The simply supported beam consists of a W530 × 66 structural steel wide-flange shape [E = 200 GPa; I = 351 × 10⁶ mm⁴]. Assume w = 45 kN/m, L₁ = 2.6 m, and L₂ = 2.6 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: v_B₁ = 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: M_C = 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: v_B₂ = 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: v_B = 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.

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: v_D₁ = 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.

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: v_D₂ = 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: v_D₃ = mm.

Part 10

Determine the total beam deflection at point D.

Answer: v_D = mm.

Question

The simply supported beam consists of a W530 × 66 structural steel wide-flange shape [E = 200 GPa; I = 351 × 10⁶ mm⁴]. Assume w = 45 kN/m, L₁ = 2.6 m, and L₂ = 2.6 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: v_B₁ = 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: M_C = 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: v_B₂ = 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: v_B = 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.

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: v_D₁ = 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.

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: v_D₂ = 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: v_D₃ = mm.

Part 10

Determine the total beam deflection at point D.

Answer: v_D = mm.

Accepted Answer

Answered: Image /qna-images/answer/cd3de88e-42a6-4689-839c-ed803572f5ad.jpg