Asked Oct 13, 2019

The simply supported wooden beam has a pin at A and a roller at B. A triangular distributed load starting at 0 kips/ft at point A and increasing to 0.8 kips/ft at point B, 9 feet from the end of the beam, is applied to the beam as shown. Also, a 15 kip point load is applied to the beam at point C at the far right end of the beam, 18 feet from point A. The beam cross section measures 6 inches in width, and 12 inches in depth as shown. The modulus of elasticity for the wood is 1600 ksi. Let x=0 at point A and increase to the right (positive to the right).Given the above information and using the double integration method, find:

  • Slope at point A 
  • Slope at point C at the far right end of the beam
  • Deflection at point C, at the far right end of the beam


12 in

Image Transcriptionclose

I5kips 08Kpo/F 12 in A lbin BEAM CROSs-SECTTON


Expert Answer

Step 1

Consider the cantilever beam as ABC.

Sketch the Free Body Diagram as shown below.


Image Transcriptionclose

I5kips 0ekp/F C A RB 'R

Step 2

Refer to Figure.

Use equilibrium equations:


Image Transcriptionclose

ΣΜ,-0 5-18-9-08- 29- -R,x9 0 3 15x18+x9 x 0.8x - R 32.4kips +Υ ΣΕ=0 1 x9x0.8 32.4 15 0 R 13.8kips Moment of inertia of the beam. bd2 I = 12 6x12 12 =864in. Flexural rigidity, EI = 1600ksix 864 in. 1382.4x10 k-in.

Step 3

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