STUDENT NAME:
Statics and Strength of Materials, Summer 2023
Open book, open notes, no cell phone, no internet, no discussions with other student teams.
Write down relevant equations, Draw sketches where necessary.
Correct choice of formulae, accurate calculations, appropriate units, well-drawn sketches, showing the work and clearly identifying your answers gets full grade for a question.
Answer all sub questions (if any) of a problem for full credit for that problem.
All questions are worth equal points
Identify your answers clearly.
TRUE or FALSE? (Write T or F in the space provided) 30 Points
1. The ball and socket joint in three dimensions produces reactions that have three component forces. ( )
2. Dry frictional force acts in the same direction as the motion. ( )
3. A wedge is an example of a machine that transforms horizontal input forces to vertical output forces. ( )
4. A self-locking screw jack is obtained when the angle of friction is less than the angle of the screw thread. ( )
5. Tension on both sides of a belt drive is equal. ( )
6. Rolling friction is approximately significantly lower than dry sliding friction. ( )
7. The Center of Gravity is the point on a body through which the total weight of the body is assumed to act. ( )
8. The moment of inertia is a value that represents the distribution of an area around an axis and is important when determining bending stress and deflection. ( )
9. Shear force acts perpendicular to the cross-sectional area of interest. ( )
10. Force couples cause pure rotation. ( )
MULPTIPLE CHOICE (Write the alphabet corresponding to the most correct alternative in the space provided) 30 Points
1. A block is placed on an incline and the angle of inclination is gradually increased. The maximum angle at which the block is about to slide down the incline is called as:
Angle of Repose
Angle of Decline
Angle of Incline
Acute Angle
Internal Angle ( )
2. If an axial stress of 200 MPa is applied to a 304 Stainless Steel rod with a maximum allowable stress of 500 MPa, the Factor of Safety is:
1.5
0.4
2.5
10
None of the above ( )
3. If three columns have the same cross-sectional area and the same Young’s modulus. A rectangular shaped column has a radius of gyration of 1.1, a square shaped column has a radius of gyration of 1.5 and a circular shaped column has radius of gyration of 2.1. Which is least likely to buckle?
Square shaped column
Circular shaped column
Rectangular shaped column
Square and rectangular
All will buckle at equal load ( )
4. The first step in solving for the forces in the members of a truss using the Method of Sections is to:
Take a section through a truss
Draw FBD of a section of the truss
Find the reactions at the support for the entire truss
Solve equilibrium equations for the truss section
Determine which members are in tension and compression ( )
5. The maximum axial stress in an object occurs at a section where:
The shear force is at a maximum
The bearing stress is at a maximum
The shear force is zero
The contact stress is at a minimum
The cross-sectional area is the smallest ( )
6. If a beam spans across an expanse and a truck stands in the middle of the beam, which portion of the beam is in tension?
The top surface of the beam
The bottom surface of the beam
The left end of the beam
The right end of the beam
None of the above ( )
7. Which support will create six reactions in 3D space?
Fixed Support
Single hinge
Cable
Smooth bearing
Ball on a smooth surface ( )
8. As a designer, you must take the material yield strength into consideration. In addition, which of the following factor(s) would you also consider during your design?
Material Cost
Material Stiffness
Material Corrosion Resistance
Material Manufacturability
All of the above ( )
9. A cantilever beam with a single point load at its free end has a bending moment diagram like a:
triangle
rectangle
parabolic spandrel
cubic curve
none of the above ( )
10. The Ninth Street Bridge (shown below) is an example of which type of bridge?
(a) Arch Bridge
(b) Girder Bridge
(c) Suspension Bridge
(d) Warren Truss Bridge
(e) Beam Bridge ( )
Solve following four problems (40 points)
1. Find resultant of forces F1, F2 and F3 as shown in the figure below (note: finding resultant means finding both – the magnitude and the direction of the resultant):
X
X
Y
Y
F1 = 300 N
F1 = 300 N
F2 = 500 N
F2 = 500 N
F3 = 800 N
F3 = 800 N
200
200
450
450
300
300
2. Move Force F shown in the figure below from point A to point B:
F = 30 lb
F = 30 lb
10”
10”
A
A
B
B
3. For the circular area shown in the figure below find the centroidal moment of inertia Ixc and Iyc and the moment of inertia about X and Y- axes Ix and Iy:
30 mm
X
Y
Xc
Yc
20 mm
10 mm
30 mm
X
Y
Xc
Yc
20 mm
10 mm
4. A 10 mm diameter, 50 mm long cylindrical bar of a metal is pulled in tension under a tensile load of 7200 N. If the metallic bar undergoes a fully elastic extension of 0.03948 mm, calculate the Young’s modulus of this metal.
