Q: A beam is loaded as shown: a $$400\,\text{N}$$ horizontal force at point C and a $$96\,\text{N}$$ vertical force at point A. What is the bending moment $$M_C at $$point C?

$$M_C = -144\,\text{N}\cdot\text{m}$$

Q: Determine the magnitude of the internal loads (normal, shear, and bending moment) at point C for the column shown with $$100\,\text{N}$$ vertical and $$80\,\text{N}$$ horizontal forces applied at the top.

$$(100\,\text{N}, 80\,\text{N}, 40\,\text{N}\cdot\text{m})$$

Question 1

A beam is designed to support loads applied perpendicularly to its axis. Why are beams often thicker at the supports than at the center of the span?

Accepted Answer

Because the internal forces (shear and moment) are typically largest at the supports, requiring more material to resist these loads.

Question 2

When determining internal forces at a section B of a beam, what is the first step according to the method of sections?

Accepted Answer

Take an imaginary cut at the place where you need to determine the internal forces.

Question 3

In a two-dimensional beam, which internal force acts perpendicular to the section?

Accepted Answer

Normal (axial) force $$N$$

Question 4

A fixed column supports a rectangular billboard. Why is the column usually thicker at the bottom than at the top?

Accepted Answer

Because the bending moment due to the applied loads is greatest at the base.

Question 5

Given a beam with a uniformly distributed load of $$3\,	ext{kip/ft}$$ over $$6\,	ext{ft}$$ and a point load of $$18\,	ext{kip} at$$ $$3\,	ext{ft}$$ from the right end, what is the vertical reaction $$B_y at $$the right support?

Accepted Answer

$$B_y = 6\,	ext{kip}$$

Question 6

After making an imaginary cut at point C in a beam and drawing the free body diagram of the right section, which internal forces should be shown at the cut surface?

Accepted Answer

Shear force $$V_C$$, normal force $$N_C$$, and bending moment $$M_C$$

Question 7

For a beam section, the loads on the left and right sides of the section at B are equal in magnitude but opposite in direction. What is the reason for this?

Accepted Answer

Because the net loads must be zero at the section when the two sides are reconnected.

Question 8

A column is loaded with a vertical $$100\,	ext{N}$$ force. At which sections are the internal loads the same?

Accepted Answer

P, Q, and R

Question 9

A column is loaded with a horizontal $$100\,	ext{N}$$ force. At which section are the internal loads largest?

Accepted Answer

Q

Question 10

In mechanics, the force component $$V$$ acting tangent to, or along the face of, the section is called the:

Accepted Answer

Shear force

Question 11

A beam is loaded as shown: a $$400\,	ext{N}$$ horizontal force at point C and a $$96\,	ext{N}$$ vertical force at point A. What is the bending moment $$M_C at $$point C?

Accepted Answer

$$M_C = -144\,	ext{N}\cdot	ext{m}$$

Question 12

Which equation of equilibrium is used to solve for the vertical reaction at a support in a beam subjected to vertical loads?

Accepted Answer

$$\sum F_y = 0$$

Question 13

A beam is subjected to a uniformly distributed load. To find the internal forces at a point not at the support, which of the following steps is NOT necessary?

Accepted Answer

Ignore the support reactions.

Question 14

A column is loaded with a horizontal $$100\,	ext{N}$$ force. At which section are the internal loads the lowest?

Accepted Answer

R

Question 15

Determine the magnitude of the internal loads (normal, shear, and bending moment) at point C for the column shown with $$100\,	ext{N}$$ vertical and $$80\,	ext{N}$$ horizontal forces applied at the top.

Accepted Answer

$$(100\,	ext{N}, 80\,	ext{N}, 40\,	ext{N}\cdot	ext{m})$$

Question 16

Which of the following best describes the bending moment $$M in a $$beam?

Accepted Answer

A moment that causes the beam to bend, acting about the section.

Question 17

In the method of sections, why is it important to choose which resulting section or piece will be easier to analyze after making the imaginary cut?

Accepted Answer

Because the geometry and external loads may be simpler on one side, making calculations easier.

Question 18

A beam is loaded with a point load at its center. Where is the maximum bending moment located?

Accepted Answer

At the center of the beam

Question 19

Which internal force is responsible for sliding one part of a beam relative to another along the section?

Accepted Answer

Shear force $$V$$

Internal Forces in Structural Members: Method of Sections and Applications

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