SS-V:1120 中間点に荷重がかかる単純支持された梁

テスト番号VS13中間点に荷重がかかるピン留めされた梁に対する最大変位と応力を求めます。

定義



図 1.

単位はSIです。

結果

最大変位に対する基準解は以下のように与えられます:(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@
ここで、
I = b h 3 12   MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamysaiabg2da9maalaaabaGaamOyaiaaykW7caWGObWaaWbaaSqa beaacaaIZaaaaaGcbaGaaGymaiaaikdaaaGaaiiOaaaa@3EDB@
最大変位に対する基準解は以下のように与えられます:(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@
ここで、
Z= b h 2 6   MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOwaiabg2da9maalaaabaGaamOyaiaaykW7caWGObWaaWbaaSqa beaacaaIYaaaaaGcbaGaaGOnaaaacaGGGcaaaa@3E33@
以下の表は、変位と応力の結果をまとめたものです。
  基準 SimSolid %差異
最大変位 [mm] 1.0714E+00 1.0764E+00 0.46%
最大応力 [MPa] 1.5000E+02 1.5011E+02 0.07%