7 7 7 q q q q A B 2 2 Q Q Q Q A2 B2 Q Q G G A G G A A B 1 1 A B G G 1 1 Q Q B B A B G A B G A1 A2 A1 A2 R R R R B1 B2 B1 B2 8 8 8 8 R Q Q R F1 F2 F3 F1 F1 F2 F3 F4 F1 G G G G F2 F2 -∆l -∆l P +∆l +∆l o' R R F F 3 3 F F 4 4 A B A B 9 9 9 9 G G G G G G A A A G G G G G G G G G B B B R G G G R A Ah Q B Q B Q B h A G A G A G G G G r'' F1 F2 F3 F4 Av A 1 F1 F1 F2 F3 F4 Av A 1 F1 AQ AQ AQ Q Q Q 2 F2 2 F2 B B B P o'' Q Q Q 2 3 3 2 3 3 R 4 4 R F3 4 4 F3 Q Q Q B 1 5 Bv 5 1 5 Bv B 5 A BQ A BQ A BQ Q Q Q F F 4 4 G G G G A G G Q A Q Q Q Q B Bh B Bh A A A A A G A G G G G B Q B Q 10 10 10 10 B B B B A B G G A B G A B G G Q Q Q Q Q Q G G A G G A G G A B A B Q Q B R'' B R'' B B Q Q A B G A B G A A Q Q R' R' A Q Q A B B Q Q Q Q A A Q B Q B Q Q Q Q q q G G G G 1 1 q q 2 2 A A R' R'' G G R' R'' 11 11 11 11 G G B B A B A B Q Q Q G G G G G G R' R'' 1 1 1 R' R'' I I I II q q 1 1 2 2 2 3 4 q q 2 2 B B R' R' A B A B A B Q Q A R'' A R'' Q Q Q 2 G G G G G G 1 1 1 1 I I II A B A B 3 G 2 2 4 12 12 12 12 15a Q Q Q G G G G G G 1 1 1 I I I II 2 2 2 3 4 G G G G A A G G A B A B A B G Q Q B G B Q Q Q 2 2 A B A B G G 2 G G G G 3 1 1 1 1 1 I I II 1 3 4 G 2 2 4 13 13 13 13 15b Q Q Q G G G G G G 1 1 1 I I I II Q G Q Q Q Q 2 2 2 3 4 A G G A G G G G A B A B A B Q Q Q Q B Q Q Q B 2 2 A B G A B G G G 2 G G G G 3 1 1 1 1 1 I I II 2 2 1 3 4 G 4 14 14 14 14 15c Q Q Q G G G G G G 1 1 1 I I I II 2 2 2 3 4 G G G G A A G G A B A B A B G Q Q B G B Q Q Q 2 2 A B A B G G 2 G G G G 3 1 1 1 1 1 I I II 2 2 1 3 4 G 4 15 15 15 15 15d Q Q A A Q Q B B B A B A 16 16 16 16 g Q Q Q G G Q G G G G G A A G G A G G G G G G G G G B B G B A B A B G A B 17 17 17 17 q q Q Q Q F Q 3 Q G G G G A min Q F A 2 A G A G max f Q max fmin Bmax F1 Q G G Bmin Q B B B A B A B Q A B A B min min A L B max min max L max 18 18 18 18 q Q G Q Q Q Q A A 2 1 F A G G A 3 Q G G Q G G F2 F 3 Q Q Q F 1 Q Q B B B A B G A B G Q B B 2 1 A B A B 1 1 A B 2 2 19 19 19 19 q q q F Q 3 Q Q Q F 2 A A F 2 F Q 3 Q Q F 1 Q B B Q B A B A B Q A B A B max max min min A B 20 20 20 20 q Q Q Q F Q 3 Q G G G G Q F A 2 A G F F G 1 2 F 3 Q F 1 Q q G Q G B B B A B A B Q A B 21 21 21 21 A B C D F g A G G G G G G C q B F G 3 Q G D Q A A F G 2 G F F 1 2 G A F G 3 Q G F G 1 Q F F G G Q B B B G G Q A B A B A B 22 22 22 22 A B C D R q 1 Q Q Q q q q 2 q Q Q Q R' R'' F F 3 3 R' Q Q F2 F2 R F1 F2 F1 F2 A F3 A F3 Q F1 Q F1 Q Q R'' Q f Q Q B max f B min Q Q Q A B A B A B 23 23 23 23 g q q G G Q Q Q F 1 G G G q F F 3 Q 2 A G g G F Q G 2 F 3 G Q A Q A Q t F1 Q b Q B Q b G B Q Q Q A B B G A B A B Q G 24 24 24 24 R G G G G G G g g q G G G G G G 1 A Q Q Q q R q q 2 1 g Q Q Q F R1 R2 R F1 1 G G F3 F2 F3 F2 G G G A G A G G G F2 F F2 F3 B R2 A G 3 G G G G G F Q F 1 1 Q G G G G B Q Q G A B B G B G A B A B Q Q G G Drawing Conventions - Latest Update 17.09.2015 symbol meaning units 3.4 mm text Arial Narrow / subscript 2.3 mm 25 25 25 A B 25 γ generic security factor Arrows & Arrowheads - Lengths Position of arrowheads γ= 1,35 security factor self-weight A B C D E F G H P Q R N N P γ= 1,5 security factor external load A B C D E F G H P Q R N N P 1 1 1 1 1 1 1 1 1 1 1 1 1 1 External force, 1 mm distance to structure / forces γ security factor material Resultant Force: 2 cm long and arrowhead 4.5 mm Support forces, use margin symbol support M A B C D E F G H P Q R N N P 2 2 2 2 2 2 2 2 2 2 2 2 2 2 σ generic stress N/mm2 MPa kN/cm2 A B C D E F G H P Q R N N P 3 3 3 3 3 3 3 3 3 3 3 3 3 3 generic strain ε mm/mm G G G G G G 20.00 15.00 F generic force kN A4 B4 C4 D4 E4 F4 G4 H4 P4 Q4 R4 N4 N4 P4 g g 1.00 N internal tension force kN A5 B5 C5 D5 E5 F5 G5 H5 P5 Q5 R5 N5 N5 P5 G G G G G G g Q Q Q External point force and support force: 1.5 cm long and arrowhead 3.5 mm N internal compression force kN A6 B6 C6 D6 E6 F6 G6 H6 P6 Q6 R6 N6 N6 P6 q q q 15.00 P prestress force kN A B C D E F G H P Q R N N P Q Q Q 7 7 7 7 7 7 7 7 7 7 7 7 7 7 15.00 15.00 Q life load kN A B C D E F G H P Q R N N P 15.00 8 8 8 8 8 8 8 8 8 8 8 8 8 8 F G dead load kN 3 Q A B C D E F G H P Q R N N P q linear life load kN/m 9 9 9 9 9 9 9 9 9 9 9 9 9 9 A B L F Q 2 F Uniformly distributed load: 0.5 cm and arrowhead 2mm A B C D R' 1 area life load kN/m2 v v v v F2 A g linear dead load kN/m Ah Bh Ch Dh R'' F 3 5.00 Q area dead load kN/m2 G Q F G Q 1 Q support force is 1.5 cm long, but in case it its represented in R resultant force kN n1 q1 Lmax Ai fa1+ fa1- fa1,d+ fa1,d- R1 R1 R1 R1 G hreolarizteodn ttaol tahned m vaegrtnicitauld ceomponents it is relatively A B C nsuopdpeos ritn r edaiacgtiroanm fso r(cwehere necessary) kN n2 q2 Lmin Ni fg1+ fg1- fg1,d+ fg1,d- G A Q G A G A B Q I II IIIIV Q Q R 15.00 15.00 1A2 3 4 5 asurebasystems (force elements where necessary) m2 mm2 nn43 ANedrf ffsc11++ ffsc11-- ffcs11,,dd++ ffsc11,,dd-- 1 R1 R1 R1 A B G B G A B G B G B A B Q l length m n5 f f R Q r1+ r1- 1 hb dweidptthh m n6 fmx+ fmx- fmx,d+ fmx,d- R1 R1 R1 G G m 26 26 26 26 n7 t thickness m ft ll+ ft ll- ft l l ,d+ ft l l ,d- R Notation - Form Diagram Case 1: vertical forces --> name always on the right side of the force, in the center E Elastic/Young’s modulus N/mm2 n8 f f f f 1 R R1 pick text from the library! t + t - t ,d+ t ,d- 1 element / subsystem numbers, from library. always in the center of the line f generic strength of material N/mm2 n9 R1 F ρ density kg/m3 I moment of inertia m4 /mm4 2.3 mm text Arial Narrow 1 2 hinge support I II IIIIV V VI VII VIIIIX X CS I q * L1 q * L2 I 3 1 2 3 4 5 6 7 8 9 CS II F CSIII 1 2 q sliding support G G G G G G A B Text for dimensions 2 mm Arial Narrow g g q chosen point by the designer resulting point (intersection etc.) G G G G G G f N kN mm cm m Case 2: diagonal forces --> name always in the interior of the structure. hinge A node numbers (Roman) (I,II, etc) from the library. Corner point in the center of the arrow. f1 8 8N 8kN 8mm 8cm 8m if possible, place the node number to the right of the node pick text from the library! symmetry 8.8 8.8N 8.8kN 8.8mm 8.8cm 8.8m G Q G also if possible below the node F f2 8.88 8.88N 8.88kN 8.88mm 8.88cm 8.88m L L B F Q otherwise use your eye. A 88 88N 88kN 88mm 88cm 88m A G A 1 2 2 I f3 88.8 88.8N 88.8kN 88.8mm 88.8cm 88.8m G L section mark 88.88 88.88N 88.88kN 88.88mm 88.88cm 88.88m G arch 1 2 A' f4 888 888N 888kN 888mm 888cm 888m G Q f G F I 5 G 1 direction of rotation in cremona A B f6 f6 88kN G G B o o' o'' o''' trial pole (force diagram) B I f A B r' r'' r''' rise point (form diagram) 7 f6 88kN 88kN 88kN G G f A 8 A B cable i intersection point of closing string A B q * L A B f 1 and line of action of resultant 9 1 2 I geometric planes m n F closing string F CS CS I B 27 27 27 27 parallel lines q * L 2 Notation - Force Diagram Cremona- Construction without notation Cremona- Construction with notation only external forces..full arrow head external eq..corner point of name goes to the center of the line q * L q * L F F 1 2 F A q Q Q Q q q q F B Q Q Q A B A B F3 F 3 Q Cremona- Construction without notation Cremona- Construction with notation A B inner forces always precise without arrowhead, internal eq..offset from inner to external 1.5 mm F2 F2 F L1 L2 Q external with an offset of 1.0 mm and with half arrow heads when internal eq is also shown Node number goes to barycenter of the triangle F1 1 F F2 2 L A A F F 2/3 1/3 3 3 Q F F 1.00 1.50 F1 Q F1 Q A Q I A Q 1 Q 1 2 I F B B Q 2 Q Q B B A B Q A B A A B A B A B q * L 1 I F 28 28 28 28 B q * L 2 Dimensioning Step 1: Pick the dimension from the library Step 2: manually adapt it to the line of the drawing by Step 3: separate the line of the dimension from rotating and streching one of its sides. drawing line a distance of 3.6 mm. dimension from the library 88kN Q Q Q q q 88 kN 88 kN q g Q Q Q line of the drawing F 2 F 2 Step 4: Pick the text box from the library which Step 5: Ungroup and erase the old text. Step 6: Copy the perpendicular line and place it fits to the text you wish to write and modify the text Build a perpendicular line through the mid point through the corner of the text margin which is of the dimension line and place the center of the text on it. more near to the dimension line. Then, move the text box to the dimension line keeping the center of the box on the first perperdicular. Then group F I F I 1 1 the text and the dimension line. 88m 13m 13m I I A B 13m A B 29 29 0 6 29 b 3. 29 1 Dimensioning f f min max Thrust lines 6 example: 54.9kN q Q Q Q q q Q Q Q g q 80.2kN A max 54.9kN A min f min A A f Bmin Q max Q B Q max Q Q B B A A B Q B Please add the units (m) (mm) like in the following way. A B max A L B max H 25 m or 25.12 m min min min min 250 mm or 25 cm 5 L H 25.1 cm or 251 mm 30 30 30 b 5.1 30 max max 1 Point types - hinges / selected points / resulting points f f min max A hinge is a hinge --cicrle with no hatch A choosen geometric point is a thin black circle with grey hatch A resulting point is black point ---> take them from the library point selected on the closing string G G G G G G intersection point --> result g g g B G G G G G G A A min max A F B 1 G G G III G G G G A G A G G II F R A 2 I G G G III G G I F G 1 II F A G G 3 F 3 B G F B G G 2 B G G G A B B B A B A B min max A B R max A B max min min 31 31 31 31 Free-Body diagram In case you draw a free body diagram, make the lines of the bars manually thicker--> 0.35 mm Force 0.28 mm Bar 0.35 mm Q Q Q q q q Q Q Q F F 3 3 F2 F2 F3 Q Force- change line properties 0.28 mm Q F 2 F F1 F 1 F 2 2 Bars - keep line properties F1 A F3 F1 A F3 q q Q G F Q 1 Q B G B Q Q B G Q Q A B A B A B 32 32 32 32 A B A B Q Q Q q q q Q Q Q F 3 Q Q F 2 F 3 Q A A G F Q 1 Q q G Q Q B B B G Q Q A B A B A B 33 33 33 33 A B C D F G G G G G G g g A G G G G G G C Q Q Q q q q F F 1 1 Q Q Q F3 G F3 G F F 2 2 F2 F2 F3 Q B A G A G D Q F F F 2 3 3 F 2 F1 G F1 G F3 Q Q F Q 1 Q F F G G Q B Q Q Q B B A B G G A B A B Q Q 34 G 34 G 34 34 A B C D R G G G G G G g g q G G G G G G 1 Q Q Q q q q q 2 Q Q Q R' R'' F 3 Q R' Q F 2 R F F 1 2 F 3 Q G Q A F G Q 1 Q R'' G f A G Q max f G B min G Q Q Q B A B G G G A B G A B Q Q B 35 35 35 35 G G q q F 3 Q F Q F F2 g F F 1 2 A F 3 Q F1 Q t b Q b B Q A B A A 36 36 36 36 R q 1 A q R q 2 1 R R 1 2 R I Q A A I N F N Q F B R 2 F F Q Q N N Q Q I I A B A A 37 37 37 37 A B g q g G G F 1 G G G P P F3 Q F2 G F Q G A G A L B 2 F 3 G Q F 1 Q G A Q B G A B B Q G 38 38 38 38 g * L g * L 1 2 Q g g P P A G G G B G G A L1 L2 G N G I I N G G G N N G B G I I A A B g * L 1 Q B 39 39 39 39 g * L 2 g * L g * L 1 2 Q P P g q N=0 N = 0 F A 3 Q A F A I F I F Q L L B 2 F 1 2 1 F 2 A F F F 3 Q F 1 Q N N Q B Q I I A A B g * L A A 1 40 40 40 40 Q B g * L 2 q g q Q F Q 2 Q F I 1 I A B 41 41 41 41 0 6 b 3. 1 q g q Q Q Q A Q Q B A B Q 42 42 42 42 5 b 5.1 1 43 43 44 44 45 45 46 46 R R q 1 q 1 q 2 q 2 R' R'' R' R'' B A R' R' R R B R'' A R'' 47 A B 47 A B R R q 1 q 1 q 2 q 2 R' R'' R' R'' R' R' R R R'' R'' max min fmax f f f min 48 48 q q A A B v max B v max B f max Bh min max Bh min f Ah min Bh min Ah min B h min A B A B v max v max v max v max L L 49 min 49 min q q A A B v min B B v min Bh max Bh max min fmin f Ah max Bh max Ah min Bh min A B A B v max v max v min v min L 50 Lmax 50 max q q A A B v max B v max B B Bh min h min Ah min Bh min Ah min B h min A B A B v max v max v max v max 51 51 q q A A B v min B B v min Bh max Bh max Ah max Bh max Ah min Bh min A B A B v max v max v min v min 52 52 q q A A B v max B v max B f max Bh min max Bh min f Ah min Bh min Ah min B h min A B A B v max v max v max v max L L min 53 min 53 ? A A A2 A1 2 1 B B B B 2 1 2 1 A B A1 B2 B1 1 A2 B2 1 A 2 54 54 q q 5r 5r 5 5 1 1 0. 0. r r A B A B 55 55 q q A B A B 56 56 q q 57 57 A B C D A B C D F F A A / C C B B / D D F F F F 58 58 A B C D A B C D q q g g N N d σd ≤ 2· b d· t σd ≤ 2· b · t t t b b b b N N d b ≤ d b ≤ 2· b · f d 2· b ·f d 59 59 R R q 1 q B 1 A q 2 q R 2 1 R' R'' R R R' R 1 2 R B R A R'' 2 60 60 A B A B 61 61 A B A B F F q q 62 62 R’’’ R 3 R'' R F R 1 2 R' F q R’ q R1 R 3 R’’’ F F R A R’ A 1 R 3 R’’’ F F R’’ R B 2 B 63 63 A B A B R F R 1 2 R' F R'' q q R’ R 1 A A F F R’’ R 2 B B 64 64 A B A B F F q q 65 65 A B A B 66 66 R 3 R' R R'' R R 1 R 2 qq q R' R 1 A A R'' R 2 B B A B A B 67 67 q q A B A B A A B B 68 68 R R 1 2 F F q q A A B B A A q R 1 1 F F B B 69 69 q R 2 2 R R 1 2 F F q q A A B B A A q R 1 1 F F B B 70 70 q R 2 2 R R 1 2 F F q q A B A B A q1 A R1 F F B B 71 71 q R 2 2 q A B v max B v max f max Bh min max Bh min f Ah min Bh min Ah min B h min A B A B v max v max v max v max L L 72 min 72 min R R q 1 q 1 q 2 q 2 R' R'' R' R'' R' R R 1 R'' R R 2 max min fmax f f f min 73 73 q g g q 0 0 6 6 b 3. b 3. 1 1 74 74 f f min max f f min max g g q q 5 5 b 5.1 b 5.1 1 1 75 75 f f min max f f min max Thrust lines 7 Taq-i Kisra Palast (Ayvan-e Kasra), Asbanbar, near Baghdad, 550 n.Chr. Thrust lines 8 Renzo Piano, Arup: Padre Pio Pilgrim Church, San Giovanni rotondo, 2004 Thrust lines 9 Renzo Piano, Arup: Padre Pio Pilgrim Church, San Giovanni rotondo, 2004 Thrust lines 10 Renzo Piano, Arup: Padre Pio Pilgrim Church, San Giovanni rotondo, 2004

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Thrust lines. 8. Renzo Piano, Arup: Padre Pio Pilgrim Church, San Giovanni rotondo, 2004 eQ. Minimum and maximum thrust in a masonry arch.

Arches 2 PDF

78 Pages·2016·61.86 MB·English

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Thrust lines. 8. Renzo Piano, Arup: Padre Pio Pilgrim Church, San Giovanni rotondo, 2004 eQ. Minimum and maximum thrust in a masonry arch.

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Publication Year:	2016
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