The OpenSees Community

Hi All,

I do have a Truss Bridge with a concrete deck. I've modeled the deck as shell, then the stringers and floor beams are all fiber sections. This model without Truss itself works perfect and I do get the same modal analysis results with CSI.

Then, the problem starts with adding the Truss members. I do have top and bottom chords, vertical and diagonal members and they have gusset plates almost at every connection i.e. top chord - vertical member connection, bottom chord - diagonal - vertical member connections.

Thus, the first question is how to create this rigid end zone details. If I use Truss elements, just a geomTransf with a rigid offset definition is enough to define the rigid offset due to a gusset plate? If so, I am confused as of the i and j node inputs for the offset. Additionally, in this approach, all RX, RY and RZ for all Truss nodes should be fixed, right?
ops.geomTransf('Linear',1,'-jntOffset',......)

Second problem is that the bottom chords are connected to the floor beams through a gusset plate, so, I need to connect the truss system to the floor beams. Considering this, what should be the best approach to model the Truss members and connect them to the moment resisting system? I see that in some models they use forceBeamColumn and define Moment Releases to model Truss members rather then directly Truss Elements, but it comes with more constraints definitions. Is this the best approach? In this scenario, what about the all constraints and zeroLength member definitions?

I was trying to play with this small example https://opensees.berkeley.edu/wiki/inde ... ss_Example. Herein, let's say I have a gusset plate the top joint where all truss members should have a rigid end zone. I defined three additional nodes, which are 5, 6 and 7. Then, defining rigidbar from 5 to 4, 6 to 4 and 7 to 4 did not work out. Or, defining more nodes to have a zeroLength member and then having rigidBars at the top end did not work too.

Overall, creating gusset plate details, Truss element definitions in terms of the connection details to the frame members got me confused a little bit. I just wanted to try different scenarios on a small example before I try them in a real bridge model. Can you please help me?

Hello All,

I do have a problem with choosing proper element and modeling approach in a bridge model where I connect the girders to each other and to a parapet.

think about that a single-span bridge has two parapets on each side and girders needs to be connected to each other and side girders should be connected to the parapet considering that they're anchored well by rebars based on the plan drawing.

I attached a basic illustration here https://app.gemoo.com/share/image-annot ... lgenerator

Problems;
1. For parapet-to-side girder connection. which element path should be followed if you look at the illustration? Then, a rigidLink seems to be the element to connect them each other, right? In case of using rigidLink, I do not think that I need to define additional constraints between the nodes.

2. For the girder-to-girder connection, the problem is that it's not certain that if there is a fully force transfer mechanism or not between the girders, details are not really known except this detail which is the connection; https://app.gemoo.com/share/image-annot ... lgenerator. There is no a real/clear spacing between the girders in the field. Thus, as an initial assumption, it's assumed to have a shear link, should it be modeled by twoNodeLink or multipleShearSpring? I'd like to be able to decrease or increase the stiffness of this member in order to see the effect of force transfer between the girders. I need to figure out the effect of this detailing, but not sure exactly how to model this.

I'd be happy for any help you could provide, thank you!

I did that example and it worked, then, I went though my code again and found my mistake while defining the coordinates op.('quad',...), thank you for the help.

Unfortunately, it didn't solve the issue, still there is nothing being outputted.

Hello,

Here is the model code for simply-supported Double Tee girder. Before I move forward to full bridge model, I'd like to verify some fundamental things such as eigenvalues, strain-stress and support reactions etc. This is an elastic analysis, that's why I chose to go with elastic uniaxial material. However, in order to monitor the strain-stress response, I use forceBeamColumn. I haven't defined any pre-stressed tendons or rebars, I'd like to see the outputs for just concrete material first.

I create a fiber section, then, I have top flange + two stems = 3 different patch('quad',.......).

Problems;
1. I can obtain support reaction using recorder, but, why I cannot output them using nodeReaction? I can't also see eleForce outputs.
2. Either using recorder or eleResponse, no way to output stress-strain at the bottom of each stem, the .txt files are all empty and stressStrain gives nothing using eleResponse. Can somebody please explain why this is happening? I tried to make them string and I was playing with it but it did not work out. I also tried to use different beam-column element but they did not work out too.
3. Under a -7.56 N/mm uniform loading on each member (assume that I remove point load at node-6), I am also trying to verify the element forces.

The goal is to obtain the strain-stress response at the last integration of element-5 and first integration of element-6 under a point load of 1000 N at node-6. The fiber location could be right stem bottom mid-point, left stem bottom mid-point or flange top mid-point. You can comment uniform loading case not to run it. The number of fibers are defined separately for the stems and the flange nfZ_top, nfY_top = 5, 20, nfZ_bottom, nfY_bottom = 20, 5.

I'd be glad if anybody help me out to figure out what the problem is. Thank you!

CODE:

def GetModel(nn):
ops.wipe()
ops.model('basic', '-ndm', 2, '-ndf', 3)

#Define unit conversion
inch_to_mm = 25.4
ft_to_mm = 304.8
ksi_to_MPa = 6.89476

Area_Tee = 498 * inch_to_mm * inch_to_mm
L_span = 42 * ft_to_mm

#Define nodes
for i in range(nn+1):
if i == 0:
ops.node(i+1, 0.0, 0.0)
else:
ops.node(i+1, (L_span/nn)*i, 0.0)

#Define support conditions
# tag, DX, DY, RZ
ops.fix(1, 1, 1, 0)
ops.fix(11, 0, 1, 0)

#Calculate uniform distributed loading on the beam
gama = 2400 #kg/m^3
g = 9.80665 #N/kg or m/s^2
Wy = round(gama * g * Area_Tee * (math.pow(10, -9)) * -1, 2) # N/mm

#Calculate the mass
ms = round(gama * Area_Tee * L_span * (math.pow(10, -9)), 2) #kg

#Define nodal masses
for i in range(nn+1):
if i == 0:
ops.mass(i+1, (ms / nn) * 0.5, (ms / nn) * 0.5, (ms / nn) * 0.5)
elif i != 0 and i != nn:
ops.mass(i+1, (ms / nn), (ms / nn), (ms / nn))
else:
ops.mass(i+1, (ms / nn) * 0.5, (ms / nn) * 0.5, (ms / nn) * 0.5)

beamSecTag = 1
transfTag = 1
intTag = 1
matTag_concrete = 1

#Define elastic uniaxial material
#uniaxialMaterial('Elastic', matTag, E, eta=0.0, Eneg=E)
fc = 5000 #psi
Ec = 57 * math.sqrt(5000) * ksi_to_MPa
ops.uniaxialMaterial('Elastic', matTag_concrete, Ec)

nfZ_top, nfY_top = 5, 20
nfZ_bottom, nfY_bottom = 20, 5
y_cg, z_cg = round(30 * inch_to_mm, 2), round(6.87 * inch_to_mm, 2)
tf = round(5 * inch_to_mm, 2)
tw = round(18 * inch_to_mm, 2)

#Flange coordinates in CCW
flange_1_y, flange_1_z = (-1 * y_cg), (-1 * z_cg) + tf
flange_2_y, flange_2_z = (-1 * y_cg), (-1 * z_cg)
flange_3_y, flange_3_z = y_cg, (-1 * z_cg)
flange_4_y, flange_4_z = y_cg, (-1 * z_cg) + tf

dist1 = round(8.75 * inch_to_mm, 2)
dist2 = round(dist1 + 1.0 * inch_to_mm, 2)
dist3 = round(dist2 + 4.50 * inch_to_mm, 2)
dist4 = round(dist3 + 1.0 * inch_to_mm, 2)

#Left web coordinates
Lweb_1_y, Lweb_1_z = y_cg - dist3, tf + tw - z_cg
Lweb_2_y, Lweb_2_z = y_cg - dist4, (-1 * z_cg) + tf
Lweb_3_y, Lweb_3_z = y_cg - dist1, (-1 * z_cg) + tf
Lweb_4_y, Lweb_4_z = y_cg - dist2, tf + tw - z_cg

#Right web coordinates
Rweb_1_y, Rweb_1_z = (-1 * y_cg) + dist2, tf + tw - z_cg
Rweb_2_y, Rweb_2_z = (-1 * y_cg) + dist1, (-1 * z_cg) + tf
Rweb_3_y, Rweb_3_z = (-1 * y_cg) + dist4, (-1 * z_cg) + tf
Rweb_4_y, Rweb_4_z = (-1 * y_cg) + dist3, tf + tw - z_cg

#Define strain-stress fiber coordinates
R_fiby, R_fibz = round(Rweb_1_y + (2.25 * inch_to_mm),2), round(tf + tw - z_cg, 2) #Right stem y and z
L_fiby, L_fibz = round(Lweb_4_y - (2.25 * inch_to_mm),2), round(tf + tw - z_cg, 2) #Left stem y and z
U_flay, U_flaz = 0.0, round(-1 * z_cg,2) #Top flange y and z

ops.section('Fiber', beamSecTag)
#patch('quad', matTag, numSubdivIJ, numSubdivJK, *crdsI, *crdsJ, *crdsK, *crdsL)
ops.patch('quad', matTag_concrete, nfZ_top, nfY_top, flange_1_y, flange_1_z, flange_2_y, flange_2_z, flange_3_y, flange_3_z, flange_4_y, flange_4_z)
ops.patch('quad', matTag_concrete, nfZ_bottom, nfY_bottom, Lweb_1_y, Lweb_1_z, Lweb_2_y, Lweb_2_z, Lweb_3_y, Lweb_3_z, Lweb_4_y, Lweb_4_z)
ops.patch('quad', matTag_concrete, nfZ_bottom, nfY_bottom, Rweb_1_y, Rweb_1_z, Rweb_2_y, Rweb_2_z, Rweb_3_y, Rweb_3_z, Rweb_4_y, Rweb_4_z)

ops.geomTransf('Linear', transfTag)
numIntgrPts = 5

#beamIntegration('Lobatto', tag, secTag, N)
ops.beamIntegration('Lobatto', intTag, beamSecTag, numIntgrPts)

#element('forceBeamColumn', eleTag, *eleNodes, transfTag, integrationTag, '-iter', maxIter=10, tol=1e-12, '-mass', mass=0.0)
eleType = 'forceBeamColumn'
for i in range(nn):
ops.element(eleType, i+1, i+1, i+2, transfTag, intTag, "-mass", 0.0)

ops.recorder('Node', '-file', re[0], '-node', 1,11, '-dof',1,2,3, 'reaction')
ops.recorder('Element', '-file', st[0], '-closeOnWrite','-ele', 5, '-section', str(5), 'fiber', str(R_fiby), str(R_fibz), 'stressStrain')
ops.recorder('Element', '-file', st[1], '-closeOnWrite','-ele', 5, '-section', '5', 'fiber', 'L_fiby', 'L_fibz', 'stressStrain')
ops.recorder('Element', '-file', st[2], '-closeOnWrite','-ele', 6, '-section', '1', 'fiber', 'R_fiby', 'R_fibz', 'stressStrain')
ops.recorder('Element', '-file', st[3], '-closeOnWrite','-ele', 6, '-section', '1', 'fiber', 'L_fiby', 'L_fibz', 'stressStrain')
ops.recorder('Element', '-file', st[4], '-closeOnWrite','-ele', 5, '-section', '5', 'fiber', 'U_flay', 'U_flaz', 'stressStrain')
ops.recorder('Element', '-file', st[5], '-closeOnWrite','-ele', 6, '-section', '1', 'fiber', 'U_flay', 'U_flaz', 'stressStrain')
stressStrain = ops.eleResponse(5, "section", 5, '-fiber', str(-457.2), str(409.7), '1', "stressStrain")

R1 = ops.nodeReaction(1, 2)
R2 = ops.nodeReaction(11, 2)
E1 = ops.eleForce(1)
#Define gravity loading
ops.timeSeries('Linear', 1)
ops.pattern('Plain', 1, 1)
#Define uniform distributed loading
#eleLoad('-ele', *eleTags, '-range', eleTag1, eleTag2, '-type', '-beamUniform', Wy, <Wz>, Wx=0.0, '-beamPoint', Py, <Pz>, xL, Px=0.0, '-beamThermal', *tempPts)
for i in range(nn):
ops.eleLoad('-ele', i+1, '-type', '-beamUniform', Wy, 0.0, 0.0)

#Define nodal load
#ops.load(6, 0.0, -1000.0, 0.0)

ops.constraints('Plain') # how it handles boundary conditions
ops.numberer('Plain') # renumber dof's to minimize band-width (optimization), if you want to
ops.system('BandGeneral') # how to store and solve the system of equations in the analysis
ops.test('NormDispIncr', 1.0e-12, 20)
ops.algorithm('Newton') # use Linear algorithm for linear analysis
ops.integrator('LoadControl', 0.1) # determine the next time step for an analysis, # apply gravity in 10 steps
ops.analysis('Static') # define type of analysis static or transient
ops.analyze(10) # perform gravity analysis

# set damping based on first eigen mode
# -fullGenLapack
eigen = ops.eigen('-genBandArpack', 3)
w, f, T = [], [], []
for k in range(len(eigen)):
w.append(math.pow(eigen[k], 0.5))
f.append(w[k] / (2*math.pi))
T.append(1 / f[k])

values_static = {
"eigen" : eigen,
"Omega" : w,
"frequencies" : f,
"period" : T,
"Mass" : ms,
"Distr. load" : Wy,
"Vertical reaction at left support" : R1,
"Vertical reaction at right support" : R2,
"Element-1 forces": E1,
"Element-5 stress and strain": stressStrain,
"Element y coordinates": R_fiby,
"Element z coordinates": R_fibz
}

for key, value in values_static.items():
print(f"{key} : {value}")

ops.wipe()
#tut +=1

return