A simply supported beam has 2 equal point loads (W/2)

  • Thread starter Thread starter SarahM1980
  • Start date Start date
  • Tags Tags
    Beam Point
Click For Summary
SUMMARY

The discussion focuses on deriving the mid-span deflection of a simply supported beam measuring 1.2m in length, subjected to two equal point loads (W/2) positioned 0.4m apart. The user has formulated the moment equation as m = W/2x - W/2(x-L/3) - W/2(x-L/6) and seeks confirmation or assistance in arriving at the deflection expression, which is suggested to be 23WL³ / 1296EI. Two methods are proposed for this derivation: using the equation w''(x) = M(x) / EI or employing the dummy force method.

PREREQUISITES
  • Understanding of beam theory and deflection analysis
  • Familiarity with the moment-curvature relationship in structural mechanics
  • Knowledge of the dummy force method for structural analysis
  • Proficiency in using the equation w''(x) = M(x) / EI for deflection calculations
NEXT STEPS
  • Study the derivation of beam deflection formulas using the moment-curvature relationship
  • Explore the dummy force method in detail for structural analysis
  • Learn about the application of the equation w''(x) = M(x) / EI in various loading scenarios
  • Investigate the effects of varying load positions on beam deflection
USEFUL FOR

Structural engineers, civil engineering students, and professionals involved in beam analysis and design will benefit from this discussion.

SarahM1980
Messages
1
Reaction score
0
I have a simply supported beam 1.2m long
it has 2 = point loads (W/2) at equal distances (0.4m) along the beam
i have been asked to derive from first principles the expression for the mid span defelction.
I have got so far m= W/2x - W/2(x-L3) - W/2(x-L/6)
and i think the answer I'm looking for is something like 23WL 3 / 1296EI


can anyone help!
 
Engineering news on Phys.org
You can either use the equation w''(x) = M(x) / EI , or a dummy force method (which I personally prefer more).
 

Similar threads

Allowable uniform loads - W beams vs. LVL
  • · Replies 2 ·
Replies
2
Views
4K
How Do You Calculate the Safe Work Load of a T Beam?
  • · Replies 1 ·
Replies
1
Views
2K
Engineering Bending Moment for Simply Supported, Overhanging Beam with two Overhangs
  • · Replies 4 ·
Replies
4
Views
4K
Deflection of partially loaded cantilever beam with non-homogeneous EI
  • · Replies 3 ·
Replies
3
Views
2K
Problem about Proof A simply supported beam
  • · Replies 2 ·
Replies
2
Views
3K
Calculating Beam Load Proportionality with Point Loads
  • · Replies 1 ·
Replies
1
Views
2K
Simply supported beam with a spring support in the middle - deflection
  • · Replies 6 ·
Replies
6
Views
4K
How Do You Calculate Deflection in a Simply Supported Overhanging Beam?
  • · Replies 3 ·
Replies
3
Views
10K
Engineering Deflection and Slope of a Simply Supported Beam
  • · Replies 8 ·
Replies
8
Views
3K
Beam with simple support at center
  • · Replies 1 ·
Replies
1
Views
4K