“Measurement of bending moment and

shear forces for structural analysis”

Azamat Omarov

ID201102658

1.Theory and background

1.1 Summary

That performed laboratory session on bending moments and shear forces requires good understanding and sufficient knowledge of axial forces. Bending is defined as a behavior of any structural element that undergoes the external load, which is applied perpendicularly to longitudinal axis. That experiment helps us to find the maximum load that can be applied to the beam with rectangular cross section. Moments are calculated by using statics theory, or multiplying perpendicularly directed load by the respective distance to the pivot point. 1.2 Objective

The main objective of that laboratory is to provide students with basic experience and thus, the comparison between calculated and measured values (software) should be demonstrated to show the ability to apply statics theory from applied mechanics module. 1.3 Theory

Shear forces

The shearing force at any section of a beam is the algebraic sum of the lateral components of the forces acting on either side of the section. F is the resultant reaction on the left of AA. As the beam is in equilibrium then resultant reaction on the right of AA must be downwards. Figure1. Shear forces diagram

Equilibrium state

∑Fx=0N; ∑Fy=0N; ∑Mo=0N.m (1)

In our case we use AA as a reference point to calculate the bending moment

Bending Moment

Bending Moment at AA is defined as the algebraic sum of the moments about the section of all forces acting on either side of the section. Bending moment is considered to be positive when the total moment on the right of AA is clockwise, whereas moment to the right of AA is anticlockwise. That type of behavior of bending moment is called sagging since it makes the beam to become concave upward. The opposite of sagging is called hogging.

Figure 2. Bending moment (sagging) diagram

2. Experimental apparatus

The provided technical equipment is a very functional device that enables students to perform laboratory sessions for mechanical, civil and structural engineering students. It help students to learn more and create a clear visualization and straightforward proof of the bending moment theory in a beam. Experiments include the ability to place the load at any point on the load line to measure the bending moment. The whole apparatus consists of hardware (device itself) and software (program for determining bending moment)

Software

Software of the STR2 is a program that enables computer to perform various tasks as with loads on the line as by virtual visualization. The computer simulation implies the usage of software without teaching hardware equipment. To put it simply, experiments could be actually conducted without the apparatus.

Figure 3. Bending moment hardware apparatus

Hardware

The high quality bending moment device consist of two parallel beams which have a cut position that acts like a pivot. To accomplish bending moment in a beam experiment students apply loads along the beam. The moment arm bridges the cut onto the laod cell thus calculating the reacting and measuring the bending moment force. Students are then able to see the force resultant on the digital display. Additionally, weighs, weighs hangers as well as student and teacher laboratory manuals are included.

3.Experiment

Figure 4. Loads and reaction forces diagram

In the first part of experiment conducted only one load of 3 available different loads were applied at the distance of 340mm from the left corner of beam (0-P2). Thus, the reaction forces and bending moment at the cut were calculated by using equilibrium state formulas provided in the theory part. Load(grams)| Load(Newtons)| Resistance R1(N)| Resistance R2(N)| Measured moment (N*m)| Calculated moment (N*m)| 100| 0.98| 0.54| 0.45| 0.04| 0.06|

200| 1.8| 1.07|...