Practical Report

Gunt Lab 3 Practical Report: Beam Introduction: A beam is subjected to two sets of external forces. These are the loads applied to the beam and reactions to the loads from the supports. The beam then transfers the external load set to the external reaction set by a system of internal forces. There are two types of internal force acting within the beam – bending moments and shear forces. The behaviour of any beam is characterised by the magnitude and distribution of these forces. At any point in the beam, the internal shear force and the internal bending moment can be represented as pairs of forces. These forces vary along the beam length and can often be represented diagrammatically as shown in the figure below.

Figure 1: Forces acting upon a beam

 

Aim: To determine the internal actions of the beam through experimental investigation, as well as to compare results by calculation using free body diagram analysis. Method:

1)The experiment is set up as shown in Figure 2. 2)The supports were positioned 800m apart on the lower frame cross member. The bending moment of the beam is centered on the supports, and aligned with adjusting screws (1). 3)The load-cell readings were observed and the values recorded. 4)Steps 1 and 2 are repeated, with 20N loads positioned using a load hangar, 200mm from the left and right support. 5)The load-cell readings were again observed and the values recorded.

Figure 2: Experiment setup

Results and Discussion: 1) Table of results Experimental Readings With loads

Shear Force, 𝑆!"# (N)

Bending moment (N)

1

39

100mm

As illustrated in the diagram above, bending moment force 𝑀!"# = 39  ×100 = 3900𝑁𝑚𝑚 Note: Force of 𝑀!"#    is only in magnitude, as direction of the force is irrelevant due to sagging in experiment. Thus, resultant bending moment force is positive.

2) Free body diagram:

3) Calculations: ΣF! = 0

𝑭𝒐𝒓  𝟎 ≤ 𝒙 < 𝟐𝟎𝟎  

ΣF! = 0  ;   𝑉! − 20𝑁 − 20𝑁 + 𝑉!   = 0 𝑉! + 𝑉!   = 40𝑁                – 𝑒𝑞𝑛  1 ΣM! = 0  ;   −20 200 −  20 600 + 800 𝑉! = 0   −4000 − 12000 + 800 𝑉! = 0   800 𝑉! = 16000   𝑉! = 20𝑁

ΣF! = 0  ;   𝑉! −   𝑉! = 0   20𝑁 −   𝑉! = 0     𝑉!   = 20𝑁

From 𝑒𝑞𝑛  1, 𝑉! + 20𝑁 = 40𝑁   𝑉! = 20𝑁

 ΣM! = 0  ; M! − 20𝑥 = 0   M! = 20𝑥

 

 

𝑭𝒐𝒓  𝟐𝟎𝟎 ≤ 𝒙 < 𝟔𝟎𝟎

ΣF! = 0  ;   𝑉! −   𝑉! − 20 = 0   20 −   𝑉! − 20 = 0     𝑉!   = 0𝑁 ΣF! = 0  ;   𝑉! −  20 − 𝑉! = 0   20 − 20 −   𝑉! = 0     𝑉!   = 0𝑁 ΣM! = 0  ; M! + 20(𝑥 − 200) − 20𝑥 = 0 M! + 20𝑥 − 4000 − 20𝑥 = 0   M! = 400

𝑭𝒐𝒓  𝟔𝟎𝟎 ≤ 𝒙 < 𝟖𝟎𝟎

ΣF! = 0  ;   𝑉! −   𝑉! − 20 − 20 = 0   20 −   𝑉! − 20 − 20 = 0     𝑉!   = −20𝑁     ΣM! = 0  ; M! + 20(𝑥 − 600) + 20(𝑥 − 200) − 20𝑥 = 0 M! + 20𝑥 − 1200 + 20𝑥 − 4000 − 20𝑥 = 0   M! + 20𝑥 − 16000 = 0   M! = 16000 − 20𝑥

𝑥

𝑉!  (𝑁)

𝑀!  (𝑁)

0

20

0

200 400 600

0 0 -20

4000 4000 4000

800

-20

0

Shear Force Diagram:

Bending Moment Diagram:

4) Calculations (at the joint): 𝐹𝑜𝑟  𝑥 = 280𝑚𝑚, 𝑉! =0N, 𝑀! = 4000𝑁 Thus, Shear Force = 0N and Bending Moment = 4000N 5) Comparison of results and values The values of shear force and bending moment at the joint listed in part 3 were equivalent to the values on the profiles calculated in part 2. Thus, it can be surmised that the diagrams in part 2 can be used to find the shear force and bending moment at any point of the beam. The discrepancies between the experimental and calculated values of S and M could be a result of a series of random errors that took place during the experiment. One of which could be due to the misalignment of the beam or failure to align the beam linearly, thus affecting the resulting in an inaccuracy in experimental values.

Conclusion: In summary, the experiment calculated the shear force and bending moment force of the beam, and confirmed the results were reasonable using free body diagram analysis and calculation. The shear force and bending moment diagrams drawn proved to be accurate in locating subsequent shear and bending moment forces at other given points along the beam. This can be extremely useful when analyzing bending in beams, especially in larger scale constructions as compared to manual testing of each individual beam. This is essential to ensure stability in structural beams during construction, as well as to increase efficiency to construction rate at sites.