Problem 256
Three rods, each of area 250 mm2, jointly support a 7.5 kN load, as shown in Fig. P-256. Assuming that there was no slack or stress in the rods before the load was applied, find the stress in each rod. Use Est = 200 GPa and Ebr = 83 GPa.
Geometric Progression, GP
Geometric progression (also known as geometric sequence) is a sequence of numbers where the ratio of any two adjacent terms is constant. The constant ratio is called the common ratio, r of geometric progression. Each term therefore in geometric progression is found by multiplying the previous one by r.
Eaxamples of GP:
Arithmetic Progression, AP
Definition
Examples of arithmetic progression are:
Pythagorean Theorem
In any right triangle, the sum of the square of the two perpendicular sides is equal to the square of the longest side. For a right triangle with legs measures $a$ and $b$ and length of hypotenuse $c$, the theorem can be expressed in the form
Formulas in Plane Trigonometry
The quadratic formula
give the roots of a quadratic equation which may be real or imaginary. The ± sign in the radical indicates that
where x1 and x2 are the roots of the quadratic equation ax2 + bx + c = 0. The sum of roots x1 + x2 and the product of roots x1·x2 are common to problems involving quadratic equation.
The roots of a quadratic equation ax2 + bx + c = 0 is given by the quadratic formula
The derivation of this formula can be outlined as follows:
See the derivation below.
Formulas in Algebra
Derivation of Formulas
Problem 255
Shown in Fig. P-255 is a section through a balcony. The total uniform load of 600 kN is supported by three rods of the same area and material. Compute the load in each rod. Assume the floor to be rigid, but note that it does not necessarily remain horizontal.
