Problem 2 0 C 20kips w=5K/F+ E A K 4ft ift * Given: The support at A is fixed and the Support at E B Find: a roller. a) Determine the reactions at the support. b) Develop the equations describing the Variations in shear and moment for each member c) Sketch the shear and moment diagram each member.

Rigid AD rod in the figure, at points A and C with two vertical elastic bars articulated at the ends vertical from point D to P intensity while standing horizontal the force is affected. Elongation stiffness of ela stic bars EA and their length is L. According to this, a) The forcesthat will occurin the elastic bars, b) the displacement of the D point of the rigid bar, c) Calculate the support reaction at point B. EA,L A B D. EA.L rijit Fa + a 2a-

P Part 2: Solve for the reactions in terms of the loads, shear and moment at dis- tance "x" from the support, how the shear and moment diagram will look like, and the maximum moment togeth- RB RA er with its location. X Reactions X Shear and Moment Diagram RA = RB = X Shear at distance "x" from A at x - P Vy = RA – P =-P = V-d X Moment at distance "x" from A at x 2 M, = R,(x) – P M-d

1.3-4 Segments AB and BCD of beam ABCD are pin connected at x = 4 m. The beam is supported by a sliding support at A and roller supports at C and D (see figure). A triangularly distributed load with peak intensity of 80 N/m acts on BC. A concentrated moment is applied at joint D. (a) Find reactions at supports A, C, and D. (b) Find internal stress resultants N, V, and M at x = 5 m. (c) Repeat parts (a) and (b) for the case of the roller support at C replaced by a linear spring of stiff- ness k, 200 kN/m (see figure). 80 N/m 200 N-m at joint D A D 4 m B\ 4 m ; 3 m Pin connection Part (c) PROBLEM 1.3-4

1.3-4 Segments AB and BCD of beam ABCD are pin connected at x = 4 m. The beam is supported by a sliding support at A and roller supports at C and D (see figure). A triangularly distributed load with peak intensity of 80 N/m acts on BC. A concentrated moment is applied at joint D. (a) Find reactions at supports A, C, and D. (b) Find internal stress resultants N, V, and M at X = 5 m. (c) Repeat parts (a) and (b) for the case of the roller support at C replaced by a linear spring of stiff- ness ky = 200 kN/m (see figure). 80 N/m 200 N-m at joint D A 4 m B 4 m 3 m Part (c) Pin connection

P (kN) d (mm) t (mm) www 85 80 25 The beam in Figure Q2(a) has a cross-section as shown in Figure Q2(b), where the values of P, d and t are given in Table Q2. (a) Determine reactions, RA and Rg. (b) Determine the shear force at section AB and bending moment at point B. (c) Determine the neutral axis and moment of inertia of the cross section of the beam (d) Det hine the maximum tensile and compressive bending stress the beam at point B. (Formula: omax =). Then, plot the bending stress distribution. (e) Determine the maximum shear stress of at section AB. (Formula: T =). P (kN) t (m d (mm) 1.6 m 0.8 m d (mm) t (mm) t(mm) (a) Figure Q2

1.3-5 Segments AB and BCD of beam A BCD are pin connected at x = 3 m. The beam is supported by a pin support at A and roller supports at C and D; the roller at D is rotated by 30° from the x axis (see figure). A trapezoidal distributed load on BC varies in intensity from 74 N/m at B to 37 N/m at C. A con- centrated moment is applied at joint A, and a 180 N inclined load is applied at the mid-span of CD. (a) Find reactions at supports A, C, and D. (b) Find the resultant force in the pin connection at B. (c) Repeat parts (a) and (b) if a rotational spring (k, is removed. = 68 N m) is added at A and the roller at C 200 N·m at 1.5 m 1.5 m joint A 180 N 74 N/m 37 N/m 4 30° 3 m 3 m 3 m Part (c) Remove roller Pin connection at C in part (c)

indeterminate structures using the force method

1. Given: A structure shown below Find: (1) Determine the magnitudes and locations of the two distributed loadings. In other words, determine the magnitude and location of the loading between A and C, and those of the loading between D and B. (2) For the member DEB, (a) take the moment at B and find the reaction at E and (b) then find By by either Fy= 0, or EMp = 0. (Recall that support conditions at B and E are rollers, so there are no reactions in x-direction.) (3) For the whole structure, 3 unknown forces and moment at A (Ax, Ay and Ma) are the only unknowns. Determine those 3 unknowns at A. 900 N/m 900 N/m B A C D 2E - 3 m 3 m - 4 m - 3 m3 m-

The L-shaped arm ABCD shown in the figurelies in a vertical plane and pivots about a horizontalpin at A. The arm has a constant cross-sectional areaand total weight W. A vertical spring of stiffness ksupports the arm at point B.(a) Obtain a formula for the elongation of thespring due to the weight of the arm.(b) Repeat part (a) if the pin support at A is movedto D.