Problem 869 | Deflection by Three-Moment Equation Jhun Vert Sat, 04/25/2020 - 03:56 pm

Problem 869
Find the value of EIδ at the center of the first span of the continuous beam in Figure P-869 if it is known that M2 = -980 lb·ft and M3 = -1082 lb·ft.
 

869-continuous-beam.gif

 

Problem 868 | Deflection by Three-Moment Equation Jhun Vert Sat, 04/25/2020 - 03:54 pm

Problem 868
Determine the values of EIδ at midspan and at the ends of the beam loaded as shown in Figure P-868.
 

868-simple-overhanging-beam-triangular-load.gif

 

Problem 866 | Deflection by Three-Moment Equation Jhun Vert Sat, 04/25/2020 - 03:48 pm

Problem 866
Determine the midspan value of EIδ for the beam shown in Fig. P-866.
 

866-simple-beam-moment-triangular.gif

 

Problem 865 | Deflection by Three-Moment Equation Jhun Vert Sat, 04/25/2020 - 03:46 pm

Problem 865
For the beam shown in Fig. P-865, compute the value of EIδ at x = 6 ft and at the end of the overhang.
 

865-simple-beam-overhang.gif

 

Problem 864 | Deflection by Three-Moment Equation Jhun Vert Sat, 04/25/2020 - 03:43 pm

Problem 864
An 18-ft beam, simply supported at 4 ft from each end, carries a uniformly distributed load of 200 lb/ft over its entire length. Compute the value of EIδ at the middle and at the ends.
 

Problem 863 | Deflection by Three-Moment Equation Jhun Vert Sat, 04/25/2020 - 03:10 pm

Problem 863
For the beam shown in Fig. P-863, determine the value of EIδ midway between the supports and at the left end.
 

863-verhang-beam-given.gif

 

Problem 862 | Deflection by Three-Moment Equation Jhun Vert Sat, 04/25/2020 - 03:07 pm

Problem 862
Determine the value of EIδ at B for the beam shown in Fig. P-862.
 

862-simple-beam-given.gif

 

Problem 860 | Deflection by Three-Moment Equation Jhun Vert Sat, 04/25/2020 - 01:38 pm

Problem 860
Determine the value of EIδ at the end of the overhang and midway between the supports for the beam shown in Fig. P-860.
 

860-overhang-beam-given.gif

 

Deflections Determined by Three-Moment Equation Jhun Vert Fri, 04/24/2020 - 11:54 pm

Summary of key points

  1. The three-moment equation can be applied at any three points in any beam. It will determine the relation among the moments at these points.
  2. The terms $6A\bar{a}/L$ and $6A\bar{b}/L$ refer to the moment diagram by parts resulting from the simply supported loads between any two adjacent points described in (1).
  3. The heights h1 and h3 from the equation
     

    $M_1L_1 + 2M_2(L_1 + L_2) + M_3L_2 + \dfrac{6A_1\bar{a}_1}{L_1} + \dfrac{6A_2\bar{b}_2}{L_2} = 6EI \left( \dfrac{h_1}{L_1} + \dfrac{h_3}{L_2} \right)$
     

    refer to the respective vertical distance of points 1 and 3 from point 2. The height h is positive if above point 2 and negative if below it.