exam 3 - past exam problems with solutions part 2 · es230 fall 2017 exam 3 – past exam problems...

ES230 Fall 2017 Exam 3 – Past Exam Problems

of 33 Exam 3 – Past Exams



1. (10 points) Determine the maximum deflection of the beam below. The beam shown has E=1000 ksi, I = 10 in4, L=100 inches, M = 1 kip-inch.

2. (3 points). Two plastic C-shaped members are to be glued together for form a hollow square cantilever box beam that will be subjected to a horizontal force. Which configuration (A or B) will minimize the shear stress on the glue?

100”

M = 1 kip-in 1 kip-in = M

Fixed Support Fixed Support

Force Force

Glue Joint Glue Joint

(A) (B)



3. (12 points).

Given: The shear force on the beam cross-section is constant over the 16” interval from A to B. It is known that the extreme-fiber normal stresses are A = 20 ksi at A and B = 15 ksi at B. The I-shaped cross-section is composed of 1”x8” flanges and a 1”x8” web. Determine the shear stress between the flange and the web, between A and B.

SIDE VIEW – Showing Normal Stresses CROSS-SECTION

A B

A = 20 ksi B = 15 ksi

A B

MAMB

3D VIEW MA causes maximum normal stress of 20 ksi MB causes maximum normal stress of 15 ksi

1”x8”Flange

1”x8”Flange

1”x8” W b

Determine here



4. (17 points). A 1.5m diameter boiler (pressure vessel) is constructed out of curved steel plates that are fastened together at their ends using a butt joint consisting of two cover plates and rivets having a diameter of 10-mm and spaced 50-mm apart, as shown. If the steam pressure in the boiler is 1.00 MPa, determine the average shear stress in the rivets.

5. (17 points). A plastic beam is constructed by gluing a C-shape to a rectangular shape. If the beam is loaded, as shown,

determine the maximum shear stress in the glue.

10mm diam rivet

10mm diam rivet

p = 1.00 MPa

1.5m Diameter Boiler Cross Section

(2) cover plates

w = 500 lbs/ft

10 ft

Cross-Section I = 241 in4

1”

10”

10”

1”1”

2”

2 ft



1. (5 points). Two 2” x 4” boards are glued together and act as a cantilever beam over a span of 20 inches, subjected to an unknown point load P. It is known that the normal bending stresses at the extreme fibers have magnitudes of 1000psi. Determine the shear stress in the glue.

2. (20 points). The steel I-beam is considered to have failed if either:

a. The normal bending stress exceeds 30 ksi, or b. The shear stress exceeds 15 ksi

Problem: Determine the maximum uniform load w that may be applied without failure occurring. Given: The beam spans 50 inches over pin and roller supports. The cross-section is composed of 1” x 10” flanges and a ½” x 18” web, as shown. NOTE: This is NOT a Mohr’s Circle problem.

2”

2”

4”

CROSS SECTION

20”

Fixed End

max = 1000psi

P

50 inches

1” x 10” Flange

1” x 10” Flange

½” x 18” Web

w = ?



3. (20 points). The steel I-beam is considered to have failed if either:

c. The normal bending stress exceeds 25 ksi, or d. The shear stress exceeds 15 ksi

Problem: Determine the maximum uniform load w that may be applied without failure occurring. Given: The beam spans 80 inches over pin and roller supports. The cross-section is composed of ½” x 10” flanges and a ½” x 19” web, as shown. NOTE: This is NOT a Mohr’s Circle problem.

80 inches

½” x 10” Flange

½” x 10” Flange

½” x 19” Web

w = ?



1. (3 points). For which location would the shear forces on the nails be greatest (circle the correct answer)? Given: The left fixed support for the beam is denoted (1) and the right free end is denoted as (2). The nails on the top of the beam are denoted B and the nails on the bottom of the beam are denoted A.

a. (1)A b. (1)B c. (2)A d. (2)B e. (1)A and (1)B (they are the same) f. (2)A and (2)B (they are the same)

2. (22 points). Draw the stresses acting on element A shown, labeling their magnitudes and directions. Do not draw any

other orientation (this is NOT a Mohr’s Circle Problem): Given: The horizontal force of 5000 lbs is applied to the top of the cantilever beam at a distance that is 5” from the centerline of the beam, as shown. The beam has a 10”x10” cross-section

A

5”

2”

3”

70” 30”

5000 lbs

10”x10” Cross Section

(1) (2)

w



1. (25 points) A box beam is fabricated from two plywood webs that are secured to the solid lumber boards at its top and bottom flanges. The beam supports a concentrated load of P=5000 lbs at the center of a 16-foot span. 3/8” diameter bolts connect the plywood webs and the solid lumber flanges at a spacing of 12 inches along the beam. Supports A and C are considered as a pin and roller. Determine:

The maximum shear stress in the plywood webs. The average shear stress in the bolts.

12”

8 ft 8 ft



1. (3 points) A hydraulic jack is shown below, consisting of a 3” diameter piston that is inside a hollow cylinder. If the piston has 3000 psi oil pressure behind it, determine the force P that this jack is currently lifting.

2. (7 points). A rural water supply system consists of a water tank that is up on a hill, supplying water to a community in the valley. If the water level is at an elevation that is 100-ft above the community it supplies, determine the minimum wall thickness needed for the supply pipe if it has an inside diameter of 4” so that the hoop stresses do not exceed 1000 psi. Given: a cubic foot of water weighs 62.4 lbs.

Water Tank

Water Level

4” diameter water supply pipe

100-ft

3” diameter piston

3000psi oil pressurebehind the piston



1. (20 points) Write the function for the deflection of beam AB, v(x) and the function for the slope of beam AB, (x), where the origin for x is at fixed support A, directed toward free-end B, then determine the maximum deflection and maximum slope of the beam. Given: Distributed load that increases linearly from 0 at A to 1 kip/inch at B. EI = 1,000,000 kip-in2.

2. (20 points) Determine the maximum force P that the gantry crane can safely support if the maximum allowable normal stress

allow = 30 ksi. Given: the gantry crane ABC is made out of hollow square tubing with outside dimensions of 3 inches and a wall thickness of ¼”. Assume the weight of the crane, itself, is negligible.

A B

w = 1 kip/inch

60 inches

x

P 100 inches

50 inches

A

B C

Side View of Gantry Crane

Cross Section of hollow square tubing

3 inches

3 inches

2.5 inches

2.5 inches



1. (20 points) Write the function for the deflection of beam AB, v(x) and the function for the slope of beam AB, (x), where the

origin for x is at fixed support A, directed toward free-end B, then determine the maximum deflection and maximum slope of the beam. Given: Distributed load that increases linearly from 0 at A to 1 kip/inch at B. EI = 1,000,000 kip-in2.

A B

w = 1 kip/inch

60 inches

x



2. (20 points) Determine the maximum force P that the gantry crane can safely support if the maximum allowable normal stress allow = 30 ksi. Given: the gantry crane ABC is made out of hollow square tubing with outside dimensions of 3 inches and a wall thickness of ¼”. Assume the weight of the crane, itself, is negligible.



1. (3 points) What is Pascal’s Law?

2. (2 points). TRUE or FALSE. The member below is a two-force member which implies that the forces on each end are

collinear and that there is no internal bending or shear forces present in the member

3. (20 points) An S-Hook is used for heavy lifting. It is made out of 2” diameter circular steel rod and is bent into a 6” radius, where the radius is measured to the centroid of the rod. Determine the maximum load P that the hook can sustain without exceeding the allowable normal stress all = 20 ksi, Assume that the most severe stresses occur at section A-A.

P

r = 6”

r = 6”

P

A A



6. (20 points): Write the v(x) function of the deflected elastic shape for the uniformly-loaded beam in terms of w, L, and EI. Then report the maximum deflection in units of feet if w=1 kip/ft, L=20-ft, and EI=20,833 kip-ft2.

Given:

w=constant

EI=constant L



13. (12 points) Use double-integration to determine the deflection at midspan. EI is constant.



1. (20 points) Write the function for the deflection v(x) of beam AB due to the concentrated moment at B, and the function for the slope (x), where the origin for x is at pinned support A, directed toward roller support B. Write these functions in terms of M, L, x, and EI. Given: Concentrated moment M at position B.

AB

M

L

x



1. (20 points) Write the function for the deflection v(x) of beam AB due to the concentrated moment at B, and the function for

the slope (x), where the origin for x is at pinned support A, directed toward roller support B. Write these functions in terms of M, L, x, and EI. Given: Concentrated moment M at position B.

exam 3 - past exam problems with solutions part 2 · es230 fall 2017 exam 3 – past exam problems...

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