SAMPLE CALCULATIONS

Compressive stress = applied force / cross sectional area

d (capped cylinder) = (64,720 lb) ¤ (pi C 5.99^2 / 4) = 2296.65 psi

Shear stress = applied force / cross sectional area

d (large beam) = (10, 430 lb) / (6” x 6”) = 289.72 psi

Tensile stress (split cylinder test) = (2 X applied force) / (pi X L X D)

d (tensile) = (2 X 38,000 lb) / (pi X 11.75” X 6.03”) = 341.44 psi

Modulus of rupture (3 point load) = s = Mc / I = (PL/4 X h/2) / ( bh^2 / 12)

MOR (large beam) = (3PL / 2bh^2) = ( 3 X 10, 430 X 20.38”) / (2 X 6.15” X 6.06^2”) = 1411.76 psi

Modulus of rupture (4 point load) = s = Mc / I = ( PL/6 X h/2) / (bh^3 / 12)

MOR (small beam #2) = (PL / bh^2) = (1088.5 lb X 18”) / (3 X 2.98^2”) = 735.44 psi

Beam theory (large beam) = t = VQ / Ib = (Vbh^2 / 8) / (bh^3b / 12) = 3V / 2bh

3 (20.38” X 6.06” X 6.15”) / 2 (6.06”)(6.15”) = 30.57 in.

Non-beam theory = t = V/A = P / 2bh

1199 lb / (2 X 2.84” X 3.09”) = 68.31 psi

E = 33(unit weight) ^3/2 (fc)^1/2

Ex. w/ silica

E = 33 [ ( 29.2 lb X 4) / (pi X (11.75 in /12”/ft) X ( 6.03”/ 12”/ft)^2 ]^3/2 X (173100)^1/2 = 25.32 X 10^6 psi

Ex. w/o silica

E = 33 (29.41 lb X 4) / [ pi X (11.94”/12”/ft) X (6.05”/12”/ft)^2 ] ^3/2 (161800)^1/2 = 23.91 X 10^6 psi

E (experimental) = slope = s/e = (80000-20000) / (.138-.115) = 2.61 X 10^6 psi