Help with Strength of Materials question

In summary, The conversation discusses finding the deflection at a specific point on a beam and the methods that can be used to solve it. The beam has a downward point load and a moment at specific distances from the left end. The two main approaches to solving this problem are the geometric and energetic methods, which include double integration, superposition, moment-area, conjugate beam, virtual work, and Castigliano's Theorem. It is suggested that the student pick one method and start working on it.
  • #1
kamikazi929
5
0
if anyone could provide any insight as to how i go about completing this question i would be grateful, i was off the week this was taught to the group and have no idea whatsoever
 

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  • #2
Well one is to find the deflection at 3m from the left end of a 6 m beam, which is therefore the midpoint.

There is a downward point load of 85 kN at 2 m from the left end and moment of 100 kN-m at 4 from the left end.

Do you know the convention on moment? The 100 kN-m moment will raise the portion of the beam on the left side, will lowering the portion of the beam on the right side, of the moment.

Do you have examples from your textbook?
 
  • #3
What methods do you know? Geometric and/or energetic?
 
  • #4
thats the thing, i had a berievement in the family and I was off college for a good time, just managing to catch up but this is in my way. missed the whole section on deflections
 
  • #5
I'll name a few:

Geometric Approach:

Double Integration
Superposition
Moment-Area
Conjugate Beam

Energetic:

Virtual Work
Castigliano's Theorem

any of them is in your course syllabus?

Usually a regular Mechanics of Material course will cover the three first geometric methods. An advanced course may include also Castigliano's Theorem.
 
  • #6
Moment-Area and Double Integration sounds familiar
 
  • #7
If its Double Integration, you will simply need to work with the differential equation:

[tex] \frac{d^{2} \nu}{dx^{2}} = \frac{M}{EI} [/tex]

Moment-Area has two theorems, you'll need to work out.

why don't you pick one and start?
 
  • #8
ill give it a bash now see what i come up with
 
  • #9
totally hit a brick wall with this one :(
 
  • #10
kamikazi929 said:
totally hit a brick wall with this one :(

Why don't you show us what you did, so we can actually help?
 

1. What is Strength of Materials?

Strength of Materials is a branch of mechanics that deals with the behavior of solid materials under various stresses and strains. It involves the study of how materials withstand and respond to applied forces, and how their internal structures and properties affect their overall strength and durability.

2. Why is Strength of Materials important?

Strength of Materials is important because it helps engineers and designers determine the appropriate materials and dimensions for a given structure or component. It also helps in predicting and preventing potential failures or deformations of materials, ensuring the safety and reliability of structures and machines.

3. What are the different types of stress and strain in Strength of Materials?

The three main types of stress in Strength of Materials are tensile stress (stretching), compressive stress (squeezing), and shear stress (sliding). Strain refers to the change in shape or size of a material caused by these stresses, and can be classified as linear, shear, or volumetric strain.

4. How do you calculate stress and strain in Strength of Materials?

The formula for stress is force over cross-sectional area (σ = F/A), where force is the applied load and cross-sectional area is the area perpendicular to the direction of the force. Strain is calculated by dividing the change in length or size of a material by its original length or size (ε = ΔL/L or ε = ΔV/V).

5. What are some common applications of Strength of Materials?

Strength of Materials is applied in a wide range of fields, including civil engineering, mechanical engineering, aerospace engineering, and material science. It is used in the design and construction of buildings, bridges, vehicles, aircraft, and other structures and machines that require strength and durability. It is also used in product development and quality control to ensure the safety and reliability of consumer products.

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