Question

Consider the power transmission-line tower shown in the accompanying figure. The members have a cross-sectional area of 10 in' and a modulus of clasticity of E - 29 101b/in?. Using ANSYS, determine i. Deflection of each joint ii. Stress in each member Reaction forces at the base iv. Verify your results. 5 at 10 ft 13 14 11 12 15 6 9 10 ft 10 7 1000 lb 10 ft 1000 1 5 10 ft 3 3 15 ft -15 ft

USE ANSYS (no hand calculations)

Answer 1

first of select the structure prefrance and select element link element.
Library of Element Types Only structural element types are shown Library of Element Types 3D finit stn 180 actuator 11 Structural Mass Link Beam Pipe Solid Shell Solid-Shell 3D finit stn 180 Element type reference number OK Apply Cancel Help
now give the material properties.
2019 R3 A Define Material Model Behavior TEP=1 UB =) IME=1 SUM SYS=0 MX =.0 MX = 0 Material Edit Favorite Help Material Models Defined Material Models Available Material Mg Linear Isotropic Properties for Material Number 1 x Linear Isotropic Material Properties for Material Number 1 T1 Temperatures EX PRXY 2.9E+07 0 Add Temperature Delete Temperature Graph OK Cancel Help
now we create a model by aplaying keypoints as per shown in below picture cordinates
| IS 3 IS lo 9 1 (30 رم12) (क) (180ر1) 3 (sa( ر) عد مر12 ( 30) Nodes های رود 2- دبل (S40 رم12- 12 (45 کر) - 13 هاک (125) (--| اک دن 2) د 5 ی رہ38) -16 (ح رہ3۔ ) 1 (0 ردی) - 2 (180 ره3-) - 3 (188ر1s0) - ا 5 - (0) 300) 300 ر170) - 6 (120 ري) ( 1 (28 ارم12) 8 (80ا 120 -) -4 (L80 راو 2) ۱o
give the cordination as per shown in below picture.goto the creat->activ coordination.

File Select List Plot PlotCtrls WorkPlane Parameters Macro MenuCtrls Help Toolbar SAVE_DB RESUM_DB QUIT POWRGRPH 13 12 11 13 14 15 POINTS ANSIS 2019 R3 TYPE NUM ACADEMIC 0. 10 AUG 1 2020 10.10.04 1 A Create Keypoints in Active Coordinate System [K] Create Keypoints in Active Coordinate System NPT Keypoint number 16 X,Y,Z Location in active CS 360 540 OK Apply Cancel Main Menu references reprocessor Element Type Real Constants Material Props 1 Sections 3 Modeling Create Keypoints On Working Plane In Active CS On Line On Line w/Ratio On Node KP between KPs Fill between KPs KP at center # Hard PT on line # Hard PT on area # Lines # Areas # Volumes # Nodes # Elements E Contact Pair # Circuit # Transducers Help @ 3 'N

we add a area of link as per below.

NODAL SOLUTION ASIS 2019 R3 ACADEMIC 15 10 16 13 A Add or Edit Link Section STEP=1 SUB =1 TIME=1 USUM (AVG) RSYS=0 DMX =.012008 SMX =.012008 [SECTYPE] Edit Link Section 1 Section Name 1 [SECDATA] Section Data Link area 10 [SECCONTROL] Section control Added Mass (Mass/Length) 0 Preferences - Preprocessor Element Type # Real Constants Material Props Sections # Section Library # Beam # Shell # Pretension Joints Reinforcing # Pipe Link 3 Add E Edit # Axis # Contact B List Sections E Delete Section # Modeling # Meshing Checking Ctrls E Numbering Ctrls + Archive Model Tension Key Tension and Compression OK Apply Cancel Help X EN .002669 .005337 .008006 .001334 .004003 .006671 .00934 .010674 .012008

now we go to the line comand and in actve cordinate and select keypoints one by one to add a elements. make sure that element atribute are correct.

below figure shows the number of elements and nodes.

13 22 15 23 9 16 10 24 16 25 14 20 2 € 29- 29 27 21 11 14 17 15 12 18 19 7 13 8 10 12 11 8 6 9 5 2 3 Y 2 X 1 2

now we do a mash. for that firs set a mesh size .

ANSYS L-K 2019 R3 L22 L23 L16 L24 L25 ACADEMIC A Global Element Sizes [ESIZE] Global element sizes and divisions (applies only to "unsized" lines) SIZE Element edge length 0 NDIV No. of element divisions - 1 - (used only if element edge length, SIZE, is blank or zero) Main Menu E Preferences Preprocessor Element Type # Real Constants Material Props # Sections e Modeling Meshing # Mesh Attributes Mesh Tool Size Cntrls Smart Size Manual Size Global 3 Size B Area Cntrls E Volu Cntrls E Other # Areas # Lines E keypoints # Layers Concentrat KP's E Mesher Opts OK Cancel Help LS 14 L3 X Ll Aconcatenate

and then do a mesh by selecting all elements.

Eile Select List Plot PlotCtrls WorkPlane Parameters Macro MenuCtrls Help D A Toolbar SAVE_DB RESUM_DB QUIT POWRGRPH 1 1 L-K ANSYS 2019 R3 L22 123 BOOOOOO L16 124 L25 Main Menu a Preferences • Preprocessor Element Type o Real Constants Material Props # Sections # Modeling ACADEMIC L26 -27 AUG 1 2020 00:52:52 14 117 415 L13 Mesh Lines s FL10 111 Pick Unpick C Box 1 L8 Single C Polygon C Loop Circle @ Count 27 ntris ntris Maximum 27 L5 Minimum = 1 Line No. = 20 O List of Items s [1] Min, Max, Inc KPs X LI OK Apply

after meshing our modle look like as shown in below.

L-K-N 2019 F ACADEM 13 15 9 LO 16 14 AUG 1 202C 00:56:1) 11. Y

now we apply the load as per below picture. for fix all dof are zero, for roller only FY is zero.
1 E-L-K-N ANSYS 2019 R3 13 MIC Apply U, ROT on Nodes [D] Apply Displacements (U, ROT) on Nodes Lab2 DOFs to be constrained 2020 5:11 All DOF UX UY UZ VELX Constant value Apply as If Constant value then: VALUE Displacement value OK Cancel Help Y. X

1 E-L-K-N ANSYS 2019 R3 X MIC 13 Apply U, ROT on Nodes [D] Apply Displacements (U,ROT) on Nodes Lab2 DOFs to be constrained 2020 5:11 All DOF UX UY UZ VELX Constant value Apply as If Constant value then: VALUE Displacement value OK Cancel Help 2 nents NN
now we add a force downward side so apply - sign.
1 E-L-K-N ANS 20 sor 13 15 10 16 ACAD Type istants Props AUG 1 00:5 Х Ctrls ng Ctrls Model g/ Ceqn A Apply F/M on Nodes [F] Apply Force/Moment on Nodes Lab Direction of force/mom Apply as If Constant value then: VALUE Force/moment value FY Constant value -1000 OK Apply Cancel Help sis Type Loads Eings oly Structural Displacement = Force/Moment On Keypoints On Nodes On Node Components e From Reactions From Mag Analy Pressure Y X

ANSYS E-L-K-N 2019 R3 13 15 10 16 14 ACADEMIC AUG 1 2020 00:56:11 nt ent ints X Components ctions Analy

after all loads are applying our modle look like as abow picture. now solve the problme and we gate a answers.

for displacment go to the Genral porst-> list resulte->nodal sol->DOF solution. we get below list.note* in list shows numbering os nodes are as per our ansys modle.

i 1 ANSYS E-L-K-N 13 15 9 10 16 14 2019 R3 ACADEMIC 11 AUG 1 2020 A PRNSOL Command File PRINTU NODAL SOLUTION PER NODE ***** POST1 NODAL DEGREE OF FREEDOM LISTING ***** LOAD STEP= 1 TIME= 1.0009 SUBSTEP- 1 LOAD CASE= THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN THE GLOBAL COORDINATE SYS NODE UX UY UZ 1 -0.35313E-017 0.0000 0.0000 2 0.0000 0.0000 0.0000 3 0.46552E-003-0.62069E-003 0.0000 4 9.62069E-003-0.62069E-003 0.0000 5 0.29270E-003-0.10307E-002 0.0000 6 0.18926E-003-0.11817E-002 0.0000 7 0.16851E-002-0.14445E-002 0.0000 8 0.85756E-003-0.15955E-002 0.0000 9 0.10086E-002-0.14445E-002 0.0000 10 0.18362E-902-0.15955E-902 0.0000 11 0.19252E-002-0.32776E-002 0.0000 12 0.76859E-003-0.37308E-002 0.0000 13 -0.64655E-003-0.10734E-001 0.0000 14 0.34914E-002-0.11490E-001 0.0000 15 9.18103E-003-0.32776E-002 0.0000 16 0.26638E-002-0.37308E-002 0.0000 USUM 0.35313E-017 0.0000 9.77586E-003 0.87779E-003 9.10714E-002 9.11968E-002 0.22195E-902 9.18114E-002 0.17618E-902 0.24326E-002 0.38012E-002 0.38091E-002 0.19754E-001 0.12008E-001 0.32826E-002 9.45841E-002 X MAXIMUM ABSOLUTE VALUES NODE 14 14 VALUE 9.34914E-002-0.11490E-001 Itino-1 rol-1 Cyr- ] 0.0000 Icoon-1 14 0.12008E-001 dDOST1) mat-1

for stress Genral porst-> list resulte->element sol->stress->von mises stress. we get stress in each element as per below picture.
PRINTS PRIN ELEMENT SOLUTION PER ELEMENT ***** POST1 ELEMENT NODAL STRESS LISTING ***** LOAD STEP= 1 TIME= 1.0000 SUBSTEP= 1 LOAD CASE= 9 THE FOLLOWING X,Y,Z VALUES ARE IN GLOBAL COORDINATES ELEMENT 1 NODE S1 1 0.56893E-012 2 9.56893E-012 LINK180 S2 0.0000 0.0000 S3 0.0000 0.0000 SINT SEQU 0.56893E-012 0.56893E-012 0.56893E-612 0.56893E-612 ELEMENT = NODE 1 3 2 S1 0.0000 0.0000 LINK180 S2 0.0000 0.0000 S3 -100.00 -100.00 SINT 100.00 100.00 SEQU 100.00 100.00 ELEMENT = NODE 2 4 3 S1 0.0000 0.0000 LINK180 S2 0.0000 0.0000 S3 -100.00 -100.00 SINT 100.00 100.00 SEQU 100.00 100.00 ELEMENT = NODE 1 4 4 S1 0.0000 0.000G LINK180 S2 0.0000 0.0000 S3 SINT SEQU -0.81061E-612 0.81061E-612 0.81061E-012 -0.81061E-012 9.81061E-012 7.81061E-012 ELEMENT = NODE 3 4 5 S1 25.000 25.000 LINK180 S2 0.0000 0.0000 S3 0.0000 0.0000 SINT 25.000 25.000 SEQU 25.000 25.000 ELEMENT NODE 3 5 6 S1 0.0000 0.0000 LINK180 S2 0.0000 0.0000 S3 -103.08 -103.08 SINT 103.08 103.08 SEQU 103.08 103.08 ELEMENT = NODE 4 6 7 S1 0.0000 0.0000 LINK180 S2 0.0000 0.0000 S3 -103.08 -103.08 SINT 103.08 103.08 SEQU 103.08 103.08 ***** POST1 ELEMENT NODAL STRESS LISTING ***** LOAD STEP= 1 TIME= 1.0000 SUBSTEP= 1 LOAD CASE= 0

A PRESOL Command File 6 0.0000 0.0000 -103.08 103.08 103.08 ***** POST1 ELEMENT NODAL STRESS LISTING ***** LOAD STEP= 1 TIME= 1.0000 SUBSTEP= 1 LOAD CASE- 0 THE FOLLOWING X,Y,Z VALUES ARE IN GLOBAL COORDINATES ELEMENT NODE 5 6 8 S1 0.0000 0.0000 LINK180 S2 0.0000 0.0000 S3 -25.000 -25.000 SINT 25.000 25.000 SEQU 25.000 25.000 ELEMENT= 9 NODE S1 0.11954E-012 5 0.11054E-012 LINK180 S2 0.0000 0.0000 S3 0.0000 0.0000 SINT SEQU 0.11654E-012 0.11054E-012 0.11054E-612 0.11054E-612 ELEMENT= NODE 5 7 10 S1 0.0000 0.0000 LINK180 S2 0.0000 0.0000 S3 -100.00 -100.00 SINT 100.00 100.00 SEQU 100.00 100.00 ELEMENT = NODE 6 8 11 S1 0.0000 0.0000 LINK180 S2 0.0000 0.0000 S3 -100.00 -100.00 SINT 100.00 100.00 SEQU 100.00 100.00 ELEMENT = NODE 5 8 12 S1 0.0000 0.0000 LINK180 S2 0.0009 0.0000 S3 SINT SEQU -0.78605E-012 0.78605E-012 0.78605E-012 -0.78605E-012 9.78605E-012 9.78605E-012 ELEMENT = 13 LINK180 NODE S1 S2 S3 SINT SEQU 7 0.0000 0.0000 -200.00 200.00 200.00 8 0.0000 0.0000 -200.00 200.00 200.00 ELEMENT = 14 LINK180 NODE S1 S2 S3 SINT SEQU 7 0.0000 0.0000 -0.19651E-012 0.19651E-012 0.19651E-012 9 0.0000 0.0000 -0.19651E-012 7.19651E-012 7.19651E-012 ***** POST1 ELEMENT NODAL STRESS LISTING ***** LOAD STEP= 1 TIME= 1.0000 SUBSTEP= 1 LOAD CASE= 0 TUE LOI LOI.IIM 9 0 7 IlhIIIE DE TU CIDOT DTT MATEO

PRESOL Command File ***** POST1 ELEMENT NODAL STRESS LISTING ***** LOAD STEP= 1 SUBSTEP= 1 TIME= 1.0000 LOAD CASE= THE FOLLOWING X,Y,Z VALUES ARE IN GLOBAL COORDINATES ELEMENT- 15 NODE S1 8 0.24564E-012 10 0.24564E-012 LINK180 S2 0.0000 0.0000 S3 0.0000 0.0000 SINT SEQU 0.24564E-012 7.24564E-012 0.24564E-612 0.24564E-012 ELEMENT = NODE 9 10 16 S1 200.00 200.00 LINK180 S2 0.0000 0.0000 S3 0.0000 0.0000 SINT 200.00 200.00 SEQU 200.00 200.00 17 ELEMENT NODE S1 0.39302E-012 8 0.39302E-012 LINK180 S2 0.0000 0.0000 9 S3 0.0000 0.0000 SINT SEQU 0.39302E-012 0.39302E-012 0.39302E-612 0.39302E-612 ELEMENT= NODE 7 11 18 S1 0.0000 0.0000 LINK180 S2 0.0000 0.0000 S3 -223.61 -223.61 SINT 223.61 223.61 SEQU 223.61 223.61 LINK180 ELEMENT = NODE 8 12 S2 19 S1 0.0000 0.0000 0.0000 0.0000 S3 -223.61 -223.61 SINT 223.61 223.61 SEQU 223.61 223.61 ELEMENT = NODE 11 13 20 S1 0.0000 0.0000 LINK180 S2 0.0000 0.0000 S3 -223.61 -223.61 SINT 223.61 223.61 SEQU 223.61 223.61 ELEMENT = 21 NODE S1 12 0.0000 14 0.0000 LINK180 S2 0.0000 0.0000 S3 -223.61 -223.61 SINT 223.61 223.61 SEQU 223.61 223.61 ***** POST1 ELEMENT NODAL STRESS LISTING ***** LOAD STEP= 1 SUBSTEP= 1 TIME 1.0000 LOAD CASE= 0 THE FOLLOWING X,Y,Z VALUES ARE IN GLOBAL COORDINATES

I'VUUVY10 n.1.2 LULUחץ Lוח חטטעט וו 1 בחרו 1עונעעע ELEMENT = 22 NODE S1 13 200.00 15 200.00 LINK180 S2 0.0000 0.0000 S3 0.0000 0.0000 SINT 200.00 200.00 SEQU 200.00 200.00 ELEMENT = NODE 15 9 23 S1 200.00 200.00 LINK180 S2 0.0000 0.0000 S3 0.0000 0.0000 SINT 200.00 200.00 SEQU 200.00 200.00 ELEMENT = NODE 10 16 24 S1 200.00 200.00 LINK180 S2 0.0000 0.0000 S3 0.0000 0.0000 SINT 200.00 200.00 SEQU 200.00 200.00 S1 LINK180 S2 0.0000 0.0000 S3 0.0000 0.0000 SINT 200.00 200.00 SEQU 200.00 200.00 ELEMENT = 25 NODE 16 200.00 14 200.00 ELEMENT = 26 NODE S1 0.0000 15 0.0000 11 LINK180 S2 0.0000 0.0000 S3 0.0000 0.0000 SINT 0.0000 0.0000 SEQU 0.0000 0.0000 ELEMENT = 27 NODE 12 0.39302E-012 16 0.39302E-012 S1 LINK180 S2 0.0000 0.0000 S3 0.0000 0.0000 SINT SEQU 0.39302E-612 0.39302E-012 0.39302E-612 0.39302E-912 28 ELEMENT = NODE 11 9 S1 0.0000 0.0000 LINK180 S2 0.0000 0.0000 S3 SINT SEQU -0.17195E-012 0.17195E-012 0.17195E-012 -0.17195E-012 0.17195E-012 0.17195E-012 ***** POST1 ELEMENT NODAL STRESS LISTING ***** LOAD STEP TIME= 1 1.0000 SUBSTEP- 1 LOAD CASE- THE FOLLOWING X,Y,Z VALUES ARE IN GLOBAL COORDINATES ELEMENT = NODE 12 10 29 S1 0.0000 0.0000 LINK180 S2 0.0000 0.0000 S3 SINT SEQU -0.51584E-612 0.51584E-612 0.51584E-012 -0.51584E-612 0.51584E-012 0.51584E-012
note* numburing in element as per below figure.

N 13 22 15 23 9 16 10 24 16 25 20 2 € 28- 29 27 21 ANSYS 2019 R3 ACADEMIC 1 2020 01:06:19 11 14 17 15 12 AUG 18 19 13 10 12 11 5 8 6 5 2 3 1 X 1

for reaction forces go to the Genral porst-> list resulte->reaction sol.

1 E-T-K-N PRRSOL Command ANSYS 13 22 15 16 10 24 16. 25 X File гос Opts PRINT REACTION SOLUTIONS PER NODE amar ***** POST1 TOTAL REACTION SOLUTION LISTING ***** CS LOAD STEP= 1 SUBSTEP= 1 TIME= 1.0000 LOAD CASE= ria THE FOLLOWING X,Y,Z SOLUTIONS ARE IN THE GLOBAL COORDINATE SYSTEM FZ 0.0000 0.0000 NODE FX FY Sumn 1 1000.0 Sumn 2 9.56893E-911 1000.0 rror TOTAL VALUES VALUE 9.56893E-011 2000.0 sting utior Soluti m Da Soly Solu ads le Data 2 3

deflection of tower as per below picture.

NODAL SOLUTION ANSYS 2019 R3 ACADEMIC 9 15 10 16 13 STEP=1 SUB =1 TIME=1 USUM (AVG) RSYS=0 DMX =.012008 SMX =.012008 AUG 1 2020 01:08:25 11 5 3 Y 1 X IN .002669 .005337 .008006 .001334 .004003 .006671 .00934 .010674 .012008