{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Homework#9-Solutions - 05Ch05.qxd 444 2:29 PM Page 444...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
444 CHAPTER 5 Stresses in Beams (Basic Topics) Solution 5.8-4 Shear stresses in a cantilever beam Eq. (5-39): t 50 * 10 6 (10,000 y 1 2 ) ( y 1 mm; t MPa) t 8,000 2(80 * 10 6 ) c (200) 2 4 y 1 2 d ( t N/mm 2 MPa) h 200 mm ( y 1 mm) I bh 3 12 80 * 10 6 mm 4 V P 8.0 kN 8,000 N t V 2 I a h 2 4 y 1 2 b Distance from the y 1 top surface (mm) (mm) 0 100 0 0 25 75 0.219 219 50 50 0.375 375 75 25 0.469 469 100 (N.A.) 0 0.500 500 G RAPH OF SHEAR STRESS t (kPa) (MPa) t t Solution 5.8-3 Maximum load M max q 5.833 1b ft q g A weight of beam per unit distance g 35 lb ft 3 A b # h h 6 in. t allow 200 psi L 8 ft b 4 in. ; M max 25.4 k-ft M max 2 AL 3 t allow qL 2 2 M 2 AL 3 t max qL 2 2 t max 3 V 2 A 3 2 A a M L + qL 2 b V M L + qL 2 Problem 5.8-4 A cantilever beam of length supports a load (see figure). The beam is made of wood with cross-sectional dimensions . Calculate the shear stresses due to the load at points located , , and from the top surface of the beam. from these results, plot a graph showing the distribution of shear stresses from top to bottom of the beam. 100 mm 75 mm 25 mm P 120 mm * 200 mm P 8.0 kN L 2 m 200 mm 120 mm L = 2 m P = 8.0 kN 05Ch05.qxd 9/25/08 2:29 PM Page 444
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
SECTION 5.8 Shear Stresses in Rectangular Beams 449 Solution 5.8-10 Simply supported wood beam L 1.2 m q g bh 181.44 N/m g 5.4 kN/m 3 S bh 2 6 1344 * 10 3 mm 3 A bh 33,600 mm 2 b 140 mm h 240 mm (a) A LLOWABLE BASED UPON BENDING STRESS Equate values of and solve for : or P 38.0 kN ; 0.3 P + 32.66 11,424 P 37,970 N P M max 11,424 N # m M max S s allow (1344 * 10 3 mm 3 )(8.5 MPa) ( P newtons; M N # m) 0.3 P + 32.66 N # m + (181.44 N/m)(1.2 m) 2 8 M max PL 4 + qL 2 8 P (1.2 m) 4 s allow 8.5 MPa s M max S P From Appendix F: Select in. beam (nominal dimensions) (b) R EPEAT ( A ) CONSIDERING THE WEIGHT OF THE BEAM R B 7.83 * 10 3 1b R B 7.725 * 10 3 1b + q beam L 2 q beam 20.964 1b ft g 35 1b ft 3 q beam g A A 86.25 in. 2 S 165.3 in. 3 ; 8 * 12 s max M S S req M max s allow S req 120.6 in. 3 beam is still satisfactory for shear. beam is still satisfactory for moment. ; Use 8 * 12 in. beam 8 * 12 S req M max s allow S req 122.3 in. 3 < S M max 2.293 * 10 4 1b-ft M max R B d qd 2 2 q total q + q beam q total 145.964 1b ft 8 * 12 A req 73.405 in. 2 < A V max R B A req 3 V max 2 t allow Problem 5.8-10 A simply supported wood beam of rectangular cross section and span length carries a concentrated load at midspan in addition to its own weight (see figure). The cross section has width and height . The weight density of the wood is .
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern