Model and solve the problem below in ANSYS and answer the
questions at the bottom of the page.
Use LINK180 (3D SPAR element). It has UX, UY and UZ DOF. No z-motion
is needed; constrain all UZ DOF, i.e., analyze this structure as a 2D system.
Steel trusses are pinned at all joints
E = 30x106 psi
Poisson's ratio = 0.3
density = 0.283 lbm/in3
Cross-section area: 1.0 sq. in.
for all outside members (on the perimeter).
For the four inside members use 0.05 sq. in.
The base is 30 feet long and the center peak is 6 feet above the base
Loads:
500 #, downward at the joints (C & D) on the left and right of center
1000 #, downward at the center peak (E)
Ignore the weight of the assembly
Constraints:
Fixed (UX, UY) at the left end and right end (A & B).
all nodes fixed in UZ to simulate 2D behavior, only.
The mass of the steel assembly: ________________ lbm.
The maximum deflection: ________________ in.
The deflection components at the peak, pin joint "E":
UX = ______ in., UY = ______ in. [Hint: list displacements at nodes]
The highest axial tensile stress : ________________ psi
In which member does the highest tensile stress occur at ?
The highest axial compressive stress : ________________ psi
In which member does the highest compressive stress occur at ?
Would the weight of the structure change the results significantly if it was included ?
TOTAL MASS = 0.55794 ("slinches") [0.55794 * Gc = 215.6 lbm]
The maximum deflection (DMX) is 0.088 in.
Displacement at peak (Node 7)
NODE UX UY
7 0.00 -0.43923E-01
The maximum tensile stress is 9763 psi in the longer, inside members.
The maximum compressive stress is -9763 psi in the shorter, inside members.
Adding the weight of the structure to the analysis would be significant (~10% higher load)
/filnam,rooftruss ! Define the
'jobname'
/title, Roof Truss Example
/prep7 ! Enter PREPROCESSING
et,1,link180 ! 3D spar (truss) elements
r,1,1 ! Larger Cross-sectional area (sq. in.)
r,2,0.05 ! Smaller Cross-sectional area (sq. in.)
mp,ex,1,30e6 ! Young's Modulus (lbf/sq.in.) i.e., Steel
mp,nuxy,1,0.3 ! Poisson's ratio
mp,dens,1,0.283/386.4 ! density/Gc
n,1,0,0 ! Define node locations
n,2,10*12,0
n,3,20*12,0
n,4,30*12,0
n,5,7.5*12,3*12
n,6,22.5*12,3*12
n,7,15*12,6*12
e,1,2 ! Define the elements, thicker cross-section
e,2,3
e,3,4
e,1,5
e,5,7
e,4,6
e,6,7
REAL,2 ! switch to the thinner cross-section
e,5,2 ! Define the elements, thinner cross-section
e,2,7
e,7,3
e,3,6
finish ! Leave PREPROCESSING
/solu ! Enter SOLUTION
antype,static ! Do a static analysis
d,1,ux,0 ! Define constraints (supports) on system
d,1,uy,0
d,4,ux,0
d,4,uy,0
d,all,UZ,0
f,5,fy,-500 ! Define the loads (forces)
f,7,fy,-1000
f,6,fy,-500
solve ! Solve the problem
finish ! Leave SOLUTION
save ! Save the model database on a file.
/post1 ! Enter POSTPROCESSING
ETABLE,force,SMISC, 1 ! Store the axial force for each LINK180
ETABLE,SXX-i,LS, 1 ! Store the direct stress in each LINK180
ETABLE,SXX-j,LS, 2
pretab ! Print the axial force and direct stress data
/pnum,sval,1 ! add numeric contour values to plots
/plopt,minm,0 ! suppress the MIN/MAX labes
pletab,force ! Plot the model with the 'faxl' data included
prdisp ! Print the node displacement solution
pldisp,1 ! Plot the deformed shape (overlay undeformed shape).
plls,SXX-i,SXX-j ! Plot the model with the direct stress data
prrsol ! Print the reaction force solution
finish ! Leave POSTPROCESSING