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ME 323 – Mechanics of Materials Examination # 2 November 5 th, 2020 Name (Print) ______________________________________________ (Last) (First) PROBLEM # 1 (25 points) A simply supported beam AH is subject to a constant distributed load q over the section BC, a moment M 0 and a concentrated force P at D. The cross section of the beam is shown below. The parameters are following: L =8 ft., q =10 lb/ft, M 0 =40 lb×ft, P =10 lb, b = 2 in. a) Draw the shear force and bending moment diagrams. Mark the values at the cross sections A, B, C, D, and H, and the maximum and minimum values along the beam. b) Determine the stress state at the points M and N which are located at the cross section C. Sketch their stress state on the given stress elements. 𝑞 𝑀 0 𝐿/ 4 𝐿/^4 𝐿/^4 𝑥 𝑦 A B C 𝐿/ 4 D H 𝑥 𝑥 𝑉 𝑥 𝑀 𝑥 0 0 𝑦 𝐂𝐫𝐨𝐬𝐬 𝐬𝐞𝐜𝐭𝐢𝐨𝐧 𝑏 𝑧
- 2 𝑏 𝑏 𝑧 𝑥 𝑦 Stress element M M 𝑃 N
- 2 𝑏 𝑧 𝑥 𝑦 Stress element N
ME 323 – Mechanics of Materials Examination # 2 November 5 th, 2020 Name (Print) ______________________________________________ (Last) (First) PROBLEM # 1
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ME 323 Examination # 2 AM SOLUTION Page 2 of 4 PROBLEM #4 ( continued) Part B – 8 points The loading on the beam shown below is not provided in the figure. The shear force V ( x ) for the beam is given below the beam, with the shear force being provided in terms of kips and the position variable x in ft. In addition, it is known that the bending moment at the left end is M (0) = 0, and there are no concentrated couples applied to the beam at any locations except, possibly, at H. For the shear force diagram provided: a) Draw the bending diagram M ( x ) on the axes provided. b) Show the loading on the beam in the figure below. No justification is needed for your answers. B (^) C D H
x
V (^) ( x ) 0 20 − 20 − 40 40
x
M (^) ( x ) 0 0 1_._ 5 3 6 9 60 − 30 40 80 / 3 20 40 20
ME 323 Examination # 2 AM SOLUTION Page 3 of 4 x M (^) ( x ) 0 20 40 − 20 − 40 Y Z a beam cross-section PROBLEM #4 ( continued) Part C – 6 points The bending moment diagram for a loaded beam is shown below. The beam is known to have the triangular cross section shown below. Provide a justification for each answer. a) At what location(s) on the beam does the maximum tensile normal stress exist? Provide both x and Y components of the location of this point(s). You are not asked to solve for this value of stress. b) At what location(s) on the beam does the maximum compressive normal stress exist? Provide both x and Y components of the location of this point(s). You are not asked to solve for this value of stress. At location B along beam: M = 40
- At Y = 0: σ = M (^) ( − a / (^3) ) I
a I ( t ensile )
- At Y = a : σ = M (^) ( 2 a / (^3) ) I
a I ( compressive ) At location C along beam: M = 20
- At Y = 0: σ = M (^) ( − a / (^3) ) I
a I ( c ompressive )
- At Y = a : σ = M (^) ( 2 a / (^3) ) I
a I ( t ensile ) Y Z a beam cross-section
x
M (^) ( x ) 0 20 40 − 20 − 40
A B C D H
