Individual Beam design
Terence Kennedy
Engr 1201-010
Introduction to Engineering Design & Principles 1
November 6th, 2022
I have neither given nor received any unauthorized help on this assignment,
nor witnessed any violation of the UNC Charlotte Code of Academic Integrity.
Signature: Terence Kennedy November 21st, 2022
Introduction
Provide a specific and measurable problem statement. Document the design and performance
requirements, constraints, and assumptions required for the project.
The purpose of the beam project was to develop an understanding of structural beams and applying the
knowledge of beam theory to create a beam that will support given loads. These are important
components for understanding the beam theory. The use of beam and structural theory can be used to
predict how much a beam will bend in order to maintain its equilibrium along both x and y axis, and to
also calculate the centroid of different shaped beams.
Design Requirements
The final beam selection had to be from one of the three beam shapes. I-Beam, H-Beam, or hollow box.
These beams were to be constructed of basswood and each piece is to be glued together. The overall
area of the cross section cannot exceed 2” by 2” or their length of 18 inches. Beams can also be
assembled by basswoods of various thicknesses if the total price of the selected basswoods does not
exceed the given price limit. They must be symmetrical along the centroid of the cross-sectional.
Beams are also required to follow their given requirements, specifically the deflections across the x and
y axis, weight of the beam and the total cost. The beam could not exceed their maximum deflections
while supporting the loads. In order to ensure that it wouldn’t exceed their deflections, equations from
the beam and structural theories can be used to evaluate many beams that could be used. The final
beam selected must be less then its weight restriction and avoid its maximum deflections once tested
Constrains & Assumptions
The main priorities were to make sure that the beams did not exceed their given deflections and weight
restrictions. The beam was to be assembled using basswood, and there were many sizes of basswood to
choose from. Though there was a vast selection of basswood to choose from, the overall weight of the
basswood had to be under the weight and deflection restrictions. The selection of basswood had to be
selected with the restrictions in mind. The mass of the glue joints was an unnoted restriction, as
choosing basswood that was close to the weight restriction could be risky.
Beam calculations are also made with the assumption that the basswood is completely dry and aligned
exactly at its centroid. External factors that could affect the weight like humidity are not considered. It’s
also assumed that the basswoods are glued precisely. If the pieces are not glued correctly, it can affect
the deflection values once tested.
Background
discussion of the beam theory concepts that were required to accomplish the project. This
section should include a description of the relevant theory or theories and the general equations
Structural theory is a theory that relates to the deformations, stresses, velocities and
accelerations of structures under a load (Obinna, 2022). Structural theory can be applied to a
numerous number of objects to predict how they will react once a load is placed upon them. The
Bernoulli-Euler Beam Theory, a product of structural theory, states that the straight lines
perpendicular to beam axis will remain straight, inextensible and perpendicular to the beam axis
after deformation (J.N Reddy, 2016, 77). A line that is drawn perpendicular to the given axis will
remain perpendicular even after the beam has reacted to a load.
The formula that relates to beam theory can be seen below:
∆=
𝑃𝐿3
48𝐸𝐼
Where P is the load, L is the distance between the supports, E is the modulus of Elasticity and I is
the moment of inertia. (Roylance, 2000, 1).
The Moment of inertia, with respect to mass, can be defined as a measure for a rigid body that is
undergoing rotational motion around a specific axis. (Zimmerman, 2019). Moment of inertia is
used to figure out how mass is distributed across an object in respect to its axis.
The formula that can be used to find the moment of inertia is
𝐼=
𝑏ℎ3
12
Beams come in different cross sectional shapes, and for the three that are provided, the moment
of inertia can be found by subtracting the space that doesn’t contribute to the moment of inertia.
References
1. O. A. Bauchau, J. I. Craig. 2009. Euler-Bernoulli beam theory
2. Ubani Obinna. May 10th, 2022. Introduction to Theory of Structures | Structural
Analysis
3. J.N Reddy. October 19th, 2016. 2.5 Theories of Straight Beams
4. David Roylance. November 30th, 2000. Beam Displacements.
5. Andrew Zimmerman. April 20th, 2019. What is Moment of Inertia in Physics?
6. Engineering ToolBox, (2008). Area Moment of Inertia - Typical Cross Sections I.