[ A_n = A_g - \sum (d_h \cdot t) + \sum \left( \frac{s^2}{4g} \cdot t \right) ]
This manual provides detailed step-by-step solutions for end-of-chapter problems. Solutions follow the AISC Specification for Structural Steel Buildings (ANSI/AISC 360) – current edition. References to provisions (e.g., Section D2, Table D3.1) refer to the AISC Specification. Chapter 2: Tension Members Problem 2.17 (Sample Problem) solution manual steel structures design and behavior
Tension member connected to gusset plate – check block shear along bolt group. [ A_n = A_g - \sum (d_h \cdot
So ( R_n = 191 \text{ kips} ) (lower governs). This is much higher than tensile fracture or yielding – thus block shear does not control. Chapter 2: Tension Members Problem 2
[ P_{n, yielding} = F_y \cdot A_g = 36 \cdot 3.75 = 135 \text{ kips} ]
[ A_{gv} = 2 \times ( \text{shear length along bolt line}) \times t = 2 \times 7.5 \times 0.5 = 7.5 \text{ in}^2 ] [ A_{nv} = A_{gv} - 2 \times (2.5 \times d_h \times t) \quad \text{(2.5 holes per shear plane)} = 7.5 - 2 \times (2.5 \times 1.0 \times 0.5) = 7.5 - 2.5 = 5.0 \text{ in}^2 ] [ A_{nt} = ( \text{gage} - d_h) \times t = (2.0 - 1.0) \times 0.5 = 0.5 \text{ in}^2 ]
For L4×4×½: ( \bar{x} = 1.13 \text{ in} ) (from AISC Manual). Length of connection ( L ) = distance between first and last bolt = 2 pitches = 6 in.