Mechanics and Materials Quiz 4 Concepts
A positive internal bending moment M causes a beam element to ___.
Bend concave upward.
A ___ beam provides reactions in the horizontal and vertical directions, as well as a reaction moment.
Cantilever
A negative internal bending moment M causes ___.
Compression bending stresses below the neutral axis, and tension bending stresses above the neutral axis.
Moment diagrams are ___ at locations where external concentrated moments are applied.
Discontinuous.
Transverse loads cause an initially straight beam to deform into a curved shape called a _______.
Elastic curve
A W18 X 55 beam is heavier than a W14 X 68 beam.
False
A negative internal bending moment bends the beam slice into a smile.
False
A positive internal bending moment bends the beam slice into a frown.
False
A transverse load is a load that acts parallel to the longitudinal axis of the member its acting on.
False
As the distance from the neutral axis decreases, the normal stress increases.
False
As the distance from the neutral surface increases, the normal stress decreases.
False
For most engineering materials, the stress-strain diagrams for both tension and compression are identical in the inelastic range.
False
For pure bending of an inelastic material, the neutral surface will pass through the centroid of the cross-sectional area.
False
For pure bending, the neutral axis cannot pass through the centroid of the cross-sectional area.
False
For wide flange beams, Ix values are smaller than Iy values.
False
If the fibers on one side of the neutral surface are compressed, the fibers on the opposite side will also be compressed.
False
If the load on a beam is small, then the beam deflection will be small. The radius of curvature will then be very small, and the curvature will be very large.
False
Moments of inertia have dimensions of length raised to the third power.
False
Nonuniform bending refers to flexure where the shear force V is equal to zero.
False
Pure bending refers to the stretching of a beam in response to constant torque.
False
The equilibrium surface is the surface that exists between the upper and lower surfaces of a beam where the beam fibers neither shorten nor elongate.
False
The intensity of the bending stress σx varies exponentially with distance y from the neutral surface.
False
The shear- force diagram can be obtained by integrating the bending moment diagram.
False
The smallest bending stress in any beam will occur at either the top or the bottom surface of the beam.
False
Transverse loads applied to a beam cause it to compress.
False
Transverse loads applied to a beam cause it to twist.
False
When subjected to pure bending, an initially straight beam deforms into the shape of an elliptical arc.
False
When the curvature is large, the radius of curvature will also be large.
False
When the curvature is small, the radius of curvature will also be small.
False
Which of the following supports generates a moment reaction?
Fixed
Which equation correctly represents the section modulus S of a doubly symmetric cross section?
Iz/c
If the shear force in a portion of a beam is constant and positive, the bending moment in this same portion of the beam is _______.
Linearly increasing
What is the name of the single surface that exists between the upper and lower surfaces of the beam where the beam fibers neither shorten nor elongate?
Neutral surface
Transverse refers to loads and sections that are ___ to the longitudinal axis of a member.
Perpendicular
A pin support allows a beam to ___ at that point. Select all that apply.
Rotate
A negative internal shear force V causes a beam element to ___.
Rotate counterclockwise.
A fixed support prevents ___ and rotation at the supported joint.
Translation
A W18 X 55 beam is deeper than a W14 X 68 beam.
True
A W18 X 55 beam is heavier than a W21 X 50 beam.
True
A negative internal bending moment bends the beam slice into a frown.
True
A positive internal bending moment bends the beam slice into a smile.
True
A successful design involves the determination of an economical cross section for the beam.
True
A transverse load is a load that acts perpendicular to the longitudinal axis of the member its acting on.
True
As the distance from the neutral axis increases, the normal stress increases.
True
As the distance from the neutral surface decreases, the normal stress decreases.
True
Assuming no external moments are applied to the beam, the change in the bending- moment diagram between any two locations is equal to the area under the shear- force curve.
True
At a minimum, a beam must be designed so that it is capable of supporting the loads acting on it without exceeding allowable bending stresses.
True
Beams are usually prismatic members.
True
Concentrated moments are most often created by other members that connect to the beam.
True
For most engineering materials, the stress-strain diagrams for both tension and compression are identical in the elastic range.
True
For pure bending, the longitudinal strain that occurs in the beam varies in proportion to the fiber's distance from the neutral surface of the beam.
True
For pure bending, the neutral axis must pass through the centroid of the cross-sectional area.
True
For wide flange beams, Ix values are larger than Iy values.
True
Forces created by snow are typically termed linearly distributed loads.
True
Forces created by wind are typically termed uniformly distributed loads.
True
If a beam is subjected to pure bending, the resultant force in the longitudinal direction must be zero.
True
If the beam is in equilibrium, they any portion of the beam that we consider must also be in equilibrium.
True
If the load on a beam is small, then the beam deflection will be small. The radius of curvature will then be very large, and the curvature will be very small.
True
In this chapter, applied loads are typically symmetric with respect to the beam's longitudinal plane of symmetry.
True
In this chapter, beams typically have a longitudinal plane of symmetry.
True
Internal shear force and the internal bending moment can be used to determine the stresses in a beam.
True
Macaulay function act like switches.
True
Macaulay function continue indefinitely for x > a.
True
Moment of inertia are always positive terms.
True
Nonuniform bonding refers to flexure where the shear force V is not equal to zero.
True
Pure bending refers to flexure of a beam in response to constant bending moments.
True
The bending moment diagram can be obtained by integrating the shear force.
True
The centroid of an area refers to the point that defines the geometric center of area.
True
The intensity of the bending stress σx varies linearly with distance y from the neutral surface.
True
The largest bending stress in any beam will occur at either the top or the bottom surface of the beam.
True
The parallel-axis theorem states that the moment of inertia for an area about an axis is equal to the area's moment of inertia about a parallel axis passing through the centroid plus the product of the area and the square of the distance between the two axes.
True
The shear force diagram can be obtained by integrating the distributed load.
True
Transverse loads applied to a beam cause it to bend.
True
Transverse loads applied to a beam cause it to flex.
True
When subjected to pure bending, an initially straight beam deforms into the shape of a circular arc.
True
When the curvature is large, the radius of curvature will be small.
True
When the curvature is small, the radius of curvature will be large.
True
When the term inside the brackets of a Macaulay function is less than zero, the function has no value.
True
σx= -My/Iz is known as the elastic flexure formula.
True
The bending moment diagram can be obtained by integrating the distributed load.
True.
A clockwise external moment will cause the bending moment diagram to jump ___.
Upward
An upward concentrated load will cause the shear- force diagram to jump ___.
Upward
Which is the most common type of structural member?
Beam
A negative internal bending moment M causes a beam element to ___.
Bend concave downward.
Beams made of two materials are called ___ beams.
Composite
If the shear force in a beam is zero, the bending moment in this same region of the beam is _______.
Constant
A counter clockwise external moment will cause the bending moment diagram to jump ___.
Downward
A downward concentrated load will cause the shear- force diagram to jump ___.
Downward.
A W18 X 55 beam is deeper than a W21 X 50 beam.
False
Equivalent beams have the same radius of curvature and distribution of bending stresses.
False
To transform one of the materials in a composite beam, the height dimension of that material must be multiplied by the modular ratio.
False
What is another term for bend?
Flex
The ratio of elastic moduli is termed the _______.
Modular ratio
Which equation correctly represents the section modulus for doubly symmetric shapes?
S= I/c
In a beam subjected to pure bending, where could the maximum bending stress σmax occur? Select all that apply.
The bottom surface, the top surface.
The modular ratio for a composite beam will become smaller as _______.
The difference between the elastic moduli becomes less.
A beam cross section that consists of two different materials can be "transformed" into an equivalent cross section consisting of a single material.
True
Equivalent beams have the same radius of curvature and distribution of bending strains.
True
The second moment of area is commonly called the moment of inertia of an area.
True
To transform one of the materials in a composite beam, the width dimension of that material must be multiplied by the modular ratio.
True
Wooden beams reinforced with steel plates are considered composite beams.
True
The slope of the bending- moment diagram is equal to the ___ of the shear force diagram at that point.
Value
The slope of the shear- force diagram is equal to the ___ of the distributed load intensity at that point.
Value
Bending moments are maximum or minimum ___.
Where the shear force diagram is zero.
Select the section modulus of a beam with a rectangular cross section.
bh²/6
Which equation correctly relates longitudinal strain to radius of curvature?
εx= -(1/ρ) γ
Select the equation that correctly expresses the relationship between beam curvature and internal bending moment.
κ = M/EIz
The most common stress-strain relationship encountered in engineering is the equation for a linear elastic material, which is defined by _______.
σ = Eε
