Portal frame lab
2.1 Cantilever:
Plot the load vs. deflection curve using below. From the load deflection curve, the modulus of the linear section can be found as:
Load (N) vs. De.lection (m)
100 90 80 70 60 50 40 30 20
Load (N) vs. De8lection (m)
10 0 0
0.00064 0.00121 0.00176 0.00229 0.00255 0.00289 0.00325 0.00428
!".!"!!".!
Gradient of curve above= !.!!"#!!.!!"#" = Kc = 16472.22 N/m
As the deflection at x of a cantilever under a load at the tip is given as
!
w(x)= !!" × x2 × (3l - x)
the elastic bending rigidity can be found from the deflection at x as
!
EI = ! .x2. (3l - x). Kc
!
= ! × (0.050)2 × ((3× 0.0230) – 0.050) ×16472.22
= 4.3925 Nm2
Using the measured horizontal distance lP and the load applied P during the test, calculate the bending moment M at the root of the cantilever. Plot the calculated moment as a function of deflection at x=50mm using the upper right part of the grid provided in page 4. From the plot, identify a characteristic point where the bending moment can be considered as the full plastic bending moment Mp.
Working:
Bending Moment at the root of the cantilever is calculated using the relationship below:
Moment = Leaver arm length at P × Applied Load (P)
M = lP × P
This was used to obtain values of moments of the beam at different lengths when a force is applied.
Measurement No.
1
2
3
Load
(N)
0
8.9
17.8
26.69
35.59
40.03
44.48
66.72
89
Width (b)
13.02
12.99
12.91
Leaver Arm Leaver (m)
Arm
(mm)
0.23
230
0.229
229
0.228
228
0.228
228
0.227
227
0.227
227
0.226
226
0.225
225
0.209
209
Thickness (d)
2.89
2.89
2.87
Moment (Nm)
0.000
2.038
4.058
6.085
8.079
9.087
10.052
15.012
Plot the load vs. deflection curve using below. From the load deflection curve, the modulus of the linear section can be found as:
Load (N) vs. De.lection (m)
100 90 80 70 60 50 40 30 20
Load (N) vs. De8lection (m)
10 0 0
0.00064 0.00121 0.00176 0.00229 0.00255 0.00289 0.00325 0.00428
!".!"!!".!
Gradient of curve above= !.!!"#!!.!!"#" = Kc = 16472.22 N/m
As the deflection at x of a cantilever under a load at the tip is given as
!
w(x)= !!" × x2 × (3l - x)
the elastic bending rigidity can be found from the deflection at x as
!
EI = ! .x2. (3l - x). Kc
!
= ! × (0.050)2 × ((3× 0.0230) – 0.050) ×16472.22
= 4.3925 Nm2
Using the measured horizontal distance lP and the load applied P during the test, calculate the bending moment M at the root of the cantilever. Plot the calculated moment as a function of deflection at x=50mm using the upper right part of the grid provided in page 4. From the plot, identify a characteristic point where the bending moment can be considered as the full plastic bending moment Mp.
Working:
Bending Moment at the root of the cantilever is calculated using the relationship below:
Moment = Leaver arm length at P × Applied Load (P)
M = lP × P
This was used to obtain values of moments of the beam at different lengths when a force is applied.
Measurement No.
1
2
3
Load
(N)
0
8.9
17.8
26.69
35.59
40.03
44.48
66.72
89
Width (b)
13.02
12.99
12.91
Leaver Arm Leaver (m)
Arm
(mm)
0.23
230
0.229
229
0.228
228
0.228
228
0.227
227
0.227
227
0.226
226
0.225
225
0.209
209
Thickness (d)
2.89
2.89
2.87
Moment (Nm)
0.000
2.038
4.058
6.085
8.079
9.087
10.052
15.012
References: Kumar, P. S. (n.d.). 2.5 Plastic analysis 2.5.1 Basics of plastic analysis. Retrieved DECEMBER 7, 2010, from www.nptel.iitm.ac.in: http://nptel.iitm.ac.in/courses/IITMADRAS/Design_Steel_Structures_II/2_industrial_building/5_plastic_analysis .pdf (Accessed 20/03/2014) Todd, M. S. (2000). Structures: theory and analysis. Hampshire, London, United Kingdom: MACMLLAN PRESS LTD. (Accessed 20/03/2014) 8