VM131

VM131
Acceleration of a Rotating Crane Boom

Overview

Reference:	F. P. Beer, E. R. Johnston, Jr., Vector Mechanics for Engineers, Statics and Dynamics, 5th Edition, McGraw-Hill Book Co., Inc., New York, NY, 1962, pg. 616, problem 15.13.
Analysis Type(s):	Static Analysis (ANTYPE = 0)
Element Type(s):	Structural Mass Elements (MASS21)
Input Listing:	vm131.dat

Test Case

Determine the acceleration at the tip P of a crane boom that has a constant angular velocity cab rotation (Ω) while being raised with a constant angular velocity (ω).

Figure 184: Rotating Crane Boom Problem Sketch

Geometric Properties

d = 34.64 ft

h = 20 ft

Ω = 0.3 rad/sec

ω = 0.5 rad/sec

Analysis Assumptions and Modeling Notes

Consider X', Y', Z' as the fixed reference coordinate system. The global Cartesian coordinate system (XYZ) is taken as attached to the cab which rotates at an angular velocity of Ω about the Y'-axis of the reference coordinate system. The boom angular velocity ω is applied about the global Z-axis. The Coriolis effect due to the rotation of the cab is modeled by putting a mass of 1 lb-sec²/ft (without rotary inertia) at point P, and constraining its degrees of freedom. The reaction forces at the mass then give the acceleration components.

Results Comparison

	Target	Mechanical APDL [1]	Ratio
a_x , ft/sec²	-11.78	-11.78	1.00
a_y , ft/sec²	-5.00	-5.00	1.00
a_z , ft/sec²	6.00	6.00	1.00

a_x, a_y, a_z are given by the reaction forces at node 1 (FX, FY, FZ respectively).