Structural Mechanics Lecture 2

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Questions and Answers

What occurs when two opposing forces are not offset and push into each other at the same point?

Bending moment

Shear stress

Tensile stress

Compressive stress (correct)

Which type of failure occurs when two parts of a structural member are pushed in different directions?

Tension failure

Compression failure

Shear failure (correct)

Bending failure

What defines the relationship between stress and strain up to the yield point in a material?

Shear force

Modulus of Elasticity (correct)

Residual deformation

Compressive strength

When an element is unloaded after reaching the yield point, what is observed?

Residual deformation Signup and view all the answers

What is the formula for calculating stress in an element?

Internal force divided by cross-sectional area Signup and view all the answers

How are internal forces represented within a structure?

Axial, shear, and bending moment diagrams Signup and view all the answers

What is indicated when the stress reaches the maximum value in a structural element?

Maximum strength of the element is reached Signup and view all the answers

What characterizes the deformation of an element due to normal stress?

Deformation is measured as the integral of elongation over length Signup and view all the answers

What is the moment of a force about a point defined as?

The force times the distance from the line of action to the point Signup and view all the answers

Under what condition can equilibrium of moments be achieved?

When the sum of the moments at a point is zero Signup and view all the answers

Which best describes co-planar forces?

Forces that act in the same plane Signup and view all the answers

What happens to rotation if all forces are co-planar and concurrent?

Rotation cannot occur Signup and view all the answers

How can different forces be combined graphically?

By vector addition Signup and view all the answers

What type of forces are characterized as acting perpendicular to the cross section of an element?

Normal forces Signup and view all the answers

What is the typical sign convention for compression in elements?

-ve sign Signup and view all the answers

What do shear forces act along?

The surface or tangent to the surface Signup and view all the answers

Which of the following best describes structural serviceability?

Limiting deflection and excessive vibration under normal loading Signup and view all the answers

What is the relationship between weight, mass, and acceleration due to gravity?

Weight = Mass x Acceleration Signup and view all the answers

Which of the following factors does NOT typically shape an engineer's choice of design and materials?

Building social networks Signup and view all the answers

What is meant by 'statics' in the context of structural engineering?

The study of bodies at rest and not in motion Signup and view all the answers

Which of the following is an important consideration when analyzing structures under loads?

Understanding the loads acting on a structure Signup and view all the answers

Which of these is NOT one of the basic definitions related to forces in engineering?

Weight as the push against an object Signup and view all the answers

In structural analysis, the correct process following the understanding of loads involves?

Interpreting the analysis results and choosing materials Signup and view all the answers

What is typically used to represent the direction of a force?

Arrows Signup and view all the answers

What is considered a permanent load that a structure needs to resist?

Weight of the structure Signup and view all the answers

Which of the following best describes a structure?

An assortment of elements that transfer loads Signup and view all the answers

Which of the following is an example of a dynamic load?

Wind gusts Signup and view all the answers

What is the purpose of drawing a Free Body Diagram?

To visualize the forces acting on a structure Signup and view all the answers

What factor differentiates live loads from static loads?

Static loads do not vary with time Signup and view all the answers

Which of the following is NOT typically an environmental action load?

Weight of building materials Signup and view all the answers

When engineers design structures, what is a key performance objective they must consider?

Functionality for specific use Signup and view all the answers

What type of force is a bending moment associated with?

Moment forces Signup and view all the answers

What must be true for a body to be in static equilibrium?

The sum of all applied forces must equal zero. Signup and view all the answers

In a 2-dimensional system, which equations represent the conditions for equilibrium?

ΣFx = 0, ΣFy = 0, ΣMz = 0 Signup and view all the answers

What does the equation F = m∙a signify in the context of forces?

Force depends on the product of mass and acceleration. Signup and view all the answers

Which statement correctly defines a moment in this context?

A moment is measured at a point and is related to the force applied and its distance from that point. Signup and view all the answers

Which of the following best describes a statically determinate structure?

It can be analyzed using equations of equilibrium alone. Signup and view all the answers

What effect does self-weight have on a structure in static equilibrium?

It contributes to the overall forces that must be balanced. Signup and view all the answers

What happens to the sum of moments around a centroid in a body at rest?

The sum of moments must be zero. Signup and view all the answers

Which of the following represents a force causing displacement along the x direction?

A lateral wind load pushing against the structure. Signup and view all the answers

Study Notes

Structural Mechanics - Supplementary Lecture Notes (Lecture 2)

Key Concepts Covered:
- Understanding and applying Newton's laws
- Understanding and applying equilibrium conditions
- Drawing free body diagrams
- Familiarity with normal forces, shear forces, and bending moment
- Understanding stress and strain under normal loads
Suggested Reading:
- Structural Mechanics by Ray Hulse & Jack Cain - Chapter 1

What is a Structure?

A structure is a collection of connected elements that transfer loads from one point to another. It's not simply a collection of separate elements.
Examples include Tower Bridge, office buildings, Wembley Stadium, and biological structures like elephants and humans.

What Loads Do Structures Resist?

Structures must resist their own weight, which is a permanent load.
They also need to resist "live loads," which are temporary or variable loads caused by things like people, machinery, and vehicles.
Other variable loads are environmental, such as wind, snow, water, waves, earthquakes, tsunamis, cyclones, flooding, and volcanic ash.

Performance Objectives for Structures

Every structure has a specific function, such as residential, commercial, or industrial.
Structures must meet two key performance objectives:
- Serviceability: The structure must function as intended under normal and frequent loads, meaning it should not deflect excessively or vibrate excessively.
- Safety: The structure must withstand extreme loads without collapsing.

Static Equilibrium

Statics is the study of bodies that are not moving.
Static equilibrium is governed by Newton's Laws.
- A body remains at rest or in uniform motion unless acted upon by a force.
- The force acting on a body is proportional to the rate of change of its momentum (impulse).
- For every action, there is an equal and opposite reaction.

Moments

A moment is a force multiplied by the perpendicular distance from the point of application of the force to a specified point.
Equilibrium of moments can be achieved when the sum of moments at a point is zero.

Forces

Forces can be combined graphically using vector addition and trigonometry.
Forces can be resolved into x and y components.

External Forces

External forces act on the boundary of a structure.
- They include externally applied forces and forces applied by supports (reactions).
External forces are categorized as normal forces, shear forces, or bending moments, based on their direction relative to the structure's cross-section.

Internal Forces

Internal forces occur within a structure at a cut section.
These forces are equal and opposite internally.
Internal forces (normal, shear, and bending moment) create stresses and strains within the structure.

Stresses and Strains

Stress is force divided by area.
Strain is the change in length divided by the original length.
Stress-strain diagrams illustrate the relationship between the two.
The stress-strain diagram includes elastic and plastic regions. A material behaves elastically until it reaches its yield point; after that, the material undergoes plastic deformation with a maximum strength value called the ultimate point, followed by failure.

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Description

Test your knowledge on key concepts of structural mechanics introduced in Lecture 2. Explore topics such as Newton's laws, equilibrium conditions, and free body diagrams. Assess your understanding of loads and stress in structures through various examples.