To determine The maximum shear stress in the T -beam at section C . To show: the result on a volume element at this point. Explanation Determination of reactions: Sketch the free-body diagram of the simple supported beam as in Figure 1. Moment about point A : Determine the vertical reaction at point B by taking moment about point A . ∑ M A = 0 B y ( 6 ) − 10 × 3 × 3 2 − 1 2 × 10 × 3 × ( 3 + 1 3 × 3 ) = 0 6 B y − 45 − 15 × 4 = 0 B y = 17.5 kN Along the vertical direction: Determine the vertical reaction at point A by resolving the vertical component of forces. ∑ F y = 0 A y + B y − 10 × 3 − 1 2 × 10 × 3 = 0 (1) Substitute 17.5 kN for B y in Equation (1). A y + 17.5 − 30 − 15 = 0 A y = 27.5 kN Shear force at point C : Consider right side section at the point C . Sketch the free-body diagram of the section BC as in Figure 2. Along the vertical l direction: Determine the shear force at point C by resolving the vertical component of forces. ∑ F y = 0 V C + B y − 1 2 × 10 3 × 1.5 × 1.5 = 0 (2) Substitute 17.5 kN for B y in equation (2). V C + 17.5 − 3.75 = 0 V C = − 13.75 kN T-Beam cross section: Sketch the cross section of the T-beam as shown in Figure 3. Calculation: Refer Figure 3. Consider the cross-section area consists of rectangles 1 and 2. The width and depth of the rectangle 1 are b 1 = 30 mm and d 1 = 150 mm . The width and depth of the rectangle 2 are b 2 = 150 mm and d 2 = 30 mm . Consider the distance from the bottom of the section to the centroid of rectangle 1, 2 as y 1 and y 2 . Consider the area of the rectangle 1 and 2 as A 1 and A 2 . Here, A 1 = b 1 d 1 = 30 × 150 = 4 , 500 mm 2 y 1 = 75 mm A 2 = b 2 d 3 = 150 × 30 = 4 , 500 mm 2 y 2 = 165 mm The location of the neutral axis is at a dstance y ¯ from the bottom of thesection. Calculate the depth of neutral axis, y ¯ using the relation: y ¯ = ∑ A y ∑ A = A 1 y 1 + A 2 y 2 A 1 + A 2 (3) Substitute 4 , 500 mm 2 for A 1 , 75 mm for y 1 , 4 , 500 mm 2 for A 2 , and 165 mm for y 2 in Equation (3). y ¯ = 4 , 500 × 75 + 4 , 500 × 75 4 , 500 + 4 , 500 = 120 mm Calculate the moment of inertia of the T-beam using the relation: I = b 1 d 1 3 12 + A 1 ( y ¯ − y 1 ) 2 + b 2 d 2 3 12 + A 2 ( y ¯ − y 2 ) 2 (4) Substitute 30 mm for b 1 , 150 mm for d 1 , 4 , 500 mm 2 for A 1 , 75 mm for y 1 , 120 mm for y ¯ , 150 mm for b 2 , 30 mm for d 2 , 4 , 500 mm 2 for A 2 , and 165 mm for y 2 in Equation (4)

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Chapter 7.2, Problem 7.25P

To determine

The maximum shear stress in the T-beam at section C.

To show: the result on a volume element at this point.

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Chapter 7.2, Problem 7.24P

Chapter 7.2, Problem 7.26P

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Chapter 7 Solutions

MECHANICS OF MATERIALS-TEXT

Ch. 7.2 - In each case, calculate the value of Q and t that...Ch. 7.2 - If the beam is subjected to a shear force of V =...Ch. 7.2 - Determine the shear stress at points A and B if...Ch. 7.2 - Determine the absolute maximum shear stress in the...Ch. 7.2 - If the beam is subjected to a shear force of V =20...Ch. 7.2 - If the beam is made from four plates and subjected...Ch. 7.2 - If the wide-flange beam is subjected to a shear of...Ch. 7.2 - If the wide-flange beam is subjected to a shear of...Ch. 7.2 - If the wide-flange beam is subjected to a shear of...Ch. 7.2 - Prob. 7.4P

Ch. 7.2 - Prob. 7.5P Ch. 7.2 - The wood beam has an allowable shear stress of...Ch. 7.2 - The shaft is supported by a thrust bearing at A...Ch. 7.2 - The shaft is supported by a thrust bearing at A...Ch. 7.2 - Determine the largest shear force V that the...Ch. 7.2 - If the applied shear force V = 18 kip, determine...Ch. 7.2 - The overhang beam is subjected to the uniform...Ch. 7.2 - *7-12. The beam has a rectangular cross section...Ch. 7.2 - Determine the maximum shear stress in the strut if...Ch. 7.2 - Determine the maximum shear force V that the strut...Ch. 7.2 - 7-15. The strut is subjected to a vertical shear...Ch. 7.2 - Prob. 7.16P Ch. 7.2 - If the beam is subjected to a shear of V=15 kN,...Ch. 7.2 - If the wide-flange beam is subjected to a shear of...Ch. 7.2 - If the wide-flange beam is subjected to a shear of...Ch. 7.2 - Prob. 7.20P Ch. 7.2 - If the beam is made from wood having an allowable...Ch. 7.2 - Determine the shear stress at point B on the web...Ch. 7.2 - Determine the maximum shear stress acting at...Ch. 7.2 - Prob. 7.24P Ch. 7.2 - 7-25. Determine the maximum shear stress in the...Ch. 7.2 - 7-26. The beam has a square cross section and is...Ch. 7.2 - The beam is slit longitudinally along both sides....Ch. 7.2 - The beam is to be cut longitudinally along both...Ch. 7.2 - The beam has a rectangular cross section and is...Ch. 7.2 - The beam in Fig.6-48f is subjected to a fully...Ch. 7.3 - The two identical boards are bolted together to...Ch. 7.3 - Two identical 20-mm-thick plates are bolted to the...Ch. 7.3 - The boards are bolted together to form the...Ch. 7.3 - The boards are bolted together to form the...Ch. 7.3 - Prob. 7.32P Ch. 7.3 - Prob. 7.33P Ch. 7.3 - Prob. 7.34P Ch. 7.3 - Prob. 7.35P Ch. 7.3 - Prob. 7.36P Ch. 7.3 - Prob. 7.37P Ch. 7.3 - Prob. 7.38P Ch. 7.3 - A beam is constructed from three boards bolted...Ch. 7.3 - The simply supported beam is built up from three...Ch. 7.3 - The simply supported beam is built up from three...Ch. 7.3 - The T-beam is constructed as shown. If each nail...Ch. 7.3 - Prob. 7.43P Ch. 7.3 - Prob. 7.44P Ch. 7.3 - Prob. 7.45P Ch. 7.3 - 7–46. The beam is subjected to a shear of V = 800...Ch. 7.3 - The beam is made from four boards nailed together...Ch. 7.3 - The beam is made from three polystyrene strips...Ch. 7.5 - A shear force of V=300 kN is applied to the box...Ch. 7.5 - A shear force of V=450 kN is applied to the box...Ch. 7.5 - A shear force of V = 18 kN is applied to the box...Ch. 7.5 - A shear force of V = 18 kN is applied to the box...Ch. 7.5 - The aluminum strut is 10 mm thick and has the...Ch. 7.5 - The aluminum strut is 10 mm thick and has the...Ch. 7.5 - Prob. 7.56P Ch. 7.5 - Prob. 7.57P Ch. 7.5 - Prob. 7.58P Ch. 7.5 - Prob. 7.59P Ch. 7.5 - The built-up beam is formed by welding together...Ch. 7.5 - The assembly is subjected to a vertical shear of V...Ch. 7.5 - 7–62. Determine the shear-stress variation over...Ch. 7.5 - 7–63. Determine the location e of the shear...Ch. 7.5 - Determine the location e of the shear center,...Ch. 7.5 - The beam supports a vertical shear of V=7 kip....Ch. 7.5 - The stiffened beam is constructed from plates...Ch. 7.5 - The pipe is subjected to a shear force of V=8 kip....Ch. 7.5 - *7–68. A thin plate of thickness t is bent to form...Ch. 7.5 - A thin plate of thickness t is bent to form the...Ch. 7.5 - 7–70. Determine the location e of the shear...Ch. 7 - The beam is fabricated from four boards nailed...Ch. 7 - The T-beam is subjected to a shear of V = 150 kN....Ch. 7 - The member is subject to a shear force of V = 2...Ch. 7 - Determine the shear stress at points B and C on...Ch. 7 - Determine the maximum shear stress acting at...

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The maximum shear stress in the T-beam at section C. To show: the result on a volume element at this point.

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Chapter 7 Solutions

The maximum shear stress in the T-beam at section C.

To show: the result on a volume element at this point.