Question 1

Which of the following statements related to shear diagrams is not correct?&#10;A)Before a shear diagram is drawn, all load distributions should be simplified into point loads&#10;B)Shear diagrams begin and end at zero shear&#10;C)The shear force at a point is the total external load on the beam at that point&#10;D)The shear line representing a uniformly distributed load is linear

Accepted Answer

The statement "the shear force at a point is the total external load on the beam at that point" is not correct. Correctly stated, the shear force at a specific point on a shear diagram can be found by summing the external loads and reactions that are occurring perpendicular to the beam to the left of the specific point.

Question 2

The Italian railway engineer Alberto Castigliano proposed two theorems related to the study of statically indeterminate structures. To which of the following properties does Castigliano's first theorem apply?

A)Deflection
B)Torsion
C)Shear stress
D)All of the above

Deflection

Accepted Answer

Italian railway engineer Alberto Castigliano's first theorem applies to deflection. In 1879, Castigliano published an original book on the study of statically indeterminate structures. His second theorem, now referred to as the "method of least work", is still in use today.

Question 3

Which of the following passages best concludes the following statement regarding Castigliano's second theorem, the Method of Least Work:"the internal work accomplished by each member or each portion of a statically indeterminate structure subjected to a set of external loads is the least possible amount necessary to …"

A)Deflect just to the point prior to failure
B)Deform in a manner consistent with its physical limitations
C)Maintain equilibrium in supporting the loads
D)None of the above

Maintain equilibrium in supporting the loads

Accepted Answer

The passage that best concludes the statement regarding Castigliano's second theorem, the Method of Least Work: "the internal work accomplished by each member or each portion of a statically indeterminate structure subjected to a set of external loads is the least possible amount necessary to …" is "maintain equilibrium in supporting the loads." Ironically, applying the least-work method to certain statically indeterminate structures can be very time-consuming and frustrating. However, the method is still in use today.

Question 4

Which of the following loading types will causes a beam to bend?&#10;A)Random&#10;B)Point&#10;C)Uniformly distributed&#10;D)B and C

Accepted Answer

The types of load that will cause a beam to bend are point loads and uniformly distributed loads. Beams that are bent experience tension on one side and compression on the other side. Tension and compression are severe forms of stress that may act on a structure.

Question 5

When sketching the shape of a bending moment of a deflected beam, which of the following conventions is commonly used?&#10;A)Positive bending moment bends beam convex upwards&#10;B)Negative bending moment bends beam concave upwards&#10;C)Positive bending moment bends beam concave upwards&#10;D)All of the above

Accepted Answer

When sketching the shape of a deflected beam, the convention used for a positive bending moment is to bend the concave upwards. When this convention is followed, the bend of the beam is exaggerated over the normal beam surface in order to demonstrate the results of a given loading.

Question 6

Which of the following conventions is used to indicate tension on a truss diagram?&#10;A)Drawing arrows away from the pins&#10;B)Drawing arrows towards the pins&#10;C)Adding the tau symbol to the diagram near the truss member in tension&#10;D)None of the above

Accepted Answer

The convention used to indicate the tension on a truss diagram is to draw arrows away from the pins. To indicate compression on a truss diagram, arrows are drawn towards the pins. Sometimes, the directions of the forces acting against a given pin are not known and have to be assumed. If a negative value results from a Method of Joints computation used to find forces, you know that you have made an incorrect assumption.

Question 7

Which of the following can be used to evaluate the impacts of combined normal and shear stresses?&#10;A)Mohr's circle&#10;B)Clapeyron's equation&#10;C)Castigliano's first theorem&#10;D)All of the above

Accepted Answer

Mohr's circle can be used to evaluate the impacts of combined normal and shear stresses. A two-dimensional representation of the normal and shear stresses can be generated using Mohr's circle. The circle provides a useful format for which quick estimations can be made on the combined state of the stresses.

Question 8

Which of the following does not influence the bending moment of a continuous beam?&#10;A)Loads&#10;B)Modulus of elasticity&#10;C)Moment of inertia&#10;D)None of the above

Accepted Answer

The loads, modulus of elasticity, and moment of inertia influence the bending moments of a continuous beam. In order to determine the bending moments for continuous beams, contiguous beam sections can be analyzed separately using unique formulas for specific geometric configurations. Determining the forces associated with statically indeterminate continuous beams can be very challenging and time consuming.

Deck 9: Material Mechanics