Problem 2: It is recommended to change the circular cross section shown in the figure by a square section carries the same maximum shear stress, suggest the dimensions of the square cross section.
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- A U-shaped cross section of constant thickness is shown in the figure. Derive the following formula for the distance e from the center of the semicircle to the shear center. Also, plot a graph showing how the distance e (expressed as the non dimensional ratio e/r varies as a function of the ratio b/r. (Let b/r range from 0 to 2.)Calculate the distance e from the cent crime of the web of a C 15 x 40 channel section to the shear center 5 (see figure). Note: For purposes of analysis, consider the flanges to be rectangles with thickness teequal to the average flange thickness given in Table F-3(a) in Appendix F.A tie-down on the deck of a sailboat consists of a bent bar boiled at both ends, as shown in the figure. The diameter dBof the bar is 1/4 in., the diameter D Wof the washers is 7/8 in., and the thickness is of the fiberglass deck is 3/8 in. If the allowable shear stress in the fiberglass is 300 psi, and the allowable bearing pressure between the washer and the fiberglass is 550 psi, what is the allowable load P allowon the tie-down?
- Calculate the distance e from the centerline of the web of a C 310 × 45 channel section to the shear center E (see figure). Note: For put poses of analysis, consider the flanges to be rectangles with thickness îrequal to the average flange thickness given in Table F-3(b) in Appendix F.The cross section of a slit square tube of constant thickness is shown in the figure. Derive the following formula for the distance e from the corner of the cross section to the shear center S: e=b22A cross section in the shape of a circular arc of constant thickness is shown in the figure. Derive the following formula for the distance e from the center of the arc to the shear center S: in which ß is in radians. Also, plot a graph showing how the distance e varies as ß varies from 0 to tl
- The Z-section of Example D-7 is subjected to M = 5 kN · m, as shown. Determine the orientation of the neutral axis and calculate the maximum tensile stress c1and maximum compressive stress ocin the beam. Use the following numerical data: height; = 200 mm, width ft = 90 mm, constant thickness a = 15 mm, and B = 19.2e. Use = 32.6 × 106 mm4 and I2= 2.4 × 10e mm4 from Example D-7A punch for making a slotted hole in ID cards is shown in the figure part a. Assume that the hole produced by the punch can be described as a rectangle (12 mm X 3 mm) with two half circles (r = 1.5 mm) on the left and the right sides. If P = 10 N and the thickness of the ID card is 1 mm, what is the average shear stress in the card?A steel plate (called a cover ploie) having cross-sectional dimensions 6,0 in. × 0.5 in. is welded along the full length of the bottom flange of a W 12 × 50 wide-flange beam (sec figure, which shows the beam cross section). What is the percent increase in the smaller section modulus (as compared to the wide-flange beam alone)?
- A beam of rectangular cross section (width/) and height supports a uniformly distributed load along its entire length L. The allowable stresses in bending and shear are and TaUow, respectively. If the beam is simply supported, what is the span length Lübelow which the shear stress governs the allowable load and above which the bending stress governs? If the beam is supported as a cantilever, what is the length L() below which the shear stress governs the allowable load and above which the bending stress governs?-15 A composite beam is constructed froma wood beam (3 in. x 6 in.) and a steel plate (3 in, wide). The wood and the steel are securely fastened to act as a single beam. The beam is subjected to a positive bending moment M. = 75 kip-in. Calculate the required thickness of the steel plate based on the following limit states: Allowable compressive stress in the wood = 2 ksi Allowable tensile stress in the wood = 2 ksi Allowable tensile stress in the steel plate = 16 ksi Assume that Ew= 1,500 ksi and es= 30,000 ksi.The cross section of a slit circular tube of constant thickness is shown in the figure, Show that the distance e from the center of the circle to the shear center S is equal to 2r in the figure part a. Find an expression for e if flanges with the same thickness as that of the tube arc added, as shown in the figure part b.