July, 2008

Problem 515
Repeat Prob. 514 to find the maximum flexural stress at section b-b

Problem 514
The right-angled frame shown in Fig. P-514 carries a uniformly distributed loading equivalent to 200 N for each horizontal projected meter of the frame; that is, the total load is 1000 N. Compute the maximum flexural stress at section a-a if the cross-section is 50 mm square.

Problem 513
A rectangular steel beam, 2 in wide by 3 in deep, is loaded as shown in Fig. P-513. Determine the magnitude and the location of the maximum flexural stress.

Problem 512
The circular bar 1 inch in diameter shown in Fig. P-512 is bent into a semicircle with a mean radius of 2 ft. If P = 400 lb and F = 200 lb, compute the maximum flexural stress developed in section a-a. Neglect the deformation of the bar.

$\displaystyle\int\sin^2x\,\cos^4x\,dx $

Problem 510
A 50-mm diameter bar is used as a simply supported beam 3 m long. Determine the largest uniformly distributed load that can be applied over the right two-thirds of the beam if the flexural stress is limited to 50 MPa.

Problem 509
A section used in aircraft is constructed of tubes connected by thin webs as shown in Fig. P-509. Each tube has a cross-sectional area of 0.20 in2. If the average stress in the tubes is no to exceed 10 ksi, determine the total uniformly distributed load that can be supported in a simple span 12 ft long. Neglect the effect of the webs.

Problem 508
Determine the minimum height h of the beam shown in Fig. P-508 if the flexural stress is not to exceed 20 MPa.

The electrical resistance of a wire varies directly as its length and inversely as the square of its diameter.
If a wire 100 cm long and 1 cm in diameter has a resistance of 5 ohms, what is the resistance of a wire of the
same material 50 cm long and 0.5 cm in diameter?

If tan x = 5/y and tan 2x = 20/y, find the value of x & y

$\displaystyle \int \frac{(x - 3) \, dx}{x^2 - 4x + 4}$

Evaluate
1. $\displaystyle \int \tan^5x \, \sec^4x \, dx$
2. $\displaystyle \int \tan^5x \, \sec^3x \, dx$

Problem 506
A flat steel bar, 1 inch wide by ¼ inch thick and 40 inches long, is bent by couples applied at the ends so that the midpoint deflection is 1.0 inch. Compute the stress in the bar and the magnitude of the couples. Use E = 29 × 10⁶ psi.

Problem 505
A high strength steel band saw, 20 mm wide by 0.80 mm thick, runs over pulleys 600 mm in diameter. What maximum flexural stress is developed? What minimum diameter pulleys can be used without exceeding a flexural stress of 400 MPa? Assume E = 200 GPa.

Problem 504
A simply supported beam, 2 in wide by 4 in high and 12 ft long is subjected to a concentrated load of 2000 lb at a point 3 ft from one of the supports. Determine the maximum fiber stress and the stress in a fiber located 0.5 in from the top of the beam at midspan.