Explanation Given information: The thickness of the plate is 2 mm . The beam is subjected to a vertical shear of 5 kN . Calculation: Calculate the moment of inertia as shown below. I = b h 3 12 + A ( y − y ¯ ) 2 Here, b is the breadth of the section, h is the height of the section, A is the area of the beam, and ( y − y ¯ ) is the centroid of the beam from the neutral axis. Calculate the moment of inertia I for the whole section as shown below. I = 2 × ( 2 × 48 3 12 + 2 × 52 3 12 + ( 20 × 2 3 12 + 20 × 2 × 25 2 ) ) = 2 × ( 18 , 432 + 23 , 434.67 + 25 , 013.33 ) = 133 , 760 mm 4 Calculate the first moment of area Q as shown below. Q = ∑ A y ¯ (1) Here, A is the area of the section and y ¯ is the centroid of the section. Calculate the shear stress τ as shown below. τ = V Q I t (2) Here V is the vertical shear. At point a : Calculate the first moment of area Q a as shown below. Q a = 2 × 24 × 12 = 576 mm 3 Thickness of the section is t a = 2 mm Calculate the shear stress as shown below. Substitute 5 kN for V , 576 mm 3 for Q , 2 mm for t , 133 , 760 mm 4 for I in Equation (2). τ a = 5 kN × 1 , 000 N 1 kN × 576 mm 3 133 , 760 mm 4 × 2 mm = 10.76 N / mm 2 × 1 MPa 1 N / mm 2 = 10.76 MPa Hence, the shear stress at point a is 10.76 MPa _ . At point b : Calculate the first moment of area using Equation (1) as shown below. Q b = 0 Hence, the shearing stress at points b is 0 _ . At point c : Calculate the first moment of area using Equation (1) as shown below. Q c = 0 − ( 12 × 2 × 25 ) = − 600 mm 3 Thickness of the section is t c = 2 mm Calculate the shear stress as shown below. Substitute 5 kN for V , 600 mm 3 for Q , 2 mm for t , 133 , 760 mm 4 for I in Equation (2). τ c = 5 kN × 1 , 000 N 1 kN × 600 mm 3 133 , 760 mm 4 × 2 mm = 11

7th Edition

ISBN: 9780073398235

Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David F. Mazurek

Publisher: McGraw-Hill Education

See similar textbooks

Videos

Question

Chapter 6.5, Problem 48P

To determine

Find the shearing stress at points a, b, c, d, and e.

Sketch the shear flow in the cross section.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.5, Problem 47P

Chapter 6.5, Problem 49P

Students have asked these similar questions

For the beam and loading shown, consider section n–nand determine (a) the largest shearing stress in that section, (b) the shearing stress at point a

The thin-walled extruded beam shown is made of aluminum and has a uni-form 3-mm wall thickness. Knowing that the shear in the beam is 5 kN, deter-mine (a) the shearing stress at point A, (b) the maximum shearing stress in the beam. Note: The dimensions given are to lines midway between the outer and inner surfaces of the beam.

A composite beam is made by attaching the timber and steel portions shown with bolts of 12-mm diameter spaced longitudinally every 200 mm. The modulus of elasticity is 10 GPa for the wood and 200 GPa for the steel. For a vertical shear of 4 kN, determine (a) the average shearing stress in the bolts, (b) the shearing stress at the center of the cross section.

Chapter 6 Solutions

Mechanics of Materials, 7th Edition

Ch. 6.2 - Three full-size 50 100-mm boards are nailed...Ch. 6.2 - For the built-up beam of Prob. 6.1, determine the...Ch. 6.2 - Three boards, each 2 in. thick, are nailed...Ch. 6.2 - A square box beam is made of two 20 80-mm planks...Ch. 6.2 - The American Standard rolled-steel beam shown has...Ch. 6.2 - The beam shown is fabricated by connecting two...Ch. 6.2 - A column is fabricated by connecting the...Ch. 6.2 - The composite beam shown is fabricated by...Ch. 6.2 - 6.9 through 6.12 For beam and loading shown,...Ch. 6.2 - 6.9 through 6.12 For beam and loading shown,...

Ch. 6.2 - 6.9 through 6.12 For beam and loading shown,...Ch. 6.2 - 6.9 through 6.12 For beam and loading shown,...Ch. 6.2 - 6.13 and 6.14 For a beam having the cross section...Ch. 6.2 - 6.13 and 6.14 For a beam having the cross section...Ch. 6.2 - For a timber beam having the cross section shown,...Ch. 6.2 - Two steel plates of 12 220-mm rectangular cross...Ch. 6.2 - Two W8 31 rolled sections may be welded at A and...Ch. 6.2 - For the beam and. loading shown, determine the...Ch. 6.2 - Fig. P6.19 6.19 A timber beam AB of length L and...Ch. 6.2 - A timber beam AB of Length L and rectangular cross...Ch. 6.2 - 6.21 and 6.22 For the beam and loading shown,...Ch. 6.2 - 6.21 and 6.22 For the beam and loading shown,...Ch. 6.2 - 6.23 and 6.24 For the beam and loading shown,...Ch. 6.2 - 6.23 and 6.24 For the beam and loading shown,...Ch. 6.2 - 6.25 through 6.28 A beam having the cross section...Ch. 6.2 - 6.25 through 6.28 A beam having the cross section...Ch. 6.2 - Prob. 27P Ch. 6.2 - 6.25 through 6.28 A beam having the cross section...Ch. 6.5 - The built-up timber beam shown is subjected to a...Ch. 6.5 - The built-up beam shown is made by gluing together...Ch. 6.5 - The built-up beam was made by gluing together...Ch. 6.5 - Several wooden planks are glued together to form...Ch. 6.5 - The built-up wooden beam shown is subjected to a...Ch. 6.5 - Knowing that a W360 122 rolled-steel beam is...Ch. 6.5 - 6.35 and 6.36 An extruded aluminum beam has the...Ch. 6.5 - 6.35 and 6.36 An extruded aluminum beam has the...Ch. 6.5 - Knowing that a given vertical shear V causes a...Ch. 6.5 - The vertical shear is 1200 lb in a beam having the...Ch. 6.5 - The vertical shear is 1200 lb in a beam having the...Ch. 6.5 - 6.40 and 6.47 The extruded aluminum beam has a...Ch. 6.5 - Prob. 41P Ch. 6.5 - Prob. 42P Ch. 6.5 - Three planks are connected as shown by bolts of...Ch. 6.5 - A beam consists of three planks connected as shown...Ch. 6.5 - A beam consists of five planks of 1.5 6-in. cross...Ch. 6.5 - Four L102 102 9.5 steel angle shapes and a 12 ...Ch. 6.5 - A plate of 14-in. thickness is corrugated as shown...Ch. 6.5 - Prob. 48P Ch. 6.5 - An extruded beam has the cross section shown and a...Ch. 6.5 - Prob. 50P Ch. 6.5 - The design of a beam calls for connecting two...Ch. 6.5 - The cross section of an extruded beam is a hollow...Ch. 6.5 - Prob. 53P Ch. 6.5 - Prob. 54P Ch. 6.5 - Prob. 55P Ch. 6.5 - 6.56 and 6.57 A composite beam is made by...Ch. 6.5 - 6.56 and 6.57 A composite beam is made by...Ch. 6.5 - Prob. 58P Ch. 6.5 - Prob. 59P Ch. 6.5 - Prob. 60P Ch. 6.6 - 6.61 through 6.64 Determine the location of the...Ch. 6.6 - 6.61 through 6.64 Determine the location of the...Ch. 6.6 - 6.61 through 6.64 Determine the location of the...Ch. 6.6 - Prob. 64P Ch. 6.6 - 6.65 through 6.68 An extruded beam has the cross...Ch. 6.6 - 6.65 through 6.68 An extruded beam has the cross...Ch. 6.6 - 6.65 through 6.68 An extruded beam has the cross...Ch. 6.6 - 6.65 through 6.68 An extruded beam has the cross...Ch. 6.6 - 6.69 through 6.74 Determine the location of the...Ch. 6.6 - Prob. 70P Ch. 6.6 - Prob. 71P Ch. 6.6 - Prob. 72P Ch. 6.6 - Prob. 73P Ch. 6.6 - Prob. 74P Ch. 6.6 - Prob. 75P Ch. 6.6 - 6.75 and 6.76 A thin-walled beam has the cross...Ch. 6.6 - 6.77 and 6.78 A thin-walled beam of uniform...Ch. 6.6 - Prob. 78P Ch. 6.6 - Prob. 79P Ch. 6.6 - Prob. 80P Ch. 6.6 - Prob. 81P Ch. 6.6 - Prob. 82P Ch. 6.6 - Prob. 83P Ch. 6.6 - Prob. 84P Ch. 6.6 - Prob. 85P Ch. 6.6 - Solve Prob. 6.85, assuming that the thickness of...Ch. 6.6 - Prob. 87P Ch. 6.6 - Prob. 88P Ch. 6 - Three boards are nailed together to form the beam...Ch. 6 - For the beam and loading shown, consider section...Ch. 6 - For the wide-flange beam with the loading shown,...Ch. 6 - For the beam and loading shown, consider section...Ch. 6 - The built-up timber beam is subjected to a 1500-lb...Ch. 6 - Knowing that a given vertical shear V causes a...Ch. 6 - Three planks are connected as shown by bolts of...Ch. 6 - Three 1 18-in. steel plates are bolted to four L6...Ch. 6 - The composite beam shown is made by welding C200 ...Ch. 6 - Prob. 98RP Ch. 6 - A thin-walled beam of uniform thickness has the...Ch. 6 - Determine the location of the shear center O of a...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Find the shearing stress at points a , b , c , d , and e . Sketch the shear flow in the cross section.

Solution Summary: The author calculates the moment of inertia I for the whole section.

Videos

Find the shearing stress at points a, b, c, d, and e.

Sketch the shear flow in the cross section.

Want to see the full answer?

Chapter 6 Solutions

Find the shearing stress at points a , b , c , d , and e . Sketch the shear flow in the cross section.

Solution Summary: The author calculates the moment of inertia I for the whole section.

Videos

Find the shearing stress at points a, b, c, d, and e. Sketch the shear flow in the cross section.

Want to see the full answer?

Chapter 6 Solutions

Find the shearing stress at points a, b, c, d, and e.

Sketch the shear flow in the cross section.