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I. OBJECTIVES
1.1 To reinforce the student’s skills in finding the forces in truss members using the method of joints.
1.2 To compare the experimentally measured truss forces with the theoretically calculated forces.
1.3 To check linearity of the measured strain versus the applied load
II. INTRODUCTION AND BACKGROUND
Trusses are used extensively in structural engineering applications. Their main advantage is that they can span large distances using a minimum amount of material. The truss that will be investigated in this experiment is a statically determinate planar truss. A planar determinate truss can have only three unknown reaction forces. The forces in the truss members can be obtained by using the method of joints. In this method, each joint of the truss is isolated in a free body diagram and the unknown member forces are determined from equilibrium (ΣΣΣΣFx = 0 and ΣΣΣΣFy = 0). For example, the force Fab in joint “a” could be found as follows:
ΣΣΣΣFY = 0
Fab sin(θθθθ) + 100 = 0 Fab = -100/sin(θθθθ) Fac
Fab
Ray = 100 N
Joint a θθθθ
y
x
a
b
c
d
e
200 N
100 N 100 N
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When using the method of joints, only two unknown member forces can be solved for at a time. The remaining joints of the truss can be isolated and unknown member forces determined.
The most practical way to experimentally determine the force in the truss member is by use of a strain gage. Since a strain gage measures strain, some conversion must be performed to obtain the force in the member.
The measured strain (εεεε) can be converted to stress (σσσσ) by using Hook’s
Law. For the case where the tensile stress is uniformly distributed over the cross sectional area it has the following form:
σσσσ = E εεεε 2.12.12.12.
where E is the modulus of elasticity of the truss member.
Steel, of which the truss members are made, has a modulus of elasticity: E = 210 GN/m 2
Once the stress in the member is determined, it can be converted into force (F) by multiplying the axial stress by the cross sectional area (A):
F = A σσσσ 2.2.2.2.2 222
III. EQUIPMENT
3.1 Structures test frame 3.2 Digital force display 3.3 Truss with strain gages 3.4 Load cell 3.5 Digital strain display 3.6 Calipers 3.7 Two power supplies for the digital force display and the load cell
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4.4 Check the strain value you calculated in section 4.1 with the experimental value to see if your result is reasonable. For the experimental strain, you must remember to subtract the strain measured for the zero Newton load case.
4.5 Unplug and disconnect the power supplies.
V Report
5.1 Convert the strain readings for the five load cases into member forces. Remember to subtract the strain measured in the zero Newton load case from the loaded values.
5.2 Compare in a table, the experimental and calculated member forces for the 500 Newton load case. Show these member forces on a sketch of the truss. Are they symmetric?
5.3 For any two of the truss members, plot the member force measured versus the applied load. Is the relationship linear?
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TRUSS MEMBER
ab GAGE#
bc GAGE#
ac GAGE#
bd GAGE#
cd GAGE#
ce GAGE#
de GAGE#
FORCE N
TABLE 1
CALCULATED TRUSS MEMBER FORCES 100 N LOAD
MEASURED STRAIN DATA
LOAD N (^) ab GAGE#
bc GAGE#
ac GAGE#
bd GAGE#
cd GAGE#
ce GAGE#
de GAGE# 0
100
200
300
400
500
LOAD N ZERO ADJUSTED STRAIN DATA
100
200
300
400
500
TABLE 2
MEASURED AND ZERO ADJUSTED STRAIN
