Practical Report: Forces in a Simple Cantilever Truss - ENGR2741

This practical report analyzes the forces within a simple cantilever truss, a fundamental concept in structural engineering. The report begins with an introduction to trusses and their importance, followed by theoretical calculations of internal forces in the truss members (AB, AC, and AD) for varying applied loads. The solution then presents experimental results, including strain measurements and calculated stresses and forces for each member. The experimental results are compared to the theoretical predictions. Further analysis includes discussing the nature of the forces (tension or compression) based on the experimental data and graphical comparisons of theoretical and experimental member forces against the applied load. The report concludes with a comparison of theoretical and experimental results, providing a discussion of experimental error and the overall success of the experiment, referencing the applied apparatus, Newtonian mechanics, and the close agreement of the measured and predicted values within the experimental errors.

PIN JOINTED FRAMEWORKS: FORCES IN A SIMPLE CANTILEVER TRUSS
INTRODUCTION
A truss would compose of at least three members that would be connected by a pin joint
configuration of triangular shape (Knippers and Speck, 2012). Many structures would be made
up of trusses; this would include buildings and bridges. Truss is one of the fundamental elements
used in engineering structural design and therefore students are expected to gather detail
understanding on how they are analyzed. Analysis of trusses may be done using simple
mechanics of Newton. Inclusion of topics of trusses in the syllabus of statics and physics would
provide an opportunity of illustrating a given interest to students while in class (Mejia et al.,
2013). The apparatus provided would make it possible to measure experimental forces in each
truss member. The applied apparatus are easy to be used and suitable to demonstrate how the
member forces would be determined either in laboratory or classroom.
The theoretical truss theory would allow to approaches to be used in determining the truss
members which includes;
 Joint methods: Considers individual joints free body diagram
 Section methods: Considers truss portion’s free body diagram
The joint method normally would be used to picture out the member’s action, to show whether
they are in tension or compression and determine their effect change (Krenk and Høgsberg,
2013) .
Results
Part 1: Theoretical calculations of internal forces in a simple truss.
Free body diagram truss
Cy
Cx
Bx D
W

Consider joint D
AC
AD 200
∑ F y=0
FAC*sin450 – 200 = 0
FAC = 282.8414 N
∑ F x=0
-FAD - FAC*cos450 = 0
-FAD = 282.8414 * cos450
FAD = - 200 N
Taking joint B
FAB
Bx FAD
∑ F y=0
FAB = 0 N
Table 1 showing other loads results calculations from 0 N to 500 N
W (Applied load) (N) FAB FAC FAD
0 0 0 0
100 0 141.4207 -100
200 0 282.8414 -200
300 0 424.2621 -300
400 0 565.6828 -400
500 0 707.1036 -500

Part 2: Experimental strain results and calculating stresses and internal forces.
Member AB
For 200 N load
ε AB=−2∗10−6
σ AB=210∗109∗−2∗1 0−6 =−420∗103
1000000 ¿ 0.42 MPa
FAB = -0.42 *106 *
π
4 ∗( 62 )
106
= -11.875 N
Member AC
For 200 N load
ε AB=48∗1 0−6
σ AB= 210∗109∗−2∗10−6
1000000 =¿ ¿ 10.08 MPa
FAB = 10.08 *106 *
π
4 ∗( 62 )
106
= 285.0422 N
Member AC
For 200 N load
ε AB=−34∗1 0−6
σ AB= 210∗109∗−34∗10−6
1000000 =¿ ¿−7.14 MPa
FAB = -7.14 *106 *
π
4 ∗( 62 )
106
= -201.905 N

Table 2 showing other loads experimental results from 0 N to 500 N
LOAD
(N)
AB AC AD
load strain stress Force strain stress Force strain stress Force
0 0 0 0 0 0 0 0 0 0
100 -1 -0.21 -5.93838 24 5.04 142.5211 -18 -3.78 -106.891
200 -2 -0.42 -11.8768 48 10.08 285.0422 -34 -7.14 -201.905
300 -2 -0.42 -11.8768 72 15.12 427.5634 -51
-
10.71 -302.857
400 -5 -1.05 -29.6919 96 20.16 570.0845 -67
-
14.07 -397.871
500 -7 -1.47 -41.5687 120 25.2 712.6056 -84
-
17.64 -498.824
Part 3: Further analysis.
Part 3(a)
From the experimental results of force of member AB the magnitude of the determined forces
are negative and its pointing away from the joints therefore, the forces would be compressive
(Beghini et al., 2014).

Part 3(b)
Graph of theoretical and experimental member force against load, W
0 100 200 300 400 500 600
-600
-400
-200
0
200
400
600
800
THEORETICAL FAB
THEORETICAL FAC
THEORETICAL FAD
EXPERIMENTAL AB
EXPERIMENTAL AC
EXPERIMENTAL AD
LOAD (N)
THEORETICAL/EXPERIMENTAL MEMBERS
FORCE
Conclusions
In conclusion, the experiment system provides a direct structural experimental test. The
experiment relies on the shared truss of three members. The truss is considered as a special
structure of major engineering interest that is easily recognized by students that studies physics
or engineering. Within the experimental errors the measurements of results using the device will
be in agreement or acceptance with the Newtonian based calculations of mechanics. The
difference between measured values and predicted values would be less than 3%.

References
Beghini, L.L., Carrion, J., Beghini, A., Mazurek, A. and Baker, W.F., 2014. Structural
optimization using graphic statics. Structural and Multidisciplinary optimization, 49(3), pp.351-
366.
Knippers, J. and Speck, T., 2012. Design and construction principles in nature and
architecture. Bioinspiration & biomimetics, 7(1), p.015002.
Krenk, S. and Høgsberg, J., 2013. Truss Structures. In Statics and Mechanics of Structures (pp.
39-89). Springer, Dordrecht.
Mejia, J.A., Goodridge, W. and Green, C., 2013, October. Enhancing engineering mechanics
statics instruction using manipulative truss models. In 2013 IEEE Frontiers in Education
Conference (FIE) (pp. 369-371). IEEE.