NTU, SADBE, Civil Engineering, BEng (Hons) Y1,
Lab experiment
DESN10044 - Introduction to Structural Analysis and Design Light Structures Lab 1: Forces in a plane pin jointed framework (Truss) Object
Experimental verification of the analytical methods for determining the forces in the members of a plane, pin-jointed, triangulated framework.
Apparatus and setup
The Tecquipment Structural Apparatus shown in Figure 1 consists of a model roof truss, symmetrical about the frame centreline, having thirteen steel rod members. The members have strain gauges, bonded to them, which are numbered as shown in Figure 1. When a member stretches or compresses, the strain gauge stretches or compresses the same rate. The Digital Strain Display shows all the members' strains. It reads in microstrain i.e., the displayed strain needs to be multiplied by 10-6 to get the actual strain value. Using the strain, the cross-sectional area, and the Young's modulus of a member, it is possible to convert the strains into member forces.
strain gauge
2
3
117
1
112
1113
30°
8
9
10
11
F
Figure 1 Arrangement of truss and strain gauges.
The load applied to the framework is shown on a Digital Force Display. The framework is mounted into two supports. One support allows pivoting only (pinned), the other support allows pivoting and linear translation (roller) thus representing an idealized simple supported system.
Test procedure
With no load on the load cell, the Digital Force Display shows zero reading (the pin should be turned to roughly zero the reading on the Digital Force Display using the control of the front of the load cell). Apply a pre-load of 20 N by turning the screw thread and again zero the load cell using the control. Take an initial set of strain gauge readings from channels 1- 13 (these represent strains from the numbered strain gauges as shown in Figure 1) on the Digital Strain Display, making sure to note the sign as well as the magnitude. These are the zero load strains. Apply loads in increments of 100 N up to 500 N, taking strain gauge readings at each increment and tabulating these in Table 1. Use a micrometer to measure the diameter of each of the rod members and hence produce an average diameter.
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NTU, SADBE, Civil Engineering, BEng (Hons) Y1,
Lab experiment
Table 1: Unmodified strain readings (ue)
Load
1
2
3
4
5
6
7
8
9
10
11
12
13
ON
100 N
200 N
300 N
400 N
500 N
Results
Determine true member strains by subtracting the zero strain readings from the corresponding column values in Table 1 and enter these in Table 2.
Table 2: True member strains (E)
Load
1
2
3
4
5
6
7
8
9
10
11
12
13
ON
0
0
0
0
0
0
0
0
0
0
0
0
0
100 N
200 N
300 N
400 N
500 N
Produce member strain vs load plots to show change in the strain with respect to the change in load for all thirteen gauges. Read off the strains at a load of 500 N to give improved estimates of the true member strains at this load. Convert the member strains to member loads (in Newtons) as follows:
Young modulus E = Strain(E) Stress(a) or, o = E x 6 , where E is 205 kN/mm2 for steel
but o = Cross sectional area(A) Force(F)
; therefore, F = o x A = Ex EX A :. F = 205- mm2 KN X reading from srain gauge X T (dia.)2 4 mm2
Calculation
Employ either Bow's Method or the Method of Joints to find calculated member forces produced by a load of 500 N.
Discussion and Conclusions
Compare the experimental and calculated values of member forces, giving percentage discrepancies by completing Table 3 (see next page).
Percentage Error or, Discripency =
calculated value lexperinmetal value - calculated value
× 100%
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NTU, SADBE, Civil Engineering, BEng (Hons) Y1,
Lab experiment
Table 3: Experimental and calculated member forces (N) with percentage discrepancies
1
2
3
4
5
6
7
8
9
10 11
12
13
Experiment (N)
Calculation (N)
Discrepancy (%)
· What sources of error are there in the experimental values?
· Do the assumptions built into pin-jointed framework theory apply fully to the experimental truss?
· Why do some of the members carry no load?
· Would it matter if these members were removed from the truss?
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