Static, Vibration Analysis and Sensitivity Analysis of Stepped Beams Using Singularity Functions

Table 1

Result comparison for static analysis.

Results	Simply supported beam		Intermediate roller-supported beam		Intermediate spring-supported beam
	FEM	Singularity	FEM	Singularity	FEM	Singularity
At 𝑥=30 in.
Deflection (in)	−4.109𝐸−2	−4.109𝐸−2	−1.161𝐸−3	−1.161𝐸−3	−3.872𝐸−2	−3.872𝐸−2
Slope (rad.)	3.053𝐸−3	3.053𝐸−3	1.421𝐸−5	1.421𝐸−5	2.873𝐸−3	2.873𝐸−3
Reactions (lbf)
𝑅1	262.5	262.5	47.940	47.940	249.747	249.747
𝑅3	N.A.		429.120	429.120	25.506	25.506
𝑅2	237.5	237.5	22.940	22.940	224.747	224.747