V. 2D Tapered Beam In-Plane Stress

To find element stress due to joint load at the fixed end of a tapered plate with one end fixed.

Reference

Crandall, S.H., & Dahl, N.C., An Introduction to the Mechanics of Solids, McGraw – Hill, Inc., 1959.

Problem

The tapered plate structure is loaded at the free end. Calculate the maximum stress at the midspan.

 E = 30,000.0 ksi

 Thickness = 2 in

 Poisson’s ratio = 0.2

 P = 4 kips

Comparison

The STAAD.Pro result is taken as average of stress in elements 9 and 11 at node 16 = 0.5(8,333.35 + 8,359.62) = 8,346.5.

Table 1. Comparison of results
Result Type Theory STAAD.Pro Difference
Maximum stress at the center (psi) 8,333 8,346.5 0.2%

STAAD Input

Tip: You can copy and paste this content directly into a .std file to run in STAAD.Pro.

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\04 Plates Shells\2D Tapered Beam In-Plane Stress.STD is typically installed with the program.

``````STAAD SPACE :A TAPERED BEAM WITH PLATE ELEMENTS
START JOB INFORMATION
ENGINEER DATE 14-Sep-18
END JOB INFORMATION
*
*  REFERENCE: CRANDALL, S. H., AND DAHL, N.C., "AN INTRODUCTION TO THE
*             MECHANICS OF SOLIDS," MCGRAW-HILL BOOK CO., INC.,
*             NEW YORK, 1978
*
INPUT WIDTH 79
UNIT INCHES POUND
JOINT COORDINATES
1 50 0 0; 2 50 -4.5 0; 3 50 -9 0; 4 45 0 0; 5 45 -4.2 0; 6 45 -8.4 0; 7 40 0 0;
8 40 -3.9 0; 9 40 -7.8 0; 10 35 0 0; 11 35 -3.6 0; 12 35 -7.2 0; 13 30 0 0;
14 30 -3.3 0; 15 30 -6.6 0; 16 25 0 0; 17 25 -3 0; 18 25 -6 0; 19 20 0 0;
20 20 -2.7 0; 21 20 -5.4 0; 22 15 0 0; 23 15 -2.4 0; 24 15 -4.8 0; 25 10 0 0;
26 10 -2.1 0; 27 10 -4.2 0; 28 5 0 0; 29 5 -1.8 0; 30 5 -3.6 0; 31 0 0 0;
32 0 -1.5 0; 33 0 -3 0;
ELEMENT INCIDENCES SHELL
1 4 5 2 1; 2 5 6 3 2; 3 7 8 5 4; 4 8 9 6 5; 5 10 11 8 7; 6 11 12 9 8;
7 13 14 11 10; 8 14 15 12 11; 9 16 17 14 13; 10 17 18 15 14; 11 19 20 17 16;
12 20 21 18 17; 13 22 23 20 19; 14 23 24 21 20; 15 25 26 23 22; 16 26 27 24 23;
17 28 29 26 25; 18 29 30 27 26; 19 31 32 29 28; 20 32 33 30 29;
ELEMENT PROPERTY
1 TO 20 THICKNESS 2
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 3e+07
POISSON 0.2
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 ALL
SUPPORTS
1 TO 3 FIXED
LOAD 1 POINT LOAD
JOINT LOAD
31 FY -4000
PERFORM ANALYSIS
PRINT ELEMENT JOINT STRESSES LIST 9 11
FINISH
``````

STAAD Output

```   ELEMENT STRESSES    FORCE,LENGTH UNITS= POUN INCH
----------------
STRESS = FORCE/UNIT WIDTH/THICK, MOMENT = FORCE-LENGTH/UNIT WIDTH
ELEMENT  LOAD       SQX        SQY          MX          MY          MXY
VONT       VONB         SX          SY          SXY
TRESCAT    TRESCAB
9      1         0.00        0.00        0.00        0.00        0.00
4157.59     4157.59       -4.32     4153.58      -71.59
4160.36     4160.36
TOP : SMAX=    4154.81 SMIN=      -5.55 TMAX=    2080.18 ANGLE=-89.0
BOTT: SMAX=    4154.81 SMIN=      -5.55 TMAX=    2080.18 ANGLE=-89.0
JOINT         0.00        0.00        0.00        0.00        0.00
16       8372.99     8372.99      -78.55     8333.17       38.19
TOP : SMAX=    8333.35 SMIN=     -78.72 TMAX=    4206.03 ANGLE= 89.7
BOTT: SMAX=    8333.35 SMIN=     -78.72 TMAX=    4206.03 ANGLE= 89.7
JOINT         0.00        0.00        0.00        0.00        0.00
17        343.34      343.34       42.49        3.59     -196.82
TOP : SMAX=     220.82 SMIN=    -174.74 TMAX=     197.78 ANGLE=-42.2
BOTT: SMAX=     220.82 SMIN=    -174.74 TMAX=     197.78 ANGLE=-42.2
JOINT         0.00        0.00        0.00        0.00        0.00
14        295.01      295.01     -107.35      -73.48     -161.24
TOP : SMAX=      71.72 SMIN=    -252.54 TMAX=     162.13 ANGLE=-48.0
BOTT: SMAX=      71.72 SMIN=    -252.54 TMAX=     162.13 ANGLE=-48.0
JOINT         0.00        0.00        0.00        0.00        0.00
13       8295.66     8295.66       93.65     8341.38       62.12
TOP : SMAX=    8341.85 SMIN=      93.18 TMAX=    4124.34 ANGLE= 89.6
BOTT: SMAX=    8341.85 SMIN=      93.18 TMAX=    4124.34 ANGLE= 89.6
11      1         0.00        0.00        0.00        0.00        0.00
4155.63     4155.63       -4.64     4149.10     -107.91
4159.35     4159.35
TOP : SMAX=    4151.91 SMIN=      -7.44 TMAX=    2079.67 ANGLE=-88.5
BOTT: SMAX=    4151.91 SMIN=      -7.44 TMAX=    2079.67 ANGLE=-88.5
JOINT         0.00        0.00        0.00        0.00        0.00
19       8323.84     8323.84      -72.93     8286.88       37.52
TOP : SMAX=    8287.05 SMIN=     -73.10 TMAX=    4180.08 ANGLE= 89.7
BOTT: SMAX=    8287.05 SMIN=     -73.10 TMAX=    4180.08 ANGLE= 89.7
JOINT         0.00        0.00        0.00        0.00        0.00
20        410.28      410.28       69.05      -21.19     -232.13
TOP : SMAX=     260.40 SMIN=    -212.54 TMAX=     236.47 ANGLE=-39.5
BOTT: SMAX=     260.40 SMIN=    -212.54 TMAX=     236.47 ANGLE=-39.5
JOINT         0.00        0.00        0.00        0.00        0.00
17        377.42      377.42     -132.29      -39.10     -207.04
TOP : SMAX=     126.52 SMIN=    -297.91 TMAX=     212.21 ANGLE=-51.3
BOTT: SMAX=     126.52 SMIN=    -297.91 TMAX=     212.21 ANGLE=-51.3
JOINT         0.00        0.00        0.00        0.00        0.00
16       8319.08     8319.08       82.05     8359.26       54.91
TOP : SMAX=    8359.62 SMIN=      81.68 TMAX=    4138.97 ANGLE= 89.6
BOTT: SMAX=    8359.62 SMIN=      81.68 TMAX=    4138.97 ANGLE= 89.6
:A TAPERED BEAM WITH PLATE ELEMENTS                      -- PAGE NO.    4
**** MAXIMUM STRESSES AMONG SELECTED PLATES AND CASES ****
MAXIMUM       MINIMUM       MAXIMUM       MAXIMUM       MAXIMUM
PRINCIPAL     PRINCIPAL       SHEAR       VONMISES       TRESCA
STRESS        STRESS        STRESS        STRESS        STRESS
8.359622E+03 -2.979081E+02  4.206035E+03  4.157588E+03  4.160359E+03
PLATE NO.      11            11             9             9             9
CASE  NO.       1             1             1             1             1
```