# Finding the deflection using the unit load method.

by willnich35
 P: 7 1. The problem statement, all variables and given/known data A uniform beam, supported by a uniform strut, is loaded as shown in Figure (Attached). Using the unit load method, determine the value of the vertical deflection at C. BEAM: E = 205 kN/mm2, I = 90 x 106 mm4. STRUT: E = 205 kN/mm2, A = 1500 mm2. 2. Relevant equations The virtual work equation, which is. 1.$$\Delta$$=$$\sum$$p$$\frac{PL}{AE}$$+$$\int$$$$\frac{mM}{EI}$$dx 3. The attempt at a solution REAL Reactions at A and B in the x and y directions: Fx = Ax + Bx = 0 Fy = Ay + 15 + (4*2) - By = 0 Mb = (15*2) - 8 - 2Ay = 0 Ay = 11 kN By = 34 kN Ax = Bx = 17 * SqRt(2) Axial Force (P) in member AB = 17 * SqRt(2) DB = 34 * SqRt(2) VIRTUAL Reactions Apply a force of 1 kN downwards at C Axial Force (p) in member AB = -2 DB = 2 * SqRt(2) I then attempted to solve the virtual work equation, however the value of A for member AC is not given. So i guess my questions are, have I started this correctly, and how do I solve the problem? Attached Thumbnails
 P: 7 Finding the deflection using the unit load method. I have an answer, which makes sense. I would greatly appreciate it if you would check it over. Ay = -11 kN By = 34 kN Ax = Bx = 34 * SqRt(2) Axial Force (P) in member DB = 34 * SqRt(3) VIRTUAL Reactions Axial Force (p) in member DB = 2 * SqRt(3) $$\frac{pPL}{AE}$$ = 1.876mm (Deflection due to axial load on DB) $$\int$$$$\frac{(-x1)(-11x1)}{EI}$$dx1 + $$\int$$$$\frac{(-x2)(-15x2)}{EI}$$dx2 Integrating between 0 and 2 for both x1 and x2 = 3.758mm (Deflection due to bending moments in beam) TOTAL DEFLECTION = 5.634mm Downwards