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

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Chapter 6.5, Problem 48P

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

Sketch the shear flow in the cross section.

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Chapter 6.5, Problem 47P

Chapter 6.5, Problem 49P

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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.

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

Sketch the shear flow in the cross section.

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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.

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

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Chapter 6 Solutions

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

Sketch the shear flow in the cross section.