c) A thin-walled, cantilever beam supports two shear loads, one in the horizontal plane at its free end and a second in the vertical plane halfway along its span as shown in Figure Q3.2. Cross-section dimensions are shown in Figure Q3.2 as well. Assume that the shear loads are such that no twisting of the beam occurs. All the panels have thickness 2 mm. 50 mm 1000 mm 25 mm 50 mm 6 3 200 N www juu 50 mm Figure Q3.2 4 25 mm 8 400 N 500 mm

c) A thin-walled, cantilever beam supports two shear loads, one in the horizontal plane at its free end and a second in the vertical plane halfway along its span as shown in Figure Q3.2. Cross-section dimensions are shown in Figure Q3.2 as well. Assume that the shear loads are such that no twisting of the beam occurs. All the panels have thickness 2 mm. 50 mm 1000 mm 25 mm 50 mm 6 3 200 N www juu 50 mm Figure Q3.2 4 25 mm 8 400 N 500 mm

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter4: Shear Forces And Bending Moments

Section: Chapter Questions

Problem 4.3.8P: At a full d raw, an archer applies a pull of 130 N to the bowstring of the bow shown in the figure....

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Example 5: Draw the shear force and bending moment diagrams for the simply supported beam as shown below. 400 N 500 N 300 N A 3m 4m 4m 5m
Two orientations of a 1 m length cantilever beam are to be considered as shown in Figure Q2(a). The beam is loaded with a uniformly distributed load w. The dimensions of the cross-section are shown in Figure Q2(b). (a) Choose the orientation that will support the highest amount of w if the allowable bending stress (in tension and compression) is 250 MPa.
A simply supported beam which has 16 mm height and 8 mm thickness is supported by pin at A and roller at F as shown in Figure Q2. Loading are applied at B, C, D and E, respectively. 20 KN 20 kN 20 kN 20 kN 8 x 16 mm E F A B 1 m 1 m 1 m 1m 1m Figure Q2: Simply suoported beam ACDEFB. (c) Draw the shear force diagram (SFD) of the beam and show your calculations. 000
For the problem shown below (left), W = 51 lbs while L1 = 4.4 inches and L2 = 12 inches. This results in the shear force diagram as shown on the right, where A, is the reaction force in the vertical direction at point A. Based on this shear diagram, what is the maximum moment in the portion of the horizontal beam from x = O to x = L1 in units of lb-in to two decimal places. (Be sure to use a negative sign to designate a negative moment if necessary.) A |--L1-——————— L2 Ay lb 0 -Ay lb W L1 L2 W -L1- BO L1- -X
Example (5): Draw the shear force and bending moment diagrams for the beam shown in Figure (2.13). 6 kN 4 kN/m Hinge D 3m 3m 2m 3m Figure (2.13)
beam ABCDE is 5 m in length and loaded as shown in Figure Q3. Draw the S.F. and B.M. diagrams for the beam, indicating all major values. Find also the value of the maximum bending stress if the beam section is rectangular 30 mm width by 60 mm depth. 3 kN 10 kNm 3 kN/m A E 1 m 1 m 1 m 2 m Figure Q2: Beam Loading
Figure Q2 shows the cross section of a beam. The beam is simply supported over a span of 6 m and carries a vertical point load of 40 kN acting at its mid-span. Calculate The position of the horizontal centroidal axis of the cross-section from its bottom. The second moment area of the cross-section about the horizontal centroidal axis The maximum shear load per unit length (metre) at the lower surface of the top flange
For the simply supported beam subjected to the loading shown, derive equations for the shear force Vand the bending moment M for any location in the beam. (Place the origin at point A.) Let a=2.50 m, b=4.25 m, PB = 45kN, and Pc = 90kN. Construct the shear- force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise. Answers: Ay = Dy= Mi i B Calculate the reaction forces Ay and Dy acting on the beam. Positive values for the reactions are indicated by the directions of the red arrows shown on the free-body diagram below. (Note: Since Ax = 0, it has been omitted from the free-body diagram.) PB a PB B a Pc a Pc C kN b KN b D X D₂ X
For the simply supported beam subjected to the loading shown, derive equations for the shear force V and the bending moment M for any location in the beam. (Place the origin at point A.) Let a-3.25 m, b=4.75 m, Pg - 35kN, and Pc = 80kN. Construct the shear- force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise. A Ay- 58.66 - Dy- Calculate the reaction forces A, and Dy acting on the beam. Positive values for the reactions are indicated by the directions of the red arrows shown on the free-body diagram below. (Note: Since Ax = 0, it has been omitted from the free-body diagram.) Answers: a 56.33 (a) V= (b) V- (c) V- B i i PB B kN с kN C Determine the shear force acting at each of the following locations: (a) x-2m (b)x - 4 m (c) x-8 m Note that x = 0 at support A. When entering your answers, use the shear-force sign convention detailed in Section 7.2. 3 3 3 KN D b kN D ·x Dy
For the simply supported beam subjected to the loading shown, derive equations for the shear force Vand the bending moment M for any location in the beam. (Place the origin at point A.) Let a=2.75 m, b=5.00 m, PB = 60KN, and Pc = 80kN. Construct the shear- force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise. Answers: Ay = Dy= tel tel a i B a Calculate the reaction forces Ay and Dy acting on the beam. Positive values for the reactions are indicated by the directions of the red arrows shown on the free-body diagram below. (Note: Since Ax = 0, it has been omitted from the free-body diagram.) PB B a PB Pc a C Pc C KN b KN D b D X D₂ X
For the simply supported beam subjected to the loading shown, derive equations for the shear force V and the bending moment M for any location in the beam. (Place the origin at point A.) Let a=2.75 m, b=5.00 m, PB = 60kN, and Pc = 80kN. Construct the shear- force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise. Answers: Ay = a Dy= a B Calculate the reaction forces Ay and Dy acting on the beam. Positive values for the reactions are indicated by the directions of the red arrows shown on the free-body diagram below. (Note: Since Ax = 0, it has been omitted from the free-body diagram.) 36.66 BO 103.33 PB a PB Pc a Pc KN b KN b D D x P X
A cross-section of a beam is shown in Figure Q2. If the shear force in this section is V 163 KN, determine the value and the location of the maximum shear stress in the section. In Figure Q2, a = 77 mm and the origin of the coordinate system is at centroid of the cross section. y= A Z= a mm; 2a mm; O 4a The vertical coordinate (y-coordinate; the y-axis serves as the axis of symmetry of the cross-section.) and horizontal coordinate (z-coordinate) of the location where the maximum shear stress occurs in the section are Figure Q2 3a a The vertical distance from the location where the maximum shear stress occurs in the section to the bottom side (AB) of the cross section can be calculated as Distance = mm