Reference no: EM132574247
Question 1: A cantilever beam AB, loaded by a uniform load and a concentrated load (see figure), is constructed of a channel section.
(a) Find the maximum tensile stress σt (in psi) and maximum compressive stress σc (in psi) if the cross section has the dimensions indicated and the moment of inertia about the z-axis (the neutral axis) is I = 3.22 in4.
Note: The uniform load represents the weight of the beam. (Use the deformation sign convention.) σt= psiσc= psi
(b) Find the maximum value of the concentrated load (in lb) if the maximum tensile stress cannot exceed 4 ksi and the maximum compressive stress is limited to 15.0 ksi. (Enter the magnitude.) lb
(c) How far from A (in ft) can load P = 250 lb be positioned if the maximum tensile stress cannot exceed 4 ksi and the maximum compressive stress is limited to 15.0 ksi?
Question 2. A fiberglass pipe is lifted by a sling, as shown in the figure.
A horizontal fiberglass pipe of length L is held up by two cables near the center of the pipe. The cables wrap around the pipe a distance s apart from each other and go up to combine into a single cable above the pipe. A force on the single cable pulls upwards on the system.
The outer diameter of the pipe is 6.8 in., its thickness is 0.25 in., and its weight density is 0.053 lb/in3. The length of the pipe is L = 35 ft
and the distance between lifting points is s = 13 ft.
(Assume the sling is centered about the midpoint of the pipe. For the stresses, enter the magnitudes.)
(a) Determine the maximum bending stress (in psi) in the pipe due to its own weight.
(b) Find the spacing s (in ft) between lift points which minimizes the bending stress.
What is the minimum bending stress (in psi)?
(c) What spacing s (in ft) leads to maximum bending stress?
What is that stress (in psi)?
Question 3. Consider the following figure.
A horizontal beam A B of length L extends rightwards from a pin support at A to a roller support B. The cross section of the beam is comprised of a horizontal segment of length b and a vertical segment of width t that goes upwards from the center of the horizontal segment. The distance from the top of the vertical segment to the bottom of the horizontal segment is h and the distance from the top of the vertical segment to the top of the horizontal segment is h1. A load P acts downwards on the beam a distance d to the left of B.
(a) Determine the maximum tensile stress σt and maximum compressive stress σc (in MPa) due to the load P acting on the simple beam AB. Data are
P = 6.9 kN,
L = 3.9 m,
d = 1.05 m,
b = 80 mm,
t = 25 mm,
h = 120 mm,
and
h1 = 90 mm.
(Use the deformation sign convention.)
σt= MPaσc= MPa
(b) Find the value of d (in m) for which tensile and compressive stresses are the largest. What are these stresses (in MPa)? (Use the deformation sign convention.)
d= mσt= MPaσc= MPa
Question 4. A cantilever beam AB, loaded by a uniform load and a concentrated load (see figure), is constructed of a channel section.
(a) Find the maximum tensile stress σt (in psi) and maximum compressive stress σc (in psi) if the cross section has the dimensions indicated and the moment of inertia about the z-axis (the neutral axis) is I = 3.22 in4.
Note: The uniform load represents the weight of the beam. (Use the deformation sign convention.)
σt= psiσc= psi
(b) Find the maximum value of the concentrated load (in lb) if the maximum tensile stress cannot exceed 4 ksi and the maximum compressive stress is limited to 15.0 ksi. (Enter the magnitude.)
(c) How far from A (in ft) can load P = 250 lb be positioned if the maximum tensile stress cannot exceed 4 ksi and the maximum compressive stress is limited to 15.0 ksi?
Question 5. A cantilever beam A B with a circular cross section and length L = 730 mm supports a load P = 850 N acting at the free end (see figure).
A horizontal cantilever beam A B of length L extends rightwards from a fixed support at A. Load P acts downward at B. The beam cross sections for parts (a) and (b) are as follows.
• (a) A solid circular cross section has diameter d.
• (b) A ring-shaped cross section has outer diameter d and wall thickness t = d⁄8.
The beam is made of steel with an allowable bending stress of 120 MPa.
(a) Determine the required diameter dmin (in mm) ((a) in the figure) of the beam, considering the effect of the beam's own weight.
(b) Determine the required diameter dmin (in mm) if the beam is hollow with wall thickness
t =
d/8
((b) in the figure).
mm
Compare the cross-sectional areas of the two designs.
Ab/Aa
=
Question 6. A propped cantilever beam ABC (see figure) has a shear release just right of the mid-span.
A horizontal propped cantilever beam A B C is fixed at its left end at A. A distance L to the right of A, there is a shear release at B. A distance L to the right of B, the right end of the beam is attached to a roller support at C. A uniformly distributed load of intensity q acts downwards on the beam between A and B. A point load P = qL acts downwards on the beam at the midpoint between B and C.
(a)
Select the most economical wood beam from the table in Appendix G; assume
q = 55 lb/ft,
L = 16 ft,
σaw = 1,750 psi,
and
τaw = 375 psi.
Include the self-weight of the beam in your design. (Enter the nominal dimensions in inches.)
in. x in.
(b)
If a C 10 ? 25 steel beam is now used for beam ABC, what is the maximum permissible value of load variable q (in lb/ft)? Assume
σas = 25 ksi
and
L = 9.2 ft.
Include the self-weight of the beam in your analysis. (Use the section modulus for axis 2-2.)
lb/ft
Question 7. A simply supported wood beam is subjected to uniformly distributed load q. The width of the beam is 6 in. and the height is 8 in.
q = 600 lb/ft
16 ft
4 ft
Determine the normal stress and the shear stress at Point C. (Enter your answers in psi. Assume the +x-axis points to the right from A. Indicate the direction with the signs of your answers.)
normal stress psishear stress psi
Question 8. A laminated wood beam on simple supports (figure part (a)) is built up by gluing together four 2 in. x 4 in. boards (actual dimensions) to form a solid beam 4 in. x 8 in. in cross section, as shown in the figure part (b).
(a) If the beam is 12 ft long, what is the allowable load P (in kips) acting at the one-third point along the beam, as shown? (Include the effects of the beam's own weight, assuming that the wood weighs 35 lb/ft3.)
kips
(b) Repeat part (a) if the beam is assembled by gluing together two 3 in. x 4 in. boards and a 2 in. x 4 in. board (see figure part (c)).
kips
Question 9. A simple log bridge in a remote area consists of two parallel logs with planks across them (see figure).
A horizontal log bridge is formed by two parallel logs of 2.5 m length and 343 mm diameter with planks perpendicular to the logs and laid across them. The left end of each log is supported by a pin support and the right end of each log is supported by a roller support. A uniformly distributed load of 963 N/m acts downwards along the length of the bridge and a point load W acts downwards on the bridge a distance x from the left end.
The logs are Douglas fir with an average diameter 343 mm. A truck moves slowly across the bridge, which spans 2.5 m. Assume that the weight of the truck is equally distributed between the two logs. Because the wheelbase of the truck is greater than 2.5 m, only one set of wheels is on the bridge at a time. Thus, the wheel load on one log is equivalent to a concentrated load W acting at any position along the span. In addition, the weight of one log and the planks it supports is equivalent to a uniform load of 963 N/m acting on the log. Determine the maximum permissible wheel load W (in kN) based upon the following.
(a) an allowable bending stress of 7.0 MPa
kN
(b) an allowable shear stress of 0.75 MPa
kN
Question 10. A vertical pole consisting of a circular tube of outer diameter 7 in. and inner diameter 6.4 in. is loaded by a linearly varying distributed force with maximum intensity of
q0.
q0 = 200 lb/ft
A tall, vertically-oriented cylinder has a height of 10 ft, inner diameter d1, and outer diameter d2. A linearly varying distributed force acts rightward on the left side of the cylinder. The maximum value q0 = 200 lb/ft acts at the bottom of the cylinder, and q linearly decreases to a value of zero acting at the top of the cylinder.
Find the maximum shear stress in the pole. (Enter your answer in ksi. Indicate the direction with the sign of your answer.)
ksi
Question 11. A sign for an automobile service station is supported by two aluminum poles of hollow circular cross section, as shown in the figure.
Two vertical poles of outer diameter d and hollow circular cross section of thickness t = d⁄10 extend upwards a distance h1 from a fixed support to the bottom of a rectangular sign of width b and continue farther upwards a distance h2 to the top of the sign. A wind load acts on the sign perpendicular to its area.
The poles are being designed to resist a wind pressure of 76 lb/ft2 against the full area of the sign. The dimensions of the poles and sign are
h1 = 20 ft, h2 = 5 ft, and b = 10 ft.
To prevent buckling of the walls of the poles, the thickness t is specified as one-tenth the outside diameter d.
(a) Determine the minimum required diameter (in inches) of the poles based upon an allowable bending stress of 7,050 psi in the aluminum.
inches
(b) Determine the minimum required diameter (in inches) based upon an allowable shear stress of 1,950 psi.
inches
Question 12. A welded steel girder having the cross section shown in the figure is fabricated of two 20 in. x 1 in. flange plates and a 60 in. x 5/16 in. web plate.
The plates are joined by four longitudinal fillet welds that run continuously throughout the length of the girder.
If the girder is subjected to a shear force of 315 kips, what force F (per inch of length of weld) must be resisted by each weld? (Enter the magnitude in kips/in. Assume that the shear force acts parallel to the y-axis.)
kips/in
Question 13. A beam of a T cross section is formed by nailing together two boards having the dimensions shown in the figure.
If the total shear force V acting on the cross section is 1,850 N and each nail may carry 440 N in shear, what is the maximum allowable nail spacing s (in mm)? (Assume that the shear force acts parallel to the y-axis and is uniformly distributed across the thickness of the web.)