SS-V: 1120 Simply Supported Beam with Mid-span Load

Test No. VS13 Find the max displacement and stress for a pinned beam with load at the midpoint.

Definition



Figure 1.

The units are SI.

Results

The reference solution for max displacement is given by:(1)
δ m a x = F L 3 48 E I   MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiabes7aKnaaBa aaleaaqaaaaaaaaaWdbiaad2gacaWGHbGaamiEaaWdaeqaaOWdbiab g2da9maalaaabaGaamOraiaaykW7caWGmbWaaWbaaSqabeaacaaIZa aaaaGcbaGaaGinaiaaiIdacaaMc8UaamyraiaaykW7caWGjbaaaiaa cckaaaa@475A@
Where,
I = b h 3 12   MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamysaiabg2da9maalaaabaGaamOyaiaaykW7caWGObWaaWbaaSqa beaacaaIZaaaaaGcbaGaaGymaiaaikdaaaGaaiiOaaaa@3EDB@
The reference solution for max displacement is given by:(2)
σ m a x = F L 4 Z   MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZnaaBa aaleaaqaaaaaaaaaWdbiaad2gacaWGHbGaamiEaaWdaeqaaOWdbiab g2da9maalaaabaGaamOraiaaykW7caWGmbaabaGaaGinaiaaykW7ca WGAbaaaiaacckaaaa@437E@
Where,
Z = b h 2 6   MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOwaiabg2da9maalaaabaGaamOyaiaaykW7caWGObWaaWbaaSqa beaacaaIYaaaaaGcbaGaaGOnaaaacaGGGcaaaa@3E33@
The following table summarizes the displacement and stress results.
  Reference SimSolid % Difference
Max Displacement [mm] 1.0714E+00 1.0764E+00 0.46%
Max Stress [MPa] 1.5000E+02 1.5011E+02 0.07%