SCE FE Civil Complete Review Guide 2026–2027

4. Shear stress \( \tau=VQ/(Ib) \). For a rectangle the maximum is \( 1.5V/A \) at the neutral axis.
5. Mohr's circle: centre \( (\sigma_x+\sigma_y)/2 \), radius \( R=\sqrt{((\sigma_x-\sigma_y)/2)^2+\tau_{xy}^2} \). Principal stresses = centre \( \pm R \); maximum in-plane shear = \( R \) (CE-T1-03).
6. Generalized Hooke's law: \( \varepsilon_x=[\sigma_x-\nu(\sigma_y+\sigma_z)]/E \), and \( G=E/(2(1+\nu)) \).
7. Euler load \( P_{cr}=\pi^2EI/(KL)^2 \). Theoretical \( K \): pinned-pinned 1.0, fixed-free 2.0, fixed-fixed 0.5, fixed-pinned about 0.7 (CE-T1-04).
8. Slenderness ratio \( KL/r \) with \( r=\sqrt{I/A} \). The larger it is, the lower the critical stress \( \sigma_{cr}=\pi^2E/(KL/r)^2 \).
9. Loads: dead = weight of permanent elements; live = occupancy and use; wind pressure varies with height, exposure and building shape. Combinations and values come from the Saudi loads code (CE-T1-05).
10. Equilibrium: \( \sum F_x=0 \), \( \sum F_y=0 \), \( \sum M=0 \). Also \( dM/dx=V \) and \( dV/dx=-w \); maximum moment occurs where \( V=0 \) (CE-T1-06).
11. A planar truss is statically determinate when \( m+r=2j \) (members + reactions = twice the number of joints).
12. Method of joints: two equilibrium equations per joint. Method of sections: cut through at most three unknown members and write a moment or force balance (CE-T1-07).
13. Two non-collinear members at an unloaded joint are both zero-force. If two of three members are collinear at an unloaded joint, the third is zero-force.
14. An influence line shows the effect of a moving unit load on a reaction, shear or moment at one point. Its shape is the deflected shape after releasing the constraint by a unit displacement (Müller-Breslau) (CE-T1-08).
15. Standard deflections: cantilever tip load \( PL^3/(3EI) \); simple beam with midspan load \( PL^3/(48EI) \); simple beam with uniform load \( 5wL^4/(384EI) \) (CE-T1-09).
16. Virtual work for trusses: \( \Delta=\sum nNL/(AE) \), where \( n \) is the member force from a unit load at the joint, in the required direction (CE-T1-10).
17. Indeterminate structures: force (compatibility) method, slope-deflection, moment distribution. Fixed-end moments are \( wL^2/12 \) for uniform load and \( PL/8 \) for a midspan point load (CE-T1-11).

Common mistakes in this chapter

• ✕ Mixing up \( I \) and \( J \): \( I \) is for bending, and \( J \) (polar moment of inertia) is for torsion.
• ✕ Forgetting that shear stress in a rectangular section is zero at the top and bottom and peaks at the neutral axis (\( 1.5V/A \)).
• ✕ Using \( I \) about the strong axis for buckling. The column buckles about the weak axis (smallest \( I \)).
• ✕ Applying Euler's formula to a short column. It holds for slender columns whose stress stays in the elastic range.
• ✕ Counting with \( m+r-2j \) and forgetting that zero means statically determinate, not that the truss carries no force.
• ✕ Placing the moving load at one fixed spot instead of finding the critical position from the influence line, where the ordinate is largest.
• ✕ Confusing stiffness \( 4EI/L \) (far end fixed) with \( 3EI/L \) (far end pinned) in moment distribution.
• ✕ Using virtual work without placing a unit load at the required point and in the required direction.