The simply supported beam consists of a W530 × 66 structural steel wide-flange shape [E = 200 GPa; I = 351 × 106 mm4]. Assume w = 50 kN/m, L1 = 2.8 m, and L2 = 2.2 m. For the loading shown, determine: (a) the beam deflection at point B. (b) the beam deflection at point D. Determine the component of the beam deflection at point B due to only the portion of the uniformly distributed load w between the supports at point A and point C.
The simply supported beam consists of a W530 × 66 structural steel wide-flange shape [E = 200 GPa; I = 351 × 106 mm4]. Assume w = 50 kN/m, L1 = 2.8 m, and L2 = 2.2 m. For the loading shown, determine: (a) the beam deflection at point B. (b) the beam deflection at point D. Determine the component of the beam deflection at point B due to only the portion of the uniformly distributed load w between the supports at point A and point C.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Question
The simply supported beam consists of a W530 × 66 structural steel wide-flange shape [E = 200 GPa; I = 351 × 106 mm4]. Assume w = 50 kN/m, L1 = 2.8 m, and L2 = 2.2 m. For the loading shown, determine:
(a) the beam deflection at point B.
(b) the beam deflection at point D.
Determine the component of the beam deflection at point B due to only the portion of the uniformly distributed load w between the supports at point A and point C.
Answer: vB1 = mm.
(a) the beam deflection at point B.
(b) the beam deflection at point D.
Determine the component of the beam deflection at point B due to only the portion of the uniformly distributed load w between the supports at point A and point C.
Answer: vB1 = mm.
Part 2
Determine the magnitude of the bending moment at point C (report a positive number) due to only the portion of the uniformly distributed load w between point C and point D.
Answer: MC = kN-m.
Answer: MC = kN-m.
Part 3
Determine the component of the beam deflection at point B due to the moment produced at point C by the portion of the uniformly distributed load w between point C and point D.
Answer: vB2 = mm.
Answer: vB2 = mm.
Part 4
Determine the total beam deflection at point B due to the combined effects of the uniformly distributed load w between the supports at point A and point C and the uniformly distributed load w between point C and point D.
Answer: vB = mm.
Answer: vB = mm.
Part 5
Determine the component of the rotation angle of the beam at point C due to only the portion of the uniformly distributed load w between the supports at point A and point C.
Answer: θC1= rad.
Answer: θC1= rad.
Part 6
Determine the component of the beam deflection at point D produced by the component of the rotation angle of the beam at point C due to only the portion of the uniformly distributed load w between the supports at point A and point C.
Answer: vD1 = mm.
Answer: vD1 = mm.
Part 7
Determine the component of the beam rotation angle at point C due to the moment produced at point C by the portion of the uniformly distributed load w between point C and point D.
Answer: θC2= rad.
Answer: θC2= rad.
Part 8
Determine the component of the beam deflection at point D due to the moment produced at point C by the portion of the uniformly distributed load w between point C and point D.
Answer: vD2 = mm.
Answer: vD2 = mm.
Part 9
Determine the cantilever deflection of the beam at point D due to the portion of the uniformly distributed load w between point C and point D. This is the deflection that would be calculated at point D assuming a fixed support at C and the distributed load w between C and D.
Answer: vD3 = mm.
Answer: vD3 = mm.
Part 10
Determine the total beam deflection at point D.
Answer: vD = mm.
Answer: vD = mm.
Transcribed Image Text:A
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